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  <TITLE>MTT: Model Transformation Tools</TITLE>
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      <TD valign="middle" align="left">[<A href=
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  <H1>MTT: Model Transformation Tools</H1><STRONG>MTT</STRONG> is a set of
  Model Transformation Tools based on bond graphs. <STRONG>MTT</STRONG>
  implements the theory to be found in the book "Metamodelling: Bond Graphs
  and Dynamic Systems" by Peter Gawthrop and Lorcan Smith published by
  Prentice Hall in 1996 (ISBN 0-13-489824-9).
  <P>It implements two features not discussed in that book:</P>
  <UL>
    <LI>bicausal bond graphs and</LI>
    <LI>hierarchical bond graphs.</LI>
  </UL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC1">1.
      Introduction</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC14">2. User
      interface</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC28">3. Creating
      Models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC33">4.
      Simulation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC51">6.
      Representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC147">7. Extending
      MTT</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC154">8.
      Documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC159">9.
      Languages</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC164">10. Language
      tools</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC174">11.
      Administration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href=
      "mtt.html#SEC193">Glossary</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC194">Index</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">-- The Detailed Node Listing
      ---</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Introduction</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC2">1.1 What is a
      representation?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC3">1.2 What is a
      transformation?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC4">1.3 What is a
      bond graph?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC5">1.4
      Variables</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC6">1.5
      Bonds</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC7">1.6
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC12">1.7 Algebraic
      loops</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC13">1.8 Switched
      systems</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Components</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC8">1.6.1
      Ports</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC9">1.6.2
      Constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC10">1.6.3 Symbolic
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC11">1.6.4 Numeric
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">User interface</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC15">2.1 Menu-driven
      interface</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC16">2.2 Command line
      interface</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC17">2.3
      Options</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC18">2.4
      Utilities</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Utilities</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC19">2.4.1
      Help</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC25">2.4.2
      Copy</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC26">2.4.3
      Clean</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Help</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC20">2.4.1.1 help
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC21">2.4.1.2 help
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC22">2.4.1.3 help
      examples</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC23">2.4.1.4 help
      crs</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC24">2.4.1.5 help
      &lt;name&gt;</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Creating Models</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC29">3.1 Quick
      start</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC30">3.2 Creating
      simple models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC31">3.3 Creating
      complex models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Creating complex models</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC32">3.3.1 Top
      level</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Simulation</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC34">4.1 Steady-state
      solutions</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC37">4.2 Simulation
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC42">4.3 Simulation
      input</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC43">4.4 Simulation
      logic</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC44">4.5 Simulation
      initial state</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC45">4.6 Simulation
      code</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Steady-state solutions</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC35">4.1.1
      Steady-state solutions (odess)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC36">4.1.2
      Steady-state solutions (ss)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Simulation parameters</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC38">4.2.1 Euler
      integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC39">4.2.2 Implicit
      integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC40">4.2.3 Runge
      Kutta IV integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC41">4.2.4 Hybrd
      algebraic solver</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Simulation code</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC46">4.6.1
      Dynamically linked functions</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Simulation output</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC48">4.7.1 Viewing
      results with gnuplot</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC49">4.7.2 Exporting
      results to SciGraphica</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Representations</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC52">6.1
      Representation summary</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC53">6.2 Defining
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC54">6.3 Verbal
      description (desc)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC55">6.4 Acausal bond
      graph (abg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC80">6.5 Stripped
      acausal bond graph (sabg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC83">6.6 Labels
      (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC103">6.7 Structure
      (struc)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC107">6.8
      Constitutive relationship (cr)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC115">6.9
      Parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC120">6.10 Causal
      bond graph (cbg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC124">6.11 Elementary
      system equations (ese)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC126">6.12
      Differential-Algebraic Equations (dae)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC131">6.13
      Constrained-state Equations (cse)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC135">6.14 Ordinary
      Differential Equations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC141">6.15 Descriptor
      matrices (dm)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC144">6.16 Report
      (rep)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Acausal bond graph (abg)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC56">6.4.1 Language
      fig (abg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC73">6.4.2 Language m
      (rbg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC75">6.4.3 Language m
      (abg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC79">6.4.4 Language
      tex (abg.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language fig (abg.fig)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC57">6.4.1.1 Icon
      library</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC58">6.4.1.2
      Bonds</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC59">6.4.1.3
      Strokes</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC60">6.4.1.4
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC62">6.4.1.6 SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple
      components - implementation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC64">6.4.1.8 Compound
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC65">6.4.1.9 Named SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC66">6.4.1.10 Coerced
      bond direction</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC67">6.4.1.11 Port
      labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC68">6.4.1.12 Vector
      port labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC69">6.4.1.13 Port
      label defaults</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC70">6.4.1.14 Vector
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC71">6.4.1.15
      Artwork</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC72">6.4.1.16 Valid
      Names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Simple components</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC62">6.4.1.6 SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple
      components - implementation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Compound components</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC65">6.4.1.9 Named SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language m (rbg.m)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC74">6.4.2.1
      Transformation abg2rbg_fig2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language m (abg.m)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC76">6.4.3.1
      Arrow-orientated causality</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC77">6.4.3.2
      Component-orientated causality</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC78">6.4.3.3
      Transformation rbg2abg_m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Stripped acausal bond graph
      (sabg)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC81">6.5.1 Language
      fig (sabg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC82">6.5.2 Stripped
      acausal bond graph (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Labels (lbl)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC84">6.6.1 SS
      component labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC85">6.6.2 Other
      component labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC86">6.6.3 Component
      names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC87">6.6.4 Component
      constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC88">6.6.5 Component
      arguments</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC89">6.6.6 Parameter
      declarations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC90">6.6.7 Units
      declarations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC91">6.6.8 Interface
      Control Definition</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC92">6.6.9
      Aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC97">6.6.10 Parameter
      passing</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style
      labels (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC102">6.6.12 Language
      tex (desc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Other component labels</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC86">6.6.3 Component
      names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC87">6.6.4 Component
      constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC88">6.6.5 Component
      arguments</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC92">6.6.9
      Aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC97">6.6.10 Parameter
      passing</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style
      labels (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Aliases</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC93">6.6.9.1 Port
      aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC94">6.6.9.2
      Parameter aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC95">6.6.9.3 CR
      aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC96">6.6.9.4
      Component aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Old-style labels (lbl)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC99">6.6.11.1 SS
      component labels (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC100">6.6.11.2 Other
      component labels (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC101">6.6.11.3
      Parameter passing (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Parameter passing
      (old-style)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC102">6.6.12 Language
      tex (desc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Structure (struc)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC104">6.7.1 Language
      txt (struc.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC105">6.7.2 Language
      tex (struc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC106">6.7.3 Language
      tex (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Constitutive relationship
      (cr)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC108">6.8.1
      Predefined constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC111">6.8.2 DIY
      constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC112">6.8.3
      Unresolved constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC113">6.8.4
      Unresolved constitutive relationships - Octave</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC114">6.8.5
      Unresolved constitutive relationships - c++</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Predefined constitutive
      relationships</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC109">6.8.1.1
      lin</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC110">6.8.1.2
      exotherm</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Parameters</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC116">6.9.1 Symbolic
      parameters (subs.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC117">6.9.2 Symbolic
      parameters for simplification (simp.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric
      parameters (numpar)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Numeric parameters
      (numpar)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text
      form (numpar.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Causal bond graph (cbg)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC121">6.10.1 Language
      fig (cbg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC122">6.10.2 Language
      m (cbg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language m (cbg.m)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC123">6.10.2.1
      Transformation abg2cbg_m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Elementary system equations
      (ese)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC125">6.11.0.1
      Transformation cbg2ese_m2r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Differential-Algebraic
      Equations (dae)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC127">6.12.1 Language
      reduce (dae.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC129">6.12.2 Language
      m (dae.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language reduce (dae.r)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC128">6.12.1.1
      Transformation ese2dae_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language m (dae.m)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC130">6.12.2.1
      Transformation dae_r2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Constrained-state Equations
      (cse)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC132">6.13.1 Language
      reduce (cse.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC134">6.13.2 Language
      m (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language reduce (cse.r)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC133">6.13.1.1
      Transformation dae2cse_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Ordinary Differential
      Equations</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC136">6.14.1 Language
      reduce (ode.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC138">6.14.2 Language
      m (ode.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC140">6.14.3 Language
      m (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language reduce (ode.r)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC137">6.14.1.1
      Transformation cse2ode_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language m (ode.m)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC139">6.14.2.1
      Transformation ode_r2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Descriptor matrices (dm)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC142">6.15.1 Language
      reduce (dm.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC143">6.15.2 Language
      m (dm.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Report (rep)</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC145">6.16.1 Language
      text (rep.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC146">6.16.2 Language
      view</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Extending MTT</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC148">7.1
      Makefiles</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC149">7.2 New (DIY)
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC153">7.3 Component
      library</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">New (DIY)
      representations</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC150">7.2.1
      Makefile</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC151">7.2.2
      Shell-script</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC152">7.2.3
      Documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Documentation</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC155">8.1
      Manual</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">On-line documentation</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC157">8.2.1 Brief
      on-line documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC158">8.2.2 Detailed
      on-line documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Languages</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC160">9.1
      Fig</A></TD>
      <TD></TD>
      <TD align="left" valign="top">r</TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC161">9.2 m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC162">9.3
      Reduce</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC163">9.4 c</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Language tools</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC165">10.1
      Views</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC166">10.2
      Xfig</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC167">10.3 Text
      editors</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC168">10.4
      Octave</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC173">10.5
      LaTeX</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Octave</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC169">10.4.1 Octave
      control system toolbox (OCST)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC170">10.4.2 Creating
      GNU Octave .oct files</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC171">10.4.3 Creating
      Matlab .mex files</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC172">10.4.4
      Embedding MTT models in Simulink</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Administration</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC175">11.1 Software
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC176">11.2 REDUCE
      setup</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC177">11.3 Octave
      setup</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC180">11.4
      Paths</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC186">11.5 File
      structure</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC188">A.1 GNU Free
      Documentation License</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC190">A.2 GNU GENERAL
      PUBLIC LICENSE</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Octave setup</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC178">11.3.1
      .octaverc</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC179">11.3.2 .oct
      file dependencies</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top">Paths</TH>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC181">11.4.1
      $MTTPATH</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC182">11.4.2
      $MTT_COMPONENTS</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC183">11.4.3
      $MTT_CRS</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC184">11.4.4
      $MTT_EXAMPLES</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC185">11.4.5
      $OCTAVE_PATH</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TH colspan="3" align="left" valign="top"></TH>
    </TR>
  </TABLE>
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  </TABLE><A name="Introduction" id="Introduction"></A>
  <H1>1. Introduction</H1><!--docid::SEC1::-->
  <P><A name="IDX1" id="IDX1"></A></P>
  <P><A name="IDX2" id="IDX2"></A></P>
  <P><STRONG>MTT</STRONG> is a set of Model Transformation Tools based on
  bond graphs. <STRONG>MTT</STRONG> implements the theory to be found in the
  book "Metamodelling: Bond Graphs and Dynamic Systems" by Peter Gawthrop and
  Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).</P>
  <P>It implements two features not discussed in that book:</P>
  <UL>
    <LI>bicausal bond graphs and</LI>
    <LI>hierarchical bond graphs.</LI>
  </UL>
  <P>In the context of software, it has been said that one good tool is worth
  many packages. UNIX is a good example of this philosophy: the user can put
  together applications from a range of ready made tools. This manual
  describes the application of this philosophy to dynamic system modeling
  embodied in <STRONG>MTT</STRONG> - a set of Model Transformation Tools each
  of which implements a single transformation between system
  representations.</P>
  <P>System representations have two attributes.</P>
  <UL>
    <LI>A Form: e.g. acausal bond graph, differential algebraic, linear
    state-space etc.</LI>
    <LI>A Language: e.g. Fig, Matlab, LaTeX, Reduce, postscript etc.</LI>
  </UL>
  <P>Transformations in <STRONG>MTT</STRONG> are accomplished using
  appropriate software (e.g. Octave/Matlab, Reduce) encapsulated in UNIX
  Bourne shell scripts. The relationships between the tools are encoded in a
  Make File; thus the user can specify a final representation and all the
  necessary intermediate transformations are automatically generated.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC2">1.1 What is a
      representation?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC3">1.2 What is a
      transformation?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC4">1.3 What is a
      bond graph?</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC5">1.4
      Variables</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC6">1.5
      Bonds</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC7">1.6
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC12">1.7 Algebraic
      loops</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC13">1.8 Switched
      systems</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="What is a Representation?"></A></P>
  <HR size="6">
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      <TD valign="middle" align="left"></TD>
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  </TABLE>
  <H2>1.1 What is a representation?</H2><!--docid::SEC2::-->
  <P><A name="IDX3" id="IDX3"></A></P>
  <P><A name="IDX4" id="IDX4"></A></P>
  <P>Physical systems have many representations. These include</P>
  <UL>
    <LI>a schematic diagram,</LI>
    <LI>a block diagram,</LI>
    <LI>a bunch of equations,</LI>
    <LI>a single differential(-algebraic) equation,</LI>
    <LI>simulation code,</LI>
    <LI>linearised state-space (or descriptor) equations,</LI>
    <LI>transfer function (of the linearised system),</LI>
    <LI>frequency response (of the linearised system),</LI>
    <LI>etc...</LI>
  </UL>
  <P>Each of these representations is related to other representations by an
  appropriate transformation (see section <A href="mtt.html#SEC3">1.2 What is
  a transformation?</A>. In many cases, a modeler is presented with a
  physical system and needs to make a model. In particular, a model, in this
  context, is a representation of the system appropriate to a particular use,
  for example:</P>
  <UL>
    <LI>simulation,</LI>
    <LI>control system design,</LI>
    <LI>optimisation</LI>
    <LI>etc.</LI>
  </UL>
  <P>Indeed, for a given physical system, the modeler would need to derive a
  number of models. This process can be viewed as a series of steps; each
  involving a transformation between representations (see section <A href=
  "mtt.html#SEC3">1.2 What is a transformation?</A>.</P>
  <P>In this context, the following considerations are relevant.</P>
  <UL>
    <LI>There is a unique `core' representation of any system. There are many
    routes from this core representation, each leading to an appropriate
    model. There are many possible routes to this core representation from
    the physical system: the route chosen is a matter of convenience.</LI>
    <LI>Because the core representation is unique, it is easy to expand the
    tool-box to include additional transformations from the physical system
    to the core representation and additional transformations from the core
    representation to the mode.</LI>
    <LI>Transformation_1 probably cannot, and certainly should not, be
    completely automated. Engineering insight, knowledge and experience is
    essential to capture the essence (with respect to the particular use) of
    the physical system whilst discarding irrelevant form.</LI>
    <LI>Representation_1 should be `close' in some sense to the Physical
    system.</LI>
    <LI>The core representation, and hence the representations leading to it,
    must contain enough information to generate all of the required
    models.</LI>
    <LI>Representations must be easily extensible: it must be possible to add
    extra components or attributes without restructuring the
    representation.</LI>
  </UL>
  <P>I happen to believe that Bond graphs (see section <A href=
  "mtt.html#SEC4">1.3 What is a bond graph?</A>) provide the most convenient
  and powerful basis for the core representation.</P>
  <P><A name="What is a Transformation?"></A></P>
  <HR size="6">
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  <H2>1.2 What is a transformation?</H2><!--docid::SEC3::-->
  <P>Each system representation (see section <A href="mtt.html#SEC2">1.1 What
  is a representation?</A> is related to other representations by an
  appropriate transformation as follows:</P>
  <UL>
    <LI>Physical system</LI>
    <LI>Transformation_1 ---&gt; Representation_1</LI>
    <LI>Transformation_2 ---&gt; Representation_2</LI>
    <LI>...</LI>
    <LI>Transformation_N ---&gt; Core representation</LI>
    <LI>Transformation_N+1 ---&gt; Representation_N+1</LI>
    <LI>Transformation_N+2 ---&gt; Representation_N+2</LI>
    <LI>...</LI>
    <LI>Transformation_N+M ---&gt; Model</LI>
  </UL>Thus modeling is seen as a sequence of transformations between
  representations.
  <P><A name="Bond graphs"></A></P>
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  <H2>1.3 What is a bond graph?</H2><!--docid::SEC4::-->
  <P><A name="IDX5" id="IDX5"></A></P>
  <P><A name="IDX6" id="IDX6"></A></P>
  <P>Bond graphs provide a graphical high-level language for describing
  dynamic systems in a precise and unambiguous fashion. They make a clear
  distinction between structure (how components are connected together), and
  behavior (the particular constitutive relationships, or physical laws,
  describing each component.</P>
  <P>They can describe a range of physical systems including:</P>
  <UL>
    <LI>Electrical systems</LI>
    <LI>Mechanical systems</LI>
    <LI>Hydraulic systems</LI>
    <LI>Chemical process systems</LI>
  </UL>
  <P>More importantly, they can describe systems which contain subsystems
  drawn from all of these domains in a uniform manner.</P>
  <P>Bond graphs are made up of components (see section <A href=
  "mtt.html#SEC7">1.6 Components</A>) connected by bonds (see section
  <A href="mtt.html#SEC6">1.5 Bonds</A>) which define the relationship
  between variables (see section <A href="mtt.html#SEC5">1.4
  Variables</A>).</P>
  <P><A name="Variables" id="Variables"></A></P>
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  <H2>1.4 Variables</H2><!--docid::SEC5::-->
  In bond graph terminology there are four sorts of variables:
  <UL>
    <LI><EM>effort</EM> variables</LI>
    <LI><EM>flow</EM> variables</LI>
    <LI><EM>integrated effort</EM> variables</LI>
    <LI><EM>integrated flow</EM> variables</LI>
  </UL>
  <P>Examples of <EM>effort</EM> variables are</P>
  <UL>
    <LI>voltage</LI>
    <LI>pressure</LI>
    <LI>force</LI>
    <LI>torque</LI>
    <LI>temperature</LI>
  </UL>
  <P>Examples of <EM>flow</EM> variables are</P>
  <UL>
    <LI>current</LI>
    <LI>volumetric flow rate</LI>
    <LI>velocity</LI>
    <LI>angular velocity</LI>
    <LI>heat flow</LI>
  </UL>
  <P>Examples of integrated <EM>flow</EM> variables are</P>
  <UL>
    <LI>charge</LI>
    <LI>volume</LI>
    <LI>momentum</LI>
    <LI>angular momentum</LI>
    <LI>heat</LI>
  </UL>
  <P><A name="Bonds" id="Bonds"></A></P>
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  <H2>1.5 Bonds</H2><!--docid::SEC6::-->
  Bonds connect components (see section <A href="mtt.html#SEC7">1.6
  Components</A>) together. Each bond carries two variables:
  <UL>
    <LI>an effort (see section <A href="mtt.html#SEC5">1.4 Variables</A>)
    variable and</LI>
    <LI>a flow (see section <A href="mtt.html#SEC5">1.4 Variables</A>)
    variable.</LI>
  </UL>Each bond has three notations associated with it:
  <UL>
    <LI>a half-arrow,</LI>
    <LI>a causal stroke and</LI>
    <LI>a causal half-stroke.</LI>
  </UL>
  <P>The half-arrow indicates two things:</P>
  <UL>
    <LI>the direction of power (or pseudo power) flow and</LI>
    <LI>the side of the bond associated with the flow variable.</LI>
  </UL>
  <P>The causal stroke indicates two things:</P>
  <UL>
    <LI>the effort variable is imposed at the same end as the stroke and</LI>
    <LI>the flow variable is imposed at the opposite end to the stroke.</LI>
  </UL>
  <P>The causal half-stoke indicates one thing:</P>
  <UL>
    <LI>if it is on the effort side of the bond, the effort variable is
    imposed at the same end as the stroke or</LI>
    <LI>if it is on the flow side of the bond, the flow variable is imposed
    at the opposite end to the stroke.</LI>
  </UL>
  <P><A name="Components" id="Components"></A></P>
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  <H2>1.6 Components</H2><!--docid::SEC7::-->
  <P>Components provide the building blocks of a dynamic system when
  connected by bonds (see section <A href="mtt.html#SEC58">6.4.1.2
  Bonds</A>). Components have the following attributes:</P>
  <DL compact>
    <DT><A name="IDX7" id="IDX7"></A> <CODE>ports</CODE></DT>
    <DD><A name="IDX8" id="IDX8"></A> provide the connections to other
    components (see section <A href="mtt.html#SEC8">1.6.1 Ports</A>)</DD>
    <DT><A name="IDX9" id="IDX9"></A> <CODE>constitutive
    relationships</CODE></DT>
    <DD><A name="IDX10" id="IDX10"></A> define how the port-variables are
    related (see section <A href="mtt.html#SEC9">1.6.2 Constitutive
    relationship</A>)</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC8">1.6.1
      Ports</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC9">1.6.2
      Constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC10">1.6.3 Symbolic
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC11">1.6.4 Numeric
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
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  <P><A name="Ports" id="Ports"></A></P>
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  <H3>1.6.1 Ports</H3><!--docid::SEC8::-->
  Components have one or more ports. Each port carries two variables, and
  effort and a flow variable (see section <A href="mtt.html#SEC5">1.4
  Variables</A>). Any pair of ports can be connected by a bond (see section
  <A href="mtt.html#SEC6">1.5 Bonds</A>); this connection is equivalent to
  saying that the effort variables at each port are identical and that the
  flow variables at each port are identical.
  <P>Ports are implemented in <STRONG>MTT</STRONG> using named SS components.
  (see section <A href="mtt.html#SEC65">6.4.1.9 Named SS components</A>).</P>
  <P>The direction of the named SS components. (see section <A href=
  "mtt.html#SEC65">6.4.1.9 Named SS components</A>) is coerced (see section
  <A href="mtt.html#SEC66">6.4.1.10 Coerced bond direction</A>) to have the
  same direction as the bons connected to the corresponding port. Thus the
  direction of the direction of the named SS components has no significance
  unless the component is at the top level.</P>
  <P><A name="Constitutive relationship"></A></P>
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  <H3>1.6.2 Constitutive relationship</H3><!--docid::SEC9::-->
  <P>The constitutive relationship of a component defines how the port
  variables are related. This relationship may be linear or non-linear. This
  typically contains symbolic parameters (see section <A href=
  "mtt.html#SEC10">1.6.3 Symbolic parameters</A>) which may be replaced, for
  the purposes of numerical analysis by numeric parameters (see section
  <A href="mtt.html#SEC11">1.6.4 Numeric parameters</A>).</P>
  <P><A name="Symbolic parameters"></A></P>
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  <H3>1.6.3 Symbolic parameters</H3><!--docid::SEC10::-->
  The constitutive relationship of a system component (see section <A href=
  "mtt.html#SEC7">1.6 Components</A>) typically contains symbolic parameters.
  For example a resistor may have a symbolic resistance r. It is convenient
  to leave such parameters as symbols when viewing equations or when
  performing symbolic analysis such as differentiation.
  <P>However, <STRONG>MTT</STRONG> allows replacement of symbolic parameters
  by numeric parameters (see section <A href="mtt.html#SEC11">1.6.4 Numeric
  parameters</A>) when appropriate.</P>
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  <H3>1.6.4 Numeric parameters</H3><!--docid::SEC11::-->
  Numerical parameters are needed to give specific values to symbolic
  parameters (see section <A href="mtt.html#SEC10">1.6.3 Symbolic
  parameters</A>) for the purposes of numeric analysis; for example:
  simulation, graph plotting or use within a numerical package such as Octave
  (see section <A href="mtt.html#SEC168">10.4 Octave</A>).
  <P><A name="Algebraic loops"></A></P>
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  <H2>1.7 Algebraic loops</H2><!--docid::SEC12::-->
  Following Chapter 3 of the book, algebraic loops appear as under-causal
  components in the bond graph. It is up to the modeler to indicate how these
  loops are to be resolved by adding appropriate SS elements.
  <P>In particular if zero junction is undercausal an SS:loop component (with
  effort output indicated by a causal stroke) with the following label file
  entry:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  loop SS unknown,zero
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>For more information, refer to: "Metamodelling: Bond Graphs and Dynamic
  Systems" by Peter Gawthrop and Lorcan Smith published by Prentice Hall in
  1996 (ISBN 0-13-489824-9).</P>
  <P><A name="Switched systems"></A></P>
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      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC1">&lt;&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC1">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>1.8 Switched systems</H2><!--docid::SEC13::-->
  <P>Some systems contain switch-like components. For example an electrical
  system may contain on-off switches and diodes and a hydraulic system may
  shut-off valves and non-return valves.</P>
  <P>Such systems are sometimes called hybrid systems. The modelling an
  simulation of such systems is the subject of current research.
  <STRONG>MTT</STRONG> implements a simple pragmatic approach to the
  modelling and simulation of such systems via two new Bond Graph
  components:</P>
  <DL compact>
    <DT><A name="IDX11" id="IDX11"></A> <CODE>ISW</CODE></DT>
    <DD><A name="IDX12" id="IDX12"></A> a switched <CODE>I</CODE>
    component</DD>
    <DT><A name="IDX13" id="IDX13"></A> <CODE>CSW</CODE></DT>
    <DD><A name="IDX14" id="IDX14"></A> a switched <CODE>C</CODE>
    component</DD>
  </DL>
  <P>These switches are user controlled through the logic representation (see
  section <A href="mtt.html#SEC43">4.4 Simulation logic</A>).</P>
  <P><A name="User interface"></A></P>
  <HR size="6">
  <A name="SEC14" id="SEC14"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
    </TR>
  </TABLE>
  <H1>2. User interface</H1><!--docid::SEC14::-->
  There are two user interfaces to <STRONG>MTT</STRONG>: a command line
  interface (see section <A href="mtt.html#SEC16">2.2 Command line
  interface</A>) and a menu-driven interface (see section <A href=
  "mtt.html#SEC15">2.1 Menu-driven interface</A>).
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC15">2.1 Menu-driven
      interface</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC16">2.2 Command line
      interface</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC17">2.3
      Options</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC18">2.4
      Utilities</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Menu-driven interface"></A></P>
  <HR size="6">
  <A name="SEC15" id="SEC15"></A>
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      ]</TD>
    </TR>
  </TABLE>
  <H2>2.1 Menu-driven interface</H2><!--docid::SEC15::-->
  The Menu-driven interface for <STRONG>MTT</STRONG> is invoked as:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>xmtt
</PRE>
      </TD>
    </TR>
  </TABLE>This will bring up a menu which should be self explanatory :-).
  Various messages will be echoed in the window from whence
  <STRONG>xMTT</STRONG> was invoked.
  <P><A name="Command line interface"></A></P>
  <HR size="6">
  <A name="SEC16" id="SEC16"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>2.2 Command line interface</H2><!--docid::SEC16::-->
  The command line interface for <STRONG>MTT</STRONG> is of the form:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt [options] &lt;system_name&gt; &lt;representation&gt; &lt;language&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <DL compact>
    <DT><A name="IDX15" id="IDX15"></A> <CODE>[options]</CODE></DT>
    <DD><A name="IDX16" id="IDX16"></A> the (optional) option switches (see
    section <A href="mtt.html#SEC17">2.3 Options</A>)</DD>
    <DT><A name="IDX17" id="IDX17"></A> <CODE>&lt;system_name&gt;</CODE></DT>
    <DD><A name="IDX18" id="IDX18"></A> the name of the system being
    transformed</DD>
    <DT><A name="IDX19" id="IDX19"></A>
    <CODE>&lt;representation&gt;</CODE></DT>
    <DD><A name="IDX20" id="IDX20"></A> the mnemonic for the system
    representation (see section <A href="mtt.html#SEC52">6.1 Representation
    summary</A>)</DD>
    <DT><A name="IDX21" id="IDX21"></A> <CODE>&lt;language&gt;</CODE></DT>
    <DD><A name="IDX22" id="IDX22"></A> the mnemonic for language for the
    representation (see section <A href="mtt.html#SEC159">9.
    Languages</A>)</DD>
  </DL>for example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc rep view
</PRE>
      </TD>
    </TR>
  </TABLE>creates a view of the report describing system rc and
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc sm m
</PRE>
      </TD>
    </TR>
  </TABLE>creates an m file (suitlable for Octave or Matlab) containing state
  matrices describing the system rc. <A name="Options" id="Options"></A>
  <HR size="6">
  <A name="SEC17" id="SEC17"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC16">&lt;</A>
      ]</TD>
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      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC14">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>2.3 Options</H2><!--docid::SEC17::-->
  <P><STRONG>MTT</STRONG> has a number of optional switches to control its
  operation. These are invoked immediately after `mtt' on the command line;
  for example:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -o -ss -cc syst cbg view
</PRE>
      </TD>
    </TR>
  </TABLE>invokes the <CODE>-o</CODE>, <CODE>-ss</CODE>, and <CODE>-cc</CODE>
  options.
  <P>If you wish to use an option all the time, use the alias function
  appropriate to the shell you are using. For example, using bash:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>alias mtt='mtt -o -ss -cc'
</PRE>
      </TD>
    </TR>
  </TABLE>Means that the previous example can be executed using
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt syst cbg view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The available options are:</P>
  <DL compact>
    <DT><A name="IDX23" id="IDX23"></A> <CODE>-q</CODE></DT>
    <DD><A name="IDX24" id="IDX24"></A> quiet mode -- suppress MTT
    banner</DD>
    <DT><A name="IDX25" id="IDX25"></A> <CODE>-A</CODE></DT>
    <DD><A name="IDX26" id="IDX26"></A> solve algebraic equations
    symbolically</DD>
    <DT><A name="IDX27" id="IDX27"></A> <CODE>-ae</CODE></DT>
    <DD><A name="IDX28" id="IDX28"></A> &lt;hybrd&gt; solve algebraic
    equations numerically (this option requires -cc or -oct)</DD>
    <DT><A name="IDX29" id="IDX29"></A> <CODE>-D</CODE></DT>
    <DD><A name="IDX30" id="IDX30"></A> debug -- leave log files etc</DD>
    <DT><A name="IDX31" id="IDX31"></A> <CODE>-I</CODE></DT>
    <DD><A name="IDX32" id="IDX32"></A> prints more information</DD>
    <DT><A name="IDX33" id="IDX33"></A> <CODE>-abg</CODE></DT>
    <DD><A name="IDX34" id="IDX34"></A> start at abg.m representation</DD>
    <DT><A name="IDX35" id="IDX35"></A> <CODE>-c</CODE></DT>
    <DD><A name="IDX36" id="IDX36"></A> c-code generation</DD>
    <DT><A name="IDX37" id="IDX37"></A> <CODE>-cc</CODE></DT>
    <DD><A name="IDX38" id="IDX38"></A> C++ code generation</DD>
    <DT><A name="IDX39" id="IDX39"></A> <CODE>-d</CODE></DT>
    <DD><A name="IDX40" id="IDX40"></A> &lt;dir&gt; use directory
    &lt;dir&gt;</DD>
    <DT><A name="IDX41" id="IDX41"></A> <CODE>-dc</CODE></DT>
    <DD><A name="IDX42" id="IDX42"></A> Maximise derivative (not integral)
    causality</DD>
    <DT><A name="IDX43" id="IDX43"></A> <CODE>-dc</CODE></DT>
    <DD><A name="IDX44" id="IDX44"></A> Maximise derivative (not integral)
    causality</DD>
    <DT><A name="IDX45" id="IDX45"></A> <CODE>-i</CODE></DT>
    <DD><A name="IDX46" id="IDX46"></A> &lt;implicit|euler|rk4&gt; Use
    implicit, euler or Runge Kutta IVintegration</DD>
    <DT><A name="IDX47" id="IDX47"></A> <CODE>-o</CODE></DT>
    <DD><A name="IDX48" id="IDX48"></A> ode is same as dae</DD>
    <DT><A name="IDX49" id="IDX49"></A> <CODE>-oct</CODE></DT>
    <DD><A name="IDX50" id="IDX50"></A> use oct files in place of m files
    where appropriate</DD>
    <DT><A name="IDX51" id="IDX51"></A> <CODE>-opt</CODE></DT>
    <DD><A name="IDX52" id="IDX52"></A> optimise code generation</DD>
    <DT><A name="IDX53" id="IDX53"></A> <CODE>-p</CODE></DT>
    <DD><A name="IDX54" id="IDX54"></A> print environment variables</DD>
    <DT><A name="IDX55" id="IDX55"></A> <CODE>-partition</CODE></DT>
    <DD><A name="IDX56" id="IDX56"></A> partition hierachical system</DD>
    <DT><A name="IDX57" id="IDX57"></A> <CODE>-r</CODE></DT>
    <DD><A name="IDX58" id="IDX58"></A> reset time stamp on
    representation</DD>
    <DT><A name="IDX59" id="IDX59"></A> <CODE>-s</CODE></DT>
    <DD><A name="IDX60" id="IDX60"></A> try to generate sensitivity BG
    (experimental)</DD>
    <DT><A name="IDX61" id="IDX61"></A> <CODE>-ss</CODE></DT>
    <DD><A name="IDX62" id="IDX62"></A> use steady-state info to initialise
    simulations</DD>
    <DT><A name="IDX63" id="IDX63"></A> <CODE>-stdin</CODE></DT>
    <DD><A name="IDX64" id="IDX64"></A> read input data from standard input
    for simulations</DD>
    <DT><A name="IDX65" id="IDX65"></A> <CODE>-sub</CODE></DT>
    <DD><A name="IDX66" id="IDX66"></A> &lt;subsystem&gt; operate on this
    subsystem</DD>
    <DT><A name="IDX67" id="IDX67"></A> <CODE>-t</CODE></DT>
    <DD><A name="IDX68" id="IDX68"></A> tidy mode (default)</DD>
    <DT><A name="IDX69" id="IDX69"></A> <CODE>-u</CODE></DT>
    <DD><A name="IDX70" id="IDX70"></A> untidy mode (leaves files in current
    dir)</DD>
    <DT><A name="IDX71" id="IDX71"></A> <CODE>-v</CODE></DT>
    <DD><A name="IDX72" id="IDX72"></A> verbose mode (multiple uses increase
    the verbosity)</DD>
    <DT><A name="IDX73" id="IDX73"></A> <CODE>-viewlevel</CODE></DT>
    <DD><A name="IDX74" id="IDX74"></A> &lt;N&gt; View N levels of
    hierachy</DD>
    <DT><A name="IDX75" id="IDX75"></A> <CODE>--version</CODE></DT>
    <DD><A name="IDX76" id="IDX76"></A> print version and exit</DD>
    <DT><A name="IDX77" id="IDX77"></A> <CODE>--versions</CODE></DT>
    <DD><A name="IDX78" id="IDX78"></A> print version of mtt and components
    and exit</DD>
  </DL>
  <P><A name="Utilities" id="Utilities"></A></P>
  <HR size="6">
  <A name="SEC18" id="SEC18"></A>
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  </TABLE>
  <H2>2.4 Utilities</H2><!--docid::SEC18::-->
  <STRONG>MTT</STRONG> provides some utilities to help you keep track of
  model building and to keep things clean and tidy. The commands, and there
  purpose are:
  <DL compact>
    <DT><A name="IDX79" id="IDX79"></A> <CODE>mtt help</CODE></DT>
    <DD><A name="IDX80" id="IDX80"></A> Lists the help/browser commands</DD>
    <DT><A name="IDX81" id="IDX81"></A> <CODE>mtt copy
    &lt;system&gt;</CODE></DT>
    <DD><A name="IDX82" id="IDX82"></A> Copies the system (ie directory and
    enclosed files) to the current working directory.</DD>
    <DT><A name="IDX83" id="IDX83"></A> <CODE>mtt rename &lt;old_name&gt;
    &lt;new_name&gt;</CODE></DT>
    <DD><A name="IDX84" id="IDX84"></A> Renames all of the defining
    representations (see section <A href="mtt.html#SEC53">6.2 Defining
    representations</A>) and textually changes each file appropriately.</DD>
    <DT><A name="IDX85" id="IDX85"></A> <CODE>mtt &lt;system&gt;
    clean</CODE></DT>
    <DD><A name="IDX86" id="IDX86"></A> Remove all files generated by
    <STRONG>MTT</STRONG> associated with system `system'.</DD>
    <DT><A name="IDX87" id="IDX87"></A> <CODE>mtt clean</CODE></DT>
    <DD><A name="IDX88" id="IDX88"></A> Remove all files generated by
    <STRONG>MTT</STRONG> associated with all systems within the current
    directory.</DD>
    <DT><A name="IDX89" id="IDX89"></A> <CODE>mtt system representation
    vc</CODE></DT>
    <DD><A name="IDX90" id="IDX90"></A> Apply version control to
    representation `representation' of system `system'.</DD>
    <DT><A name="IDX91" id="IDX91"></A> <CODE>mtt system vc</CODE></DT>
    <DD><A name="IDX92" id="IDX92"></A> Apply version control to all
    representations (under version control) system `system'.</DD>
  </DL>These are described in more detail in the following sections.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC19">2.4.1
      Help</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC25">2.4.2
      Copy</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC26">2.4.3
      Clean</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Help" id="Help"></A></P>
  <HR size="6">
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  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>2.4.1 Help</H3><!--docid::SEC19::-->
  <STRONG>MTT</STRONG> implements a browser to keep track of all the systems,
  subsystems and constitutive relationships that you, and others may write.
  It is invoked in the following ways:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>       mtt help representations
       mtt help components
       mtt help examples 
       mtt help crs
       mtt help representations &lt;match_string&gt;
       mtt help components &lt;match_string&gt;
       mtt help examples  &lt;match_string&gt;
       mtt help crs &lt;match_string&gt;
       mtt help &lt;component_or_example_or_CR_name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC20">2.4.1.1 help
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC21">2.4.1.2 help
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC22">2.4.1.3 help
      examples</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC23">2.4.1.4 help
      crs</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC24">2.4.1.5 help
      &lt;name&gt;</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="help representations"></A></P>
  <HR size="6">
  <A name="SEC20" id="SEC20"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC21">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>2.4.1.1 help representations</H4><!--docid::SEC20::-->
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help representations
</PRE>
      </TD>
    </TR>
  </TABLE>lists all of the representations (see section <A href=
  "mtt.html#SEC51">6. Representations</A>) available in <STRONG>MTT</STRONG>.
  These may change as the version number of <STRONG>MTT</STRONG> increases.
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help representations &lt;match_string&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>lists those representation which contain the string
  <CODE>match_string</CODE>. This string can be any regular expression (see
  standard Linux documentation under <CODE>awk</CODE>). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help representations descriptor
</PRE>
      </TD>
    </TR>
  </TABLE>gives all representations containing the word
  <CODE>descriptor</CODE>.
  <P><A name="help components"></A></P>
  <HR size="6">
  <A name="SEC21" id="SEC21"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC20">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC22">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>2.4.1.2 help components</H4><!--docid::SEC21::-->
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help components
</PRE>
      </TD>
    </TR>
  </TABLE>lists all of the components (see section <A href=
  "mtt.html#SEC7">1.6 Components</A>) available in <STRONG>MTT</STRONG>.
  These may change as the version number of <STRONG>MTT</STRONG> increases.
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help components &lt;match_string&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>lists those component which contain the string
  <CODE>match_string</CODE>. This string can be any regular expression (see
  standard Linux documentation under <CODE>awk</CODE>). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help components source
</PRE>
      </TD>
    </TR>
  </TABLE>gives all components containing the word <CODE>component</CODE>.
  <P><A name="help examples"></A></P>
  <HR size="6">
  <A name="SEC22" id="SEC22"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC21">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC23">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>2.4.1.3 help examples</H4><!--docid::SEC22::-->
  <P>This command provides a good way to get started in <STRONG>MTT</STRONG>.
  having found an interesting example, copy it to your working directory
  using</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy &lt;example_name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>(see section <A href="mtt.html#SEC25">2.4.2 Copy</A>)
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples
</PRE>
      </TD>
    </TR>
  </TABLE>lists all of the examples available in <STRONG>MTT</STRONG>. This
  list will change as more examples are added.
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples &lt;match_string&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>lists those component which contain the string
  <CODE>match_string</CODE>. This string can be any regular expression (see
  standard Linux documentation under <CODE>awk</CODE>). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples pharmokinetic
</PRE>
      </TD>
    </TR>
  </TABLE>gives all examples containing the word <CODE>pharmokinetic</CODE>.
  <P><A name="help crs"></A></P>
  <HR size="6">
  <A name="SEC23" id="SEC23"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC22">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC24">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>2.4.1.4 help crs</H4><!--docid::SEC23::-->
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help crs
</PRE>
      </TD>
    </TR>
  </TABLE>lists all of the constitutive relationships (see section <A href=
  "mtt.html#SEC9">1.6.2 Constitutive relationship</A>) available in
  <STRONG>MTT</STRONG>. These may change as the version number of
  <STRONG>MTT</STRONG> increases.
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help crs &lt;match_string&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>lists those constitutive relationships which contain the string
  <CODE>match_string</CODE>. This string can be any regular expression (see
  standard Linux documentation under <CODE>awk</CODE>). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help crs sin
</PRE>
      </TD>
    </TR>
  </TABLE>gives all crs containing the word <CODE>sin</CODE>.
  <P><A name="help &amp;lt;name&amp;gt;"></A></P>
  <HR size="6">
  <A name="SEC24" id="SEC24"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC23">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC25">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC19">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>2.4.1.5 help &lt;name&gt;</H4><!--docid::SEC24::-->
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help &lt;name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>gives a detailed description of the entity called
  <CODE>name</CODE>.
  <P><A name="Copy" id="Copy"></A></P>
  <HR size="6">
  <A name="SEC25" id="SEC25"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC24">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC26">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC18">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>2.4.2 Copy</H3><!--docid::SEC25::-->
  <P><STRONG>MTT</STRONG> provides a way of copying examples to your working
  directory:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy &lt;example_name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Use the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples
</PRE>
      </TD>
    </TR>
  </TABLE>(see section <A href="mtt.html#SEC22">2.4.1.3 help examples</A>) to
  find something of interest.
  <P>Note that components and constitutive relationships are automatically
  copied when required.</P>
  <P><A name="Clean" id="Clean"></A></P>
  <HR size="6">
  <A name="SEC26" id="SEC26"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC25">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC27">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC18">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>2.4.3 Clean</H3><!--docid::SEC26::-->
  <STRONG>MTT</STRONG> generates a lot of representations in a number of
  languages. Some of these you will edit yourself; others can always be
  recreated by <STRONG>MTT</STRONG>. It makes sense, therefore to have a
  utility that removes all of these other files when you have finished
  actively working with a particular system. These are two versions:
  <OL>
    <LI><CODE>mtt system clean</CODE></LI>
    <LI><CODE>mtt clean</CODE></LI>
  </OL>The first removes all files that can be regenerated with
  <STRONG>MTT</STRONG> associated with system `system'; the second removes
  all such files associated with all systems in the current working
  directory.
  <P>The files which remain after such a clean are the Defining
  representations (see section <A href="mtt.html#SEC53">6.2 Defining
  representations</A>).</P>
  <P><A name="Version control"></A></P>
  <HR size="6">
  <A name="SEC27" id="SEC27"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC26">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC28">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC18">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC28">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>2.4.4 Version control</H3><!--docid::SEC27::-->
  <P>When you are working on a modeling project, it is easy to forget what
  changes you made to a system and why you made them. Sometimes, you may
  regret some changes and wish to revert to an earlier version: even if you
  use .old files this may be difficult to achieve safely.</P>
  <P>These are very similar problems to those faced by software developers
  and can be solved in the same way: using version
  control.<STRONG>MTT</STRONG> provides version control using the standard
  GNU Revision Control System (RCS). This is hidden from the user, but is
  fully complementary to direct use of RCS (e.g. via emacs vc commands) to
  the more experienced user who wishes to do so.</P>
  <P>The only files that you should ever change (i.e. the ones never
  overwritten by <STRONG>MTT</STRONG>) are the Defining representations (see
  section <A href="mtt.html#SEC53">6.2 Defining representations</A>).</P>
  <P>All of the files, with the exception of <CODE>system_abg.fig</CODE>, are
  initially created by <STRONG>MTT</STRONG> and contain the RCS header for
  version control.</P>
  <P>The <STRONG>MTT</STRONG> version control will automatically expand this
  part of the text to include all change comments that you give it -- so will
  direct use of RCS (e.g. via emacs vc commands)</P>
  <P>The <STRONG>MTT</STRONG> version commands are as follows:</P>
  <DL compact>
    <DT><A name="IDX93" id="IDX93"></A> <CODE>mtt system representation
    vc</CODE></DT>
    <DD><A name="IDX94" id="IDX94"></A> Apply version control to
    representation `representation' of system `system'.</DD>
    <DT><A name="IDX95" id="IDX95"></A> <CODE>mtt system vc</CODE></DT>
    <DD><A name="IDX96" id="IDX96"></A> Apply version control to all
    representations (under version control) system `system'.</DD>
  </DL>
  <P>The first is appropriate after you have made a revision to a single
  file. It will prompt you for a change comment; this will be automatically
  included in the file header. In addition, enough information will be saved
  to enable any version to be retrieved via RCS.</P>
  <P>The second is appropriate to record the state of the entire model. This
  assumes that all relevant files have been recorded by the first version of
  the command. Once again, old versions of the entire model can be retrieved
  using the relevant RCS commands.</P>
  <P>A subdirectory `RCS' is created to hold this information. You need not
  bother about the contents, except that you must not delete any files within
  `RCS'.</P>
  <P><A name="Creating Models"></A></P>
  <HR size="6">
  <A name="SEC28" id="SEC28"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC27">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC29">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC14">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_Top">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC33">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H1>3. Creating Models</H1><!--docid::SEC28::-->
  <P><STRONG>MTT</STRONG> helps you to analyse and transform system models --
  ultimately the process of capturing the real world in a model is up to you.
  This chapter discusses the <STRONG>MTT</STRONG> aspects of creating a
  model. For convenience, this is divided into creating simple models and
  creating complex models.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC29">3.1 Quick
      start</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC30">3.2 Creating
      simple models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC31">3.3 Creating
      complex models</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Quick start"></A></P>
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  <H2>3.1 Quick start</H2><!--docid::SEC29::-->
  <P>It is probably worth a quick skim though <STRONG>MTT</STRONG> to get a
  flavour of what it can do before plunging into the detail of the rest of
  this document. Here is a series of commands to do this.</P>
  <P>Copy an initial set of files describing the bond graph.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy rc
</PRE>
      </TD>
    </TR>
  </TABLE>Move to it.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>cd rc
</PRE>
      </TD>
    </TR>
  </TABLE>View the acausal bond graph (the system is called "rc").
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc abg view
</PRE>
      </TD>
    </TR>
  </TABLE>View the causal bond graph of the system.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc cbg view
</PRE>
      </TD>
    </TR>
  </TABLE>View the corresponding ordinary differential equations (ode).
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc ode view
</PRE>
      </TD>
    </TR>
  </TABLE>View the system (output) step response
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc sro view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>An alternative (but more general) way of achieving the same result
  is</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -c rc odeso view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>View the system transfer function</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc tf view
</PRE>
      </TD>
    </TR>
  </TABLE>View the log modulus frequency response of the system.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc lmfr view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>View the log modulus frequency response of the system for 100
  logarithmically spaced frequencies in the range 0.1 to 10 radians per
  second.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc lmfr view 'W=logspace(-1,1,100);'
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><STRONG>MTT</STRONG> has a report generation ((see section <A href=
  "mtt.html#SEC144">6.16 Report (rep)</A>) facility which can generate a
  hypertext description of the system.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc rep hview
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The report contents are specified by the rep representation (see section
  <A href="mtt.html#SEC144">6.16 Report (rep)</A>), in this case the
  corresponding file is:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>% %% Outline report file for system rc (rc_rep.txt)

mtt rc abg tex
mtt rc struc tex
mtt rc cbg ps
mtt rc ode tex
mtt rc ode dvi
mtt rc sm tex
mtt rc tf tex
mtt rc tf dvi
mtt rc sro ps
mtt rc lmfr ps
mtt rc odes h
mtt rc numpar txt
mtt rc input txt
mtt -c rc odeso ps
mtt rc rep txt
</PRE>
      </TD>
    </TR>
  </TABLE>A non-hypertext version can be viewed using:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc rep view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Now have a go at modifying the bond graph.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc abg fig
</PRE>
      </TD>
    </TR>
  </TABLE>This brings up the bond graph in Xfig (see section <A href=
  "mtt.html#SEC166">10.2 Xfig</A>). Try creating a system with two rs and 2
  cs.
  <P>More examples can be found using</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples
</PRE>
      </TD>
    </TR>
  </TABLE>Details of an example can be found using
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help &lt;example_name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>and copied using
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy &lt;example_name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Lots of examples are available.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt help examples
</PRE>
      </TD>
    </TR>
  </TABLE>lists them and
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy &lt;name&gt;
</PRE>
      </TD>
    </TR>
  </TABLE>gets you an example.
  <P>A number of examples are to be found &lt;A
  HREF="http://www.mech.gla.ac.uk/~peterg/software/MTT/examples/Examples/Examples.html"&gt;
  here&lt;/A&gt;.</P>
  <P><A name="Creating simple models"></A></P>
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  <H2>3.2 Creating simple models</H2><!--docid::SEC30::-->
  <P>For then purposes of this section, simple models are those which are
  built up from bond graphs involving predefined components. In contrast,
  more complex systems (see section <A href="mtt.html#SEC31">3.3 Creating
  complex models</A>) need to be built up hierarchically.</P>
  <P>The recommended sequence of steps to create a simple model is:</P>
  <OL>
    <LI>Decide on a name for the system; let us call it `syst' for the
    purposes of this discussion.</LI>
    <LI>Invoke the Bond Graph editor to draw the acausal Bond Graph.
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>  mtt syst abg fig
</PRE>
          </TD>
        </TR>
      </TABLE>
    </LI>
    <LI>Draw the Bond Graph (see section <A href="mtt.html#SEC56">6.4.1
    Language fig (abg.fig)</A>), including the bonds (see section <A href=
    "mtt.html#SEC6">1.5 Bonds</A>), the components (see section <A href=
    "mtt.html#SEC7">1.6 Components</A>) and any artwork (see section <A href=
    "mtt.html#SEC71">6.4.1.15 Artwork</A>) to make the Bond Graph more
    readable. The graphical editor xfig is (see section <A href=
    "mtt.html#SEC166">10.2 Xfig</A>) is self-explanatory. The icon library is
    helpful here (see see section <A href="mtt.html#SEC57">6.4.1.1 Icon
    library</A>).</LI>
    <LI>Add causal strokes (see section <A href="mtt.html#SEC59">6.4.1.3
    Strokes</A>) where needed to define causality. As a general rule, use the
    minimum number of strokes needed to define the problem; this will often
    be only on the <CODE>SS</CODE> components. (see section <A href=
    "mtt.html#SEC62">6.4.1.6 SS components</A>). Save the bond graph.</LI>
    <LI>View the corresponding causal bond graph.
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>  mtt syst cbg view
</PRE>
          </TD>
        </TR>
      </TABLE>
      <OL>
        <LI>At this stage, <STRONG>MTT</STRONG> will warn you that the
        labeled components do not appear in the label file - this can safely
        be ignored.</LI>
        <LI><STRONG>MTT</STRONG> will indicate the percentage of components
        which are causally complete -- ideally this will be 100\%. Components
        which are not causally complete will be listed.</LI>
        <LI>A view of the causal bond graph will be created. The added causal
        strokes are indicated in blue, undercausal components in green and
        overcausal components in red.</LI>
        <LI>If the bond graph is causally complete, proceed to the next step,
        otherwise think hard and return to the first step.</LI>
      </OL>
    </LI>
    <LI>At this stage, no constitutive relationships have been defined.
    Nevertheless, <STRONG>MTT</STRONG> will proceed in a semi-qualitative
    fashion by assuming that all constitutive relationships are unity (and
    therefore linear). It may be useful at this stage to view various derived
    representations to check the overall model properties before proceeding
    further. For example:
      <OL>
        <LI>View the system Differential-algebraic equations
          <TABLE>
            <TR>
              <TD></TD>
              <TD class="example">
                <PRE>mtt syst dae view
</PRE>
              </TD>
            </TR>
          </TABLE>
        </LI>
        <LI>View the system state matrices
          <TABLE>
            <TR>
              <TD></TD>
              <TD class="example">
                <PRE>mtt syst sm view
</PRE>
              </TD>
            </TR>
          </TABLE>
        </LI>
        <LI>View the system transfer function
          <TABLE>
            <TR>
              <TD></TD>
              <TD class="example">
                <PRE>mtt syst tf view
</PRE>
              </TD>
            </TR>
          </TABLE>
        </LI>
        <LI>View the system step response
          <TABLE>
            <TR>
              <TD></TD>
              <TD class="example">
                <PRE>mtt syst sro view
</PRE>
              </TD>
            </TR>
          </TABLE>
        </LI>
      </OL>
    </LI>
    <LI>As well as creating the causal bond graph, <STRONG>MTT</STRONG> has
    also generated templates for other text files (see section <A href=
    "mtt.html#SEC53">6.2 Defining representations</A>) used to further
    specify the system. These can now be edited using your favorite text
    editor (see section <A href="mtt.html#SEC167">10.3 Text
    editors</A>).</LI>
    <LI>
      <STRONG>MTT</STRONG> will now generate the representations (see section
      <A href="mtt.html#SEC52">6.1 Representation summary</A>)that you
      desire. For example the system can be simulated by
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>mtt syst odeso view
</PRE>
          </TD>
        </TR>
      </TABLE><STRONG>MTT</STRONG> will complain if a component is named in
      the bond graph but not in the label file and vice versa. This mainly to
      catch typing errors.
    </LI>
  </OL>
  <P><A name="Creating complex models"></A></P>
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  <H2>3.3 Creating complex models</H2><!--docid::SEC31::-->
  <P>Complex models -- in distinction to simple models (see section <A href=
  "mtt.html#SEC30">3.2 Creating simple models</A>) -- have a hierarchical
  structure. In particular, bond graph components can be created by
  specifying their bond graph. Typically, such components will have more than
  one port (see section <A href="mtt.html#SEC8">1.6.1 Ports</A>); within each
  component, ports are represented by named SS components (see section
  <A href="mtt.html#SEC65">6.4.1.9 Named SS components</A>); outwith each
  component, ports are unambiguously identified by labels (see section
  <A href="mtt.html#SEC67">6.4.1.11 Port labels</A>) and vector labels (see
  section <A href="mtt.html#SEC68">6.4.1.12 Vector port labels</A>).</P>
  <P>Complex models are thus created by conceptually decomposing the system
  into simple subsystems, and then creating the corresponding bond graphs.
  The procedure for simple systems (see section <A href="mtt.html#SEC30">3.2
  Creating simple models</A>) is then followed using the top level system
  (see section <A href="mtt.html#SEC32">3.3.1 Top level</A>);
  <STRONG>MTT</STRONG> then recursively operates on the lower level
  systems.</P>
  <P>The report representation (see section <A href="mtt.html#SEC144">6.16
  Report (rep)</A>) provides a convenient way of viewing a complex
  system.</P>
  <P>An example of such a system can be created as follows:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy twolink
mtt twolink rep hview
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The result is &lt;A
  HREF="./examples/twolink/twolink_rep/twolink_rep.html"&gt;
  here&lt;/A&gt;.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC32">3.3.1 Top
      level</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Top level"></A></P>
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  <H3>3.3.1 Top level</H3><!--docid::SEC32::-->
  The top level of a complex model contains subsystems but is not, itself,
  contained by other systems. It has the following special features:
  <UL>
    <LI>its name is used in the mtt command as the system name.</LI>
    <LI>all named SS componenents (see section <A href=
    "mtt.html#SEC65">6.4.1.9 Named SS components</A>) are treated as ordinary
    SS components (see section <A href="mtt.html#SEC62">6.4.1.6 SS
    components</A>).</LI>
  </UL>
  <P><A name="Simulation" id="Simulation"></A></P>
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  <H1>4. Simulation</H1><!--docid::SEC33::-->
  One purpose of modelling is to simulate the modeled dynamic system.
  Although this is just another transformation (see section <A href=
  "mtt.html#SEC3">1.2 What is a transformation?</A>) and therefore is covered
  in the appropriate chapter (see section <A href="mtt.html#SEC51">6.
  Representations</A>), it is important enough to be given its own chapter.
  <P>Simulation is typically performed using an appropriate simulation
  language (which is often inappropriately conflated with modelling tools).
  <STRONG>MTT</STRONG> provides a number of alternative routes to simulation
  based on the following representations (see section <A href=
  "mtt.html#SEC51">6. Representations</A>):</P>
  <DL compact>
    <DT><A name="IDX97" id="IDX97"></A> <CODE>cse</CODE></DT>
    <DD><A name="IDX98" id="IDX98"></A> constrained-state differential
    equation form</DD>
    <DT><A name="IDX99" id="IDX99"></A> <CODE>ode</CODE></DT>
    <DD><A name="IDX100" id="IDX100"></A> ordinary differential (or
    state-space) equations</DD>
  </DL>in each case these equations may be linear or nonlinear.
  <P>Special cases of numerical simulation, appropriate to <EM>linear</EM>
  systems, are:</P>
  <DL compact>
    <DT><A name="IDX101" id="IDX101"></A> <CODE>ir</CODE></DT>
    <DD><A name="IDX102" id="IDX102"></A> impulse response - state</DD>
    <DT><A name="IDX103" id="IDX103"></A> <CODE>iro</CODE></DT>
    <DD><A name="IDX104" id="IDX104"></A> impulse response - output</DD>
    <DT><A name="IDX105" id="IDX105"></A> <CODE>sr</CODE></DT>
    <DD><A name="IDX106" id="IDX106"></A> impulse response - state</DD>
    <DT><A name="IDX107" id="IDX107"></A> <CODE>sro</CODE></DT>
    <DD><A name="IDX108" id="IDX108"></A> impulse response - output</DD>
  </DL>
  <P>There are a number of languages (see section <A href=
  "mtt.html#SEC159">9. Languages</A>) which can be used to describe these
  representations for the purposes of numerical simulation:</P>
  <DL compact>
    <DT><A name="IDX109" id="IDX109"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX110" id="IDX110"></A> <CODE>octave</CODE> a high-level
    interactive language for numerical computation.</DD>
    <DT><A name="IDX111" id="IDX111"></A> <CODE>c</CODE></DT>
    <DD><A name="IDX112" id="IDX112"></A> <CODE>gcc</CODE> a c compiler.</DD>
    <DT><A name="IDX113" id="IDX113"></A> <CODE>cc</CODE></DT>
    <DD><A name="IDX114" id="IDX114"></A> <CODE>g++</CODE> a C++ front-end to
    gcc.</DD>
  </DL>
  <P>There are a number solution algorithms available:</P>
  <UL>
    <LI>explicit solution via the matrix exponential</LI>
    <LI>backward Euler integration (explicit)</LI>
    <LI>forward Euler integration (implicit)</LI>
    <LI>Runge Kutta IV integration (explicit, fixed step)</LI>
    <LI>Hybrd algebraic solver (MINPACK, Octave fsolve)</LI>
  </UL>
  <P>However, all combinations of representation, language and solution
  method are not supported by <STRONG>MTT</STRONG> at the moment. Given a
  system `system', some recommended commands are:</P>
  <DL compact>
    <DT><A name="IDX115" id="IDX115"></A> <CODE>mtt system iro
    view</CODE></DT>
    <DD><A name="IDX116" id="IDX116"></A> creates the impulse response of a
    <EM>linear</EM> system via the system_sm.m representation using explicit
    solution via the matrix exponential.</DD>
    <DT><A name="IDX117" id="IDX117"></A> <CODE>mtt system sro
    view</CODE></DT>
    <DD><A name="IDX118" id="IDX118"></A> creates the step response of a
    <EM>linear</EM> system via the system_sm.m representation using explicit
    solution via the matrix exponential.</DD>
    <DT><A name="IDX119" id="IDX119"></A> <CODE>mtt -c system odeso
    view</CODE></DT>
    <DD><A name="IDX120" id="IDX120"></A> creates the response of a
    <EM>nonlinear</EM> system via the system_ode.c representation using
    implicit integration.</DD>
    <DT><A name="IDX121" id="IDX121"></A> <CODE>mtt -c -i euler system odeso
    view</CODE></DT>
    <DD><A name="IDX122" id="IDX122"></A> creates the response of a
    <EM>nonlinear</EM> system via the system_ode.c representation using euler
    integration.</DD>
  </DL>
  <P>Simulation parameters are described in the system_simpar.txt file (see
  section <A href="mtt.html#SEC37">4.2 Simulation parameters</A>).</P>
  <P>The steady-state solution of a system can also be "simulated"(see
  section <A href="mtt.html#SEC34">4.1 Steady-state solutions</A>).</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC34">4.1 Steady-state
      solutions</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC37">4.2 Simulation
      parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC42">4.3 Simulation
      input</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC43">4.4 Simulation
      logic</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC44">4.5 Simulation
      initial state</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC45">4.6 Simulation
      code</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Steady-state solutions"></A></P>
  <HR size="6">
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  <H2>4.1 Steady-state solutions</H2><!--docid::SEC34::-->
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC35">4.1.1
      Steady-state solutions (odess)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC36">4.1.2
      Steady-state solutions (ss)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Steady-state solutions - numerical(odess)"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>4.1.1 Steady-state solutions (odess)</H3><!--docid::SEC35::-->
  <P><STRONG>MTT</STRONG> can compute the steady-state solutions of an
  ordinary differential equation; this used the octave function `fsolve'. The
  solution is computed as a function of time using the input specified in the
  input file. The simulation parameter file (see section <A href=
  "mtt.html#SEC37">4.2 Simulation parameters</A>) is used to provide the time
  scales.</P>
  <P>For example</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy rc
cd rc
mtt rc odess view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Steady-state solutions - symbolic (ss)"></A></P>
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  </TABLE>
  <H3>4.1.2 Steady-state solutions (ss)</H3><!--docid::SEC36::-->
  A rudimentary form of steady-state solution exists in mtt. The steady
  states and inouts are supplied by the user in the file system_simpar.r and
  the corresponding output and sate derivative computed by
  <STRONG>MTT</STRONG> using
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system ss view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>For example</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy rc
cd rc
mtt rc sspar view
mtt rc ss view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Simulation parameters"></A></P>
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  </TABLE>
  <H2>4.2 Simulation parameters</H2><!--docid::SEC37::-->
  <P>Simulation parameters are set in the system_simpar.txt file. At the
  moment this sets the following variables:</P>
  <UL>
    <LI>LAST the last simulation time</LI>
    <LI>DT the incremental time (for plotting)</LI>
    <LI>STEPFACTOR the number of integration steps per DT -- thus the
    integration interval is DT/STEPFACTOR</LI>
    <LI>WMIN Minimum frequency = 10^WMIN</LI>
    <LI>WMAX Maximum frequency = 10^WMAX</LI>
    <LI>WSTEPS Number of Frequency steps.</LI>
    <LI>INPUT The input index for frequency response</LI>
  </UL>
  <P>There are a number of solution algorithms</P>
  <UL>
    <LI>Euler basic Euler integration (see section <A href=
    "mtt.html#SEC38">4.2.1 Euler integration</A>). This method is simple, but
    not recommended for stiff systems.</LI>
    <LI>Implicit semi-implicit integration (see section <A href=
    "mtt.html#SEC39">4.2.2 Implicit integration</A>) - uses the smx
    representation to give stability.</LI>
    <LI>Runge Kutta IV fixed step Runge Kutta fourth order integration (see
    section <A href="mtt.html#SEC40">4.2.3 Runge Kutta IV
    integration</A>).</LI>
    <LI>Hybrd numerical algebraic equation solver</LI>
  </UL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC38">4.2.1 Euler
      integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC39">4.2.2 Implicit
      integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC40">4.2.3 Runge
      Kutta IV integration</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC41">4.2.4 Hybrd
      algebraic solver</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Euler integration"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>4.2.1 Euler integration</H3><!--docid::SEC38::-->
  Euler integration approximates the solution of the Ordinary Differential
  Equation
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>dx/dt = f(x,u)
</PRE>
      </TD>
    </TR>
  </TABLE>by
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>x := x + f(x,u)*DDT
</PRE>
      </TD>
    </TR>
  </TABLE>where
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>DDT = DT/STEPFACTOR
</PRE>
      </TD>
    </TR>
  </TABLE>If the system is linear, stability is ensured if the integer
  STEPFACTOR is chosen to be greater than the real number
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>(maximum eigenvalue of -A)*DT/2
</PRE>
      </TD>
    </TR>
  </TABLE>where A is the nxn matrix appearing in
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>f(x,u) = Ax + Bu
</PRE>
      </TD>
    </TR>
  </TABLE>If the system is non linear, the linearised system matrix A should
  act as a guide to the choice of STEPFACTOR.
  <P><A name="Implicit integration"></A></P>
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  </TABLE>
  <H3>4.2.2 Implicit integration</H3><!--docid::SEC39::-->
  Implicit integration approximates the solution of the Ordinary Differential
  Equation
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>dx/dt = f(x,u)
</PRE>
      </TD>
    </TR>
  </TABLE>by
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>(I-A*DT)x := (I-A*DT)x + f(x,u)DT
</PRE>
      </TD>
    </TR>
  </TABLE>where A is the linearised system matrix. This implies the solution
  of N (=number of states) linear equations at each sample interval. The
  OCTAVE version used the `\' operator to solve the set of linear equations,
  the C version uses LU decomposition.
  <P>If the system is linear, stability is ensured unconditionaly. If the
  system is non-linear, then the method still works well.</P>
  <P>This method is nice in that choice of DT trades of accuracy against
  computation time without compromising stability. In addition, the correct
  stready-state values are achieved.</P>
  <P>This approach can also be used for constrained state equations of the
  form:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>E(x) dx/dt = f(x,u)
</PRE>
      </TD>
    </TR>
  </TABLE>where E(x) is a state-dependent matrix. The approximate solution is
  then given by:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>(E(x)-A*DT)x := (E(x)-A*DT)x + f(x,u)DT
</PRE>
      </TD>
    </TR>
  </TABLE>which reduces to the ordinary differential equation case when
  E(x)=I.
  <P>The _smx representation includes the E matrix.</P>
  <P><A name="Runge Kutta IV integration"></A></P>
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  </TABLE>
  <H3>4.2.3 Runge Kutta IV integration</H3><!--docid::SEC40::-->
  Runge Kutta IV approximates the solution of the Ordinary Differential
  Equation
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>dx/dt = f(x,t)
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>by</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>x := x + (DT/6)*(k1 + 2*k2 + 2*k3 + k4)
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>where</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>k1 := f(x,t)
k2 := f(x+(1/2)*k1,t+(1/2)*DT)
k3 := f(x+(1/2)*k2,t+(1/2)*DT)
k4 := f(x+k3,t+DT)
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The <STRONG>MTT</STRONG> implementation of Runge-Kutta integration is a
  fourth order, fixed-step, explicit integration method.</P>
  <P>For some systems of equations, the increased accuracy of using a fourth
  order method can allow larger step-lengths to be used than would allowed by
  the lower order Euler integration method.</P>
  <P>It should be noted that during the interemediate calculations (k1...k4),
  the input vector <CODE>u</CODE> is not advanced w.r.t. time; the system
  inputs are assumed to be constant over the period of the integration
  step-length.</P>
  <P><A name="Hybrd algebraic solver"></A></P>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>4.2.4 Hybrd algebraic solver</H3><!--docid::SEC41::-->
  <P>The hybrd algebraic solver of <A href=
  "http://www.netlib.org/minpack/hybrd.f">MINPACK</A>, which is used by
  Octave in the <CODE>fsolve</CODE> routine, may be used in conjunction with
  one of the other integration methods to solve semi-explicit, index 1,
  differential algebraic equations; these may be generated in
  <STRONG>MTT</STRONG> models by use of <CODE>unknown</CODE> SS Components
  see section <A href="mtt.html#SEC84">6.6.1 SS component labels</A>.</P>
  <P>This method requires that compiled simulation code is used; either -cc
  or -oct. To perform a simulation based on a model <CODE>sys</CODE>,</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -cc -ae hybrd -i euler sys odeso view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><STRONG>MTT</STRONG> will attempt to minimise the residual error at each
  integration time-step using the hybrd routine.</P>
  <P>This method of simulation is particularly well suited to stiff systems
  where very fast dynamics are of little interest. Care must be taken to
  ensure that an acceptable level of convergence is achieved by the solver
  for the system under investigation.</P>
  <P><A name="Simulation input"></A></P>
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  <H2>4.3 Simulation input</H2><!--docid::SEC42::-->
  This is defined in the system_input.txt file. A default file is created
  automatically by <STRONG>MTT</STRONG>. This is done explicitly by
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system input txt
</PRE>
      </TD>
    </TR>
  </TABLE>If the file already exists, the same command checks that all inputs
  are defined and that all defined inputs exist in the system and promts the
  user to correct discrepancies.
  <P>Inputs are defined by the full system name appearing in the structure
  file (see section <A href="mtt.html#SEC103">6.7 Structure (struc)</A>).
  They can depend on states (again defined by name), time (defined by t) and
  parameters</P>
  <P>For example:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>system_pump_l_1_u      = 4e5*atm;
system_pump_r_1_u       = 4e5*(t&lt;10)*atm;
system_ss_i             = 0*kg;
system_ss_o             = 3e-3*kg;
system_v_1_u            = (t&gt;10);
system_v_ll_1_u         = 1;
system_v_lr_1_u         = (t&lt;10);
system_v_ul_1_u         = 0;
system_v_ur_1_u         = (t&gt;10);
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Simulation logic"></A></P>
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  </TABLE>
  <H2>4.4 Simulation logic</H2><!--docid::SEC43::-->
  This is defined in the system_logic.txt file. A default file is created
  automatically by <STRONG>MTT</STRONG>. This is done explicitly by
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system logic txt
</PRE>
      </TD>
    </TR>
  </TABLE>If the file already exists, the same command checks that the logic
  corresponding to all switch states (see section <A href=
  "mtt.html#SEC13">1.8 Switched systems</A>) are defined and that all defined
  logic exists in the system and promts the user to correct discrepancies.
  <P>Logical inputs are defined by the full system name corresponding to
  MTT_switch components appearing in the structure file (see section <A href=
  "mtt.html#SEC103">6.7 Structure (struc)</A>) <EM>with `_logic'
  appended</EM>. They can depend on states (again defined by name), time
  (defined by t) and parameters</P>
  <P>For example:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>bounce_ground_1_mtt_switch_logic       = bounce_intf_1_mtt3&lt;0;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Simulation initial state"></A></P>
  <HR size="6">
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  </TABLE>
  <H2>4.5 Simulation initial state</H2><!--docid::SEC44::-->
  This is defined in the system_state.txt file. A default file is created
  automatically by <STRONG>MTT</STRONG>. This is done explicitly by
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system state txt
</PRE>
      </TD>
    </TR>
  </TABLE>If the file already exists, the same command checks that all states
  are defined and that all defined states exist in the system and prompts the
  user to correct discrepancies.
  <P>States are defined by the full system name appearing in the structure
  file (see section <A href="mtt.html#SEC103">6.7 Structure (struc)</A>).
  They can depend on parameters. For example</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>system_c_l     = (1e4/k_l)/kg;
system_c_ll     = (1e4/k_s)/kg;
system_c_lr     = (1e4/k_s)/kg;
system_c_u      = (1e4/k_l)/kg;
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Simulation code"></A></P>
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      ]</TD>
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  </TABLE>
  <H2>4.6 Simulation code</H2><!--docid::SEC45::-->
  simulation code can be generated by <STRONG>MTT</STRONG> in the form of the
  <CODE>ode2odes</CODE> transformation. This can be produced in a number of
  languages, including .m, .oct, C and C++ see section <A href=
  "mtt.html#SEC159">9. Languages</A>.
  <P>To generate simulation code in C:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -c [options] sys ode2odes c
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Similarly, to generate C++ code:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -cc [options] sys ode2odes cc
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>To generate an executable based on the C++ representation:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -cc [options] sys ode2odes exe
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC46">4.6.1
      Dynamically linked functions</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Dynamically linked functions"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>4.6.1 Dynamically linked functions</H3><!--docid::SEC46::-->
  <P>Some model representations can be compiled into dynamically loaded code
  (shared objects) which are compiled prior to use in other modelling and
  simulation environments; in particular, .oct files can be generated for use
  in GNU Octave (see section <A href="mtt.html#SEC170">10.4.2 Creating GNU
  Octave .oct files</A>) and .mex files can be generated for use in Matlab
  (see section <A href="mtt.html#SEC171">10.4.3 Creating Matlab .mex
  files</A>) or Simulink (see section <A href="mtt.html#SEC172">10.4.4
  Embedding MTT models in Simulink</A>). The use of compiled (and possibly
  compiler-optimised) code can offer significant processing speed advantages
  over equivalent interpreted functions (e.g. .m files) for computationally
  intensive procedures.</P>
  <P>The C++ code generated by <STRONG>MTT</STRONG> allows the same code to
  be generated as standalone code, Octave .oct files or Matlab .mexglx files.
  Although <STRONG>MTT</STRONG> usually takes care of the compilation
  options, if it is necessary to compile the code on a machine on which
  <STRONG>MTT</STRONG> is not installed, the appropriate flag should be
  passed to the compiler pre-processor:</P>
  <UL>
    <LI><CODE>-DCODEGENTARGET=STANDALONE</CODE></LI>
    <LI><CODE>-DCODEGENTARGET=OCTAVEDLD</CODE></LI>
    <LI><CODE>-DCODEGENTARGET=MATLABMEX</CODE></LI>
  </UL>
  <P><A name="Simulation output"></A></P>
  <HR size="6">
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  </TABLE>
  <H2>4.7 Simulation output</H2><!--docid::SEC47::-->
  The view (see section <A href="mtt.html#SEC165">10.1 Views</A>)
  representation provides a graphical representation of the results of a
  simulation; the postscript language provides the same thing in a form that
  can be included in a document.
  <P>These are two simulation output representations</P>
  <DL compact>
    <DT><A name="IDX123" id="IDX123"></A> <CODE>odes</CODE></DT>
    <DD><A name="IDX124" id="IDX124"></A> ordinary differential equation
    solution (states)</DD>
    <DT><A name="IDX125" id="IDX125"></A> <CODE>odeso</CODE></DT>
    <DD><A name="IDX126" id="IDX126"></A> ordinary differential equation
    solution (output)</DD>
  </DL>
  <P>Particular output variables can be selected by adding a fourth argument
  in one of 2 forms</P>
  <DL compact>
    <DT><A name="IDX127" id="IDX127"></A>
    <CODE>'name1;name2;..;namen'</CODE></DT>
    <DD><A name="IDX128" id="IDX128"></A> plot the variables with names na1
    .. namen against time</DD>
    <DT><A name="IDX129" id="IDX129"></A> <CODE>'name1:name2'</CODE></DT>
    <DD><A name="IDX130" id="IDX130"></A> plot the variable with name2
    against that with name 1</DD>
  </DL>
  <P>An example of plotting a single variable against time is:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V'
</PRE>
      </TD>
    </TR>
  </TABLE>An example of plotting one variable against another is:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V:OttoCycle_cycle_P'
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC48">4.7.1 Viewing
      results with gnuplot</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC49">4.7.2 Exporting
      results to SciGraphica</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Viewing results with gnuplot"></A></P>
  <HR size="6">
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      <TD valign="middle" align="left"></TD>
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  </TABLE>
  <H3>4.7.1 Viewing results with gnuplot</H3><!--docid::SEC48::-->
  <P>Simulation plots may be conveniently selected, viewed with <A href=
  "http://www.gnuplot.org">gnuplot</A> and saved to file (in PostScript
  format) using the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt [options] rc gnuplot view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>This will cause a menu to be displayed, from which states and outputs
  may be selected for viewing. Clicking on a <EM>parameter name</EM> will, by
  default, cause the time history of the selected parameter to be
  displayed.</P>
  <P>As with <STRONG>xMTT</STRONG> (see section <A href="mtt.html#SEC15">2.1
  Menu-driven interface</A>), the Wish Tcl/Tk interpreter must be installed
  to make use of this feature.</P>
  <P><A name="Exporting results to SciGraphica"></A></P>
  <HR size="6">
  <A name="SEC49" id="SEC49"></A>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC47">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H3>4.7.2 Exporting results to SciGraphica</H3><!--docid::SEC49::-->
  <P>Simulation results can be converted into an XML-format <A href=
  "http://scigraphica.sourceforge.net">SciGraphica</A> (version 0.61)
  <EM>.sg</EM> file with the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt [options] sys odes sg
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The SciGraphica file will contain two worksheets, X_sys and Y_sys,
  containing the state and output time-histories from the simulation.</P>
  <P><A name="Sensitivity models"></A></P>
  <HR size="6">
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  </TABLE>
  <H1>5. Sensitivity models</H1><!--docid::SEC50::-->
  <P>The sensitivity model of a system is a set of equations giving the
  sensitivity of the system outputs with respect to system parameters.
  <STRONG>MTT</STRONG> has built in methods for assisting with the
  development of such models.</P>
  <P>This feature is experimental at the moment, but the following example
  gives an idea of what can be achieved.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt copy rc
cd rc
mtt -s src ode view
mtt -s src odeso view
</PRE>
      </TD>
    </TR>
  </TABLE>The sensitivity system src is automatically created from the system
  rc using the predefined sR and sC components together with vector junctions
  (see section <A href="mtt.html#SEC70">6.4.1.14 Vector Components</A>). The
  four outputs are the two system outputs plus the two sensitivity functions.
  <P>An alternative route is to create the sensitivity functions by symbolic
  differentiation. The following sensitivity representations are
  available:</P>
  <DL compact>
    <DT><A name="IDX131" id="IDX131"></A> <CODE>scse</CODE></DT>
    <DD><A name="IDX132" id="IDX132"></A> sensitivity constrained-state
    equations</DD>
    <DT><A name="IDX133" id="IDX133"></A> <CODE>sm</CODE></DT>
    <DD><A name="IDX134" id="IDX134"></A> sensitivity state matrices</DD>
    <DT><A name="IDX135" id="IDX135"></A> <CODE>scsm</CODE></DT>
    <DD><A name="IDX136" id="IDX136"></A> sensitivity constrained-state
    matrices</DD>
  </DL>
  <P><A name="Representations" id="Representations"></A></P>
  <HR size="6">
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  <H1>6. Representations</H1><!--docid::SEC51::-->
  <P>As discussed in <A href="mtt.html#SEC2">1.1 What is a
  representation?</A>, a system has many representations. The purpose of
  <STRONG>MTT</STRONG> is to provide an easy way to generate such
  representation by applying the appropriate sequence of transformations. The
  representations supported by <STRONG>MTT</STRONG> are summarised in
  <A href="mtt.html#SEC52">6.1 Representation summary</A>.</P>
  <P>There is a two-fold division of representations into those with which
  the user defines the system and its various attributes, and those which are
  derived from these. The <EM>defining representations</EM> are listed in
  <A href="mtt.html#SEC53">6.2 Defining representations</A>.</P>
  <P>Each representation is implemented in one or more languages depending on
  its use. These languages are discussed in <A href="mtt.html#SEC159">9.
  Languages</A> and are associated with appropriate tools for modifying or
  viewing the representations.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC52">6.1
      Representation summary</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC53">6.2 Defining
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC54">6.3 Verbal
      description (desc)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC55">6.4 Acausal bond
      graph (abg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC80">6.5 Stripped
      acausal bond graph (sabg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC83">6.6 Labels
      (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC103">6.7 Structure
      (struc)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC107">6.8
      Constitutive relationship (cr)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC115">6.9
      Parameters</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC120">6.10 Causal
      bond graph (cbg)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC124">6.11 Elementary
      system equations (ese)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC126">6.12
      Differential-Algebraic Equations (dae)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC131">6.13
      Constrained-state Equations (cse)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC135">6.14 Ordinary
      Differential Equations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC141">6.15 Descriptor
      matrices (dm)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC144">6.16 Report
      (rep)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Representation summary"></A></P>
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  </TABLE>
  <H2>6.1 Representation summary</H2><!--docid::SEC52::-->
  <P>Some of the the representations available in <STRONG>MTT</STRONG> are
  (in alphabetical order):</P>
  <DL compact>
    <DT><A name="IDX137" id="IDX137"></A> <CODE>abg</CODE></DT>
    <DD><A name="IDX138" id="IDX138"></A> acausal bond graph</DD>
    <DT><A name="IDX139" id="IDX139"></A> <CODE>cbg</CODE></DT>
    <DD><A name="IDX140" id="IDX140"></A> causal bond graph</DD>
    <DT><A name="IDX141" id="IDX141"></A> <CODE>cr</CODE></DT>
    <DD><A name="IDX142" id="IDX142"></A> constitutive relationship for each
    subsystem</DD>
    <DT><A name="IDX143" id="IDX143"></A> <CODE>cse</CODE></DT>
    <DD><A name="IDX144" id="IDX144"></A> constrained-state equations</DD>
    <DT><A name="IDX145" id="IDX145"></A> <CODE>csm</CODE></DT>
    <DD><A name="IDX146" id="IDX146"></A> constrained-state matrices</DD>
    <DT><A name="IDX147" id="IDX147"></A> <CODE>dae</CODE></DT>
    <DD><A name="IDX148" id="IDX148"></A> differential-algebraic
    equations</DD>
    <DT><A name="IDX149" id="IDX149"></A> <CODE>daes</CODE></DT>
    <DD><A name="IDX150" id="IDX150"></A> dae solution - state</DD>
    <DT><A name="IDX151" id="IDX151"></A> <CODE>daeso</CODE></DT>
    <DD><A name="IDX152" id="IDX152"></A> dae solution - output</DD>
    <DT><A name="IDX153" id="IDX153"></A> <CODE>def</CODE></DT>
    <DD><A name="IDX154" id="IDX154"></A> definitions - system orders
    etc.</DD>
    <DT><A name="IDX155" id="IDX155"></A> <CODE>desc</CODE></DT>
    <DD><A name="IDX156" id="IDX156"></A> Verbal description of system</DD>
    <DT><A name="IDX157" id="IDX157"></A> <CODE>dm</CODE></DT>
    <DD><A name="IDX158" id="IDX158"></A> descriptor matrices</DD>
    <DT><A name="IDX159" id="IDX159"></A> <CODE>ese</CODE></DT>
    <DD><A name="IDX160" id="IDX160"></A> elementary system equations</DD>
    <DT><A name="IDX161" id="IDX161"></A> <CODE>fr</CODE></DT>
    <DD><A name="IDX162" id="IDX162"></A> frequency response</DD>
    <DT><A name="IDX163" id="IDX163"></A> <CODE>input</CODE></DT>
    <DD><A name="IDX164" id="IDX164"></A> numerical input declaration</DD>
    <DT><A name="IDX165" id="IDX165"></A> <CODE>ir</CODE></DT>
    <DD><A name="IDX166" id="IDX166"></A> impulse response - state</DD>
    <DT><A name="IDX167" id="IDX167"></A> <CODE>iro</CODE></DT>
    <DD><A name="IDX168" id="IDX168"></A> impulse response - output</DD>
    <DT><A name="IDX169" id="IDX169"></A> <CODE>lbl</CODE></DT>
    <DD><A name="IDX170" id="IDX170"></A> label file</DD>
    <DT><A name="IDX171" id="IDX171"></A> <CODE>lmfr</CODE></DT>
    <DD><A name="IDX172" id="IDX172"></A> loglog modulus frequency
    response</DD>
    <DT><A name="IDX173" id="IDX173"></A> <CODE>lpfr</CODE></DT>
    <DD><A name="IDX174" id="IDX174"></A> semilog phase frequency
    response</DD>
    <DT><A name="IDX175" id="IDX175"></A> <CODE>nifr</CODE></DT>
    <DD><A name="IDX176" id="IDX176"></A> Nichols style frequency
    response</DD>
    <DT><A name="IDX177" id="IDX177"></A> <CODE>numpar</CODE></DT>
    <DD><A name="IDX178" id="IDX178"></A> numerical parameter
    declaration</DD>
    <DT><A name="IDX179" id="IDX179"></A> <CODE>nyfr</CODE></DT>
    <DD><A name="IDX180" id="IDX180"></A> Nyquist style frequency
    response</DD>
    <DT><A name="IDX181" id="IDX181"></A> <CODE>obs</CODE></DT>
    <DD><A name="IDX182" id="IDX182"></A> observer equations for CGPC</DD>
    <DT><A name="IDX183" id="IDX183"></A> <CODE>ode</CODE></DT>
    <DD><A name="IDX184" id="IDX184"></A> ordinary differential
    equations</DD>
    <DT><A name="IDX185" id="IDX185"></A> <CODE>odes</CODE></DT>
    <DD><A name="IDX186" id="IDX186"></A> ode solution - state</DD>
    <DT><A name="IDX187" id="IDX187"></A> <CODE>odes</CODE></DT>
    <DD><A name="IDX188" id="IDX188"></A> ODE simulation header file</DD>
    <DT><A name="IDX189" id="IDX189"></A> <CODE>odeso</CODE></DT>
    <DD><A name="IDX190" id="IDX190"></A> ode solution - output</DD>
    <DT><A name="IDX191" id="IDX191"></A> <CODE>odess</CODE></DT>
    <DD><A name="IDX192" id="IDX192"></A> ode numerical steady-states -
    states</DD>
    <DT><A name="IDX193" id="IDX193"></A> <CODE>odesso</CODE></DT>
    <DD><A name="IDX194" id="IDX194"></A> ode numerical steady-states -
    outputs</DD>
    <DT><A name="IDX195" id="IDX195"></A> <CODE>rbg</CODE></DT>
    <DD><A name="IDX196" id="IDX196"></A> raw bond graph</DD>
    <DT><A name="IDX197" id="IDX197"></A> <CODE>rep</CODE></DT>
    <DD><A name="IDX198" id="IDX198"></A> report</DD>
    <DT><A name="IDX199" id="IDX199"></A> <CODE>rfe</CODE></DT>
    <DD><A name="IDX200" id="IDX200"></A> robot-form equations</DD>
    <DT><A name="IDX201" id="IDX201"></A> <CODE>sabg</CODE></DT>
    <DD><A name="IDX202" id="IDX202"></A> stripped acausal bond graph</DD>
    <DT><A name="IDX203" id="IDX203"></A> <CODE>simp</CODE></DT>
    <DD><A name="IDX204" id="IDX204"></A> simplification information</DD>
    <DT><A name="IDX205" id="IDX205"></A> <CODE>sm</CODE></DT>
    <DD><A name="IDX206" id="IDX206"></A> state matrices</DD>
    <DT><A name="IDX207" id="IDX207"></A> <CODE>smx</CODE></DT>
    <DD><A name="IDX208" id="IDX208"></A> state matrices containing explicit
    states and inputs</DD>
    <DT><A name="IDX209" id="IDX209"></A> <CODE>sms</CODE></DT>
    <DD><A name="IDX210" id="IDX210"></A> ode</DD>
    <DT><A name="IDX211" id="IDX211"></A> <CODE>smss</CODE></DT>
    <DD><A name="IDX212" id="IDX212"></A> SM simulation header file</DD>
    <DT><A name="IDX213" id="IDX213"></A> <CODE>sr</CODE></DT>
    <DD><A name="IDX214" id="IDX214"></A> step response - state</DD>
    <DT><A name="IDX215" id="IDX215"></A> <CODE>sro</CODE></DT>
    <DD><A name="IDX216" id="IDX216"></A> step response - output</DD>
    <DT><A name="IDX217" id="IDX217"></A> <CODE>ss</CODE></DT>
    <DD><A name="IDX218" id="IDX218"></A> steady-state equations</DD>
    <DT><A name="IDX219" id="IDX219"></A> <CODE>sspar</CODE></DT>
    <DD><A name="IDX220" id="IDX220"></A> steady-state definition</DD>
    <DT><A name="IDX221" id="IDX221"></A> <CODE>struc</CODE></DT>
    <DD><A name="IDX222" id="IDX222"></A> structure - list of inputs, outputs
    and states</DD>
    <DT><A name="IDX223" id="IDX223"></A> <CODE>sub</CODE></DT>
    <DD><A name="IDX224" id="IDX224"></A> Executable subsystem list</DD>
    <DT><A name="IDX225" id="IDX225"></A> <CODE>sub</CODE></DT>
    <DD><A name="IDX226" id="IDX226"></A> LaTeX subsystem list</DD>
    <DT><A name="IDX227" id="IDX227"></A> <CODE>sympar</CODE></DT>
    <DD><A name="IDX228" id="IDX228"></A> symbolic parameters</DD>
    <DT><A name="IDX229" id="IDX229"></A> <CODE>tf</CODE></DT>
    <DD><A name="IDX230" id="IDX230"></A> transfer function</DD>
  </DL>A complete list can be found via the <CODE>help representations</CODE>
  command (see section <A href="mtt.html#SEC20">2.4.1.1 help
  representations</A>).
  <P>Many of these representations have more than one language (see section
  <A href="mtt.html#SEC51">6. Representations</A>) associated with them.</P>
  <P>Some of these representations define the system (see section <A href=
  "mtt.html#SEC53">6.2 Defining representations</A>).</P>
  <P><A name="Defining representations"></A></P>
  <HR size="6">
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  </TABLE>
  <H2>6.2 Defining representations</H2><!--docid::SEC53::-->
  <P>The following representations define the system and therefore must,
  ultimately, be defined by the user. However, all of these are assigned
  default values by <STRONG>MTT</STRONG> and may then be subsequently edited
  (see section <A href="mtt.html#SEC167">10.3 Text editors</A>) viewed or
  operated on by the appropriate tools (see section <A href=
  "mtt.html#SEC164">10. Language tools</A>).</P>
  <DL compact>
    <DT><A name="IDX231" id="IDX231"></A> <CODE>system_abg.fig</CODE></DT>
    <DD><A name="IDX232" id="IDX232"></A> the acausal bond graph (see section
    <A href="mtt.html#SEC55">6.4 Acausal bond graph (abg)</A>)</DD>
    <DT><A name="IDX233" id="IDX233"></A> <CODE>system_lbl.txt</CODE></DT>
    <DD><A name="IDX234" id="IDX234"></A> the label file (see section
    <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>)</DD>
    <DT><A name="IDX235" id="IDX235"></A> <CODE>system_desc.tex</CODE></DT>
    <DD><A name="IDX236" id="IDX236"></A> the description file (see section
    <A href="mtt.html#SEC158">8.2.2 Detailed on-line documentation</A>)</DD>
    <DT><A name="IDX237" id="IDX237"></A> <CODE>system_simp.r</CODE></DT>
    <DD><A name="IDX238" id="IDX238"></A> algebraic simplifications to make
    output more readable (see section <A href="mtt.html#SEC117">6.9.2
    Symbolic parameters for simplification (simp.r)</A>)</DD>
    <DT><A name="IDX239" id="IDX239"></A> <CODE>system_subs.r</CODE></DT>
    <DD><A name="IDX240" id="IDX240"></A> algebraic substitutions to resolve,
    eq trig. identities (see section <A href="mtt.html#SEC116">6.9.1 Symbolic
    parameters (subs.r)</A>)</DD>
    <DT><A name="IDX241" id="IDX241"></A> <CODE>system_simpar.txt</CODE></DT>
    <DD><A name="IDX242" id="IDX242"></A> simulation parameters (see section
    <A href="mtt.html#SEC37">4.2 Simulation parameters</A>)</DD>
    <DT><A name="IDX243" id="IDX243"></A> <CODE>system_numpar.txt</CODE></DT>
    <DD><A name="IDX244" id="IDX244"></A> numerical parameters (see section
    <A href="mtt.html#SEC118">6.9.3 Numeric parameters (numpar)</A>)</DD>
    <DT><A name="IDX245" id="IDX245"></A> <CODE>system_input.txt</CODE></DT>
    <DD><A name="IDX246" id="IDX246"></A> the system input for simulations
    (see section <A href="mtt.html#SEC42">4.3 Simulation input</A>)</DD>
    <DT><A name="IDX247" id="IDX247"></A> <CODE>system_logic.txt</CODE></DT>
    <DD><A name="IDX248" id="IDX248"></A> the switching logic for simulations
    (see section <A href="mtt.html#SEC43">4.4 Simulation logic</A>)</DD>
    <DT><A name="IDX249" id="IDX249"></A> <CODE>system_sspar.r</CODE></DT>
    <DD><A name="IDX250" id="IDX250"></A> defines the system steady-state
    (see section <A href="mtt.html#SEC36">4.1.2 Steady-state solutions
    (ss)</A>)</DD>
  </DL>
  <P><A name="Verbal description (desc)"></A></P>
  <HR size="6">
  <A name="SEC54" id="SEC54"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC55">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.3 Verbal description (desc)</H2><!--docid::SEC54::-->
  <P>Systems can be documented in LaTeX using the _desc.tex file. This file
  is included in the report (see section <A href="mtt.html#SEC144">6.16
  Report (rep)</A>) if the abg tex option is included in the rep.txt file. As
  usual, <STRONG>MTT</STRONG> provides a default text file to be edited by
  the user (see section <A href="mtt.html#SEC167">10.3 Text editors</A>).</P>
  <P><A name="Acausal bond graph (abg)"></A></P>
  <HR size="6">
  <A name="SEC55" id="SEC55"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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  </TABLE>
  <H2>6.4 Acausal bond graph (abg)</H2><!--docid::SEC55::-->
  <P>The acausal bond graph is the main input to <STRONG>MTT</STRONG>. It is
  up to you, as a system modeler, to distill the essential aspects of the
  system that you wish to model and capture this information in the form of a
  bond graph.</P>
  <P>The inexperienced modeler may wish to look in one of the standard
  textbooks and copy some bond graphs of systems to get going.</P>
  <P>To create the acausal bond graph of system `sys' in language fig
  type:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys abg fig
</PRE>
      </TD>
    </TR>
  </TABLE>To create the acausal bond graph of system `sys' in language m
  type:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys abg m
</PRE>
      </TD>
    </TR>
  </TABLE>To view the acausal bond graph of system `sys' type:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys abg view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC56">6.4.1 Language
      fig (abg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC73">6.4.2 Language m
      (rbg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC75">6.4.3 Language m
      (abg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC79">6.4.4 Language
      tex (abg.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Language fig (abg.fig)"></A></P>
  <HR size="6">
  <A name="SEC56" id="SEC56"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
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  </TABLE>
  <H3>6.4.1 Language fig (abg.fig)</H3><!--docid::SEC56::-->
  <P>A bond graph is made up of:</P>
  <DL compact>
    <DT><A name="IDX251" id="IDX251"></A> <CODE>bonds</CODE></DT>
    <DD><A name="IDX252" id="IDX252"></A> To connect components
    together.</DD>
    <DT><A name="IDX253" id="IDX253"></A> <CODE>strokes</CODE></DT>
    <DD><A name="IDX254" id="IDX254"></A> To indicate causality.</DD>
    <DT><A name="IDX255" id="IDX255"></A> <CODE>components</CODE></DT>
    <DD><A name="IDX256" id="IDX256"></A> Either simple or compound.</DD>
    <DT><A name="IDX257" id="IDX257"></A> <CODE>artwork</CODE></DT>
    <DD><A name="IDX258" id="IDX258"></A> Irrelevant to the system but useful
    to the user.</DD>
  </DL>
  <P>An icon library of bonds, components and other symbols is available
  within xfig (see section <A href="mtt.html#SEC57">6.4.1.1 Icon
  library</A>).</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC57">6.4.1.1 Icon
      library</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC58">6.4.1.2
      Bonds</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC59">6.4.1.3
      Strokes</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC60">6.4.1.4
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC62">6.4.1.6 SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple
      components - implementation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC64">6.4.1.8 Compound
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC65">6.4.1.9 Named SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC66">6.4.1.10 Coerced
      bond direction</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC67">6.4.1.11 Port
      labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC68">6.4.1.12 Vector
      port labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC69">6.4.1.13 Port
      label defaults</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC70">6.4.1.14 Vector
      Components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC71">6.4.1.15
      Artwork</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC72">6.4.1.16 Valid
      Names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="icon library"></A></P>
  <HR size="6">
  <A name="SEC57" id="SEC57"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.1 Icon library</H4><!--docid::SEC57::-->
  A number of predefined iconic symbols are available within xfig.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>Click onto the library icon
Click onto the library pull-down menu and select BondGraph
Select iconic symbols from the presented list
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="bonds" id="bonds"></A></P>
  <HR size="6">
  <A name="SEC58" id="SEC58"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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  </TABLE>
  <H4>6.4.1.2 Bonds</H4><!--docid::SEC58::-->
  <P>Bonds are represented by polylines with two segments. They must be the
  default style (i.e. plain not dashed or dotted). The shortest segment is
  taken to be the half-arrow. its positioning is significant because:</P>
  <UL>
    <LI>It points in the direction of power flow; thus a bond normally points
    towards C, I and R components.</LI>
    <LI>the corresponding side of the bond indicates flow causality; the
    other side represents effort causality. This is significant when using
    casual half-strokes (see section <A href="mtt.html#SEC59">6.4.1.3
    Strokes</A>). Please adopt the convention of having the half-arrows below
    horizontal bonds and to the right of vertical bonds.</LI>
  </UL>
  <P><A name="strokes" id="strokes"></A></P>
  <HR size="6">
  <A name="SEC59" id="SEC59"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.3 Strokes</H4><!--docid::SEC59::-->
  <P>Causal strokes are represented by single-segment polylines. There are
  two sorts of strokes:</P>
  <UL>
    <LI><EM>Full</EM> strokes: these are the usual bond-graph strokes and
    determine both the effort and flow causality in the usual way. The
    <EM>centre</EM> of the stroke should be at about one end of the bond and
    be at right angles to it.</LI>
    <LI><EM>Half</EM> strokes: these are an innovation in
    <STRONG>MTT</STRONG> and allow you to specify the effort and flow
    causality independently. The <EM>end</EM> of the stroke should be at
    about one end of the bond and be at right angles to it. If the causal
    half-stroke is on the <EM>same</EM> side as the half-arrow (see section
    <A href="mtt.html#SEC58">6.4.1.2 Bonds</A>) then it determines
    <EM>flow</EM> causality; if, on the other hand, it is on the
    <EM>opposite</EM> side to the half-arrow (see section <A href=
    "mtt.html#SEC58">6.4.1.2 Bonds</A>) then it determines <EM>effort</EM>
    causality. Two half strokes on the <EM>same</EM>, but on
    <EM>opposite</EM> sides of the bond are equivalent to a a full stroke at
    the same end of the bond.</LI>
  </UL>
  <P><STRONG>MTT</STRONG> is reasonably forgiving; but a neat diagram will be
  less ambiguous to you as well as to <STRONG>MTT</STRONG>.</P>
  <P>Causality is indicated as follows:</P>
  <UL>
    <LI><EM>Effort</EM> is imposed at the <EM>same</EM> end as the
    stroke.</LI>
    <LI><EM>Flow</EM> is imposed at the <EM>opposite</EM> end as the
    stroke.</LI>
  </UL>
  <P><A name="components" id="components"></A></P>
  <HR size="6">
  <A name="SEC60" id="SEC60"></A>
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  </TABLE>
  <H4>6.4.1.4 Components</H4><!--docid::SEC60::-->
  <P>Components are represented by a text string in fig. The recommended
  style is: 20pt, Times-Roman and centre justified.</P>
  <P>The component text string can be of the following forms:</P>
  <DL compact>
    <DT><A name="IDX259" id="IDX259"></A> <CODE>type</CODE></DT>
    <DD>
      <A name="IDX260" id="IDX260"></A> Just the type of the component is
      indicated. Components may be either Simple components (see section
      <A href="mtt.html#SEC61">6.4.1.5 Simple components</A>) or Compound
      components (see section <A href="mtt.html#SEC64">6.4.1.8 Compound
      components</A>). For example:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>R
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
    <DT><A name="IDX261" id="IDX261"></A> <CODE>type:label</CODE></DT>
    <DD>
      <A name="IDX262" id="IDX262"></A> Both the type and the label of the
      component are given. The type must be a valid name (see section
      <A href="mtt.html#SEC72">6.4.1.16 Valid Names</A>.The name provides a
      link to more information to be found in See section <A href=
      "mtt.html#SEC83">6.6 Labels (lbl)</A>. For example:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>R:r
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
    <DT><A name="IDX263" id="IDX263"></A> <CODE>type:label:cr</CODE></DT>
    <DD>
      <A name="IDX264" id="IDX264"></A> Not only are the type and the label
      of the component given, but also the component cr argument. The type
      must be a valid name (see section <A href="mtt.html#SEC72">6.4.1.16
      Valid Names</A>.The name provides a link to more information to be
      found in See section <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>. For
      example:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>R:r:flow,r
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
    <DT><A name="IDX265" id="IDX265"></A>
    <CODE>type:label:expression</CODE></DT>
    <DD>
      <A name="IDX266" id="IDX266"></A> Expression is a mathematical
      expression relating the effort (called mtt_e) to the flow (called
      mtt_f). For example the following three forms are equivalent
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>R:r:mtt_e=r*mtt_f
R:r:mtt_e-r*mtt_f=0
R:r:mtt_f=mtt_e/r
</PRE>
          </TD>
        </TR>
      </TABLE>A non-linear example is:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>R:r:mtt_e = sin(mtt_f)
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
    <DT><A name="IDX267" id="IDX267"></A> <CODE>type*n</CODE></DT>
    <DD>
      <A name="IDX268" id="IDX268"></A> The name, together with the number
      `<SAMP>n</SAMP>' of repetitions of the component, are given. This
      repetition only makes sense if the component has an even number of
      ports (see section <A href="mtt.html#SEC67">6.4.1.11 Port labels</A>);
      n copies of the component are concatenated with odd Named ports (see
      section <A href="mtt.html#SEC67">6.4.1.11 Port labels</A>) of the
      component being connected to the even Named ports of the previous
      component in the chain in numerical order. This feature is particularly
      useful if the component is compound and can be used for, example to
      give a lumped approximation of a distributed system. For example:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>MySystem*25
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
    <DT><A name="IDX269" id="IDX269"></A> <CODE>type:label*n</CODE></DT>
    <DD>
      <A name="IDX270" id="IDX270"></A> This complete form and is a
      combination of the simpler forms. For example:
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>MySystem:MyLabel*25
</PRE>
          </TD>
        </TR>
      </TABLE>
    </DD>
  </DL>
  <P><A name="Simple components"></A></P>
  <HR size="6">
  <A name="SEC61" id="SEC61"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC60">&lt;</A>
      ]</TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.5 Simple components</H4><!--docid::SEC61::-->
  <P>The following simple components are defined in MTT.</P>
  <DL compact>
    <DT><A name="IDX271" id="IDX271"></A> <CODE>R</CODE></DT>
    <DD><A name="IDX272" id="IDX272"></A> Standard one-port R</DD>
    <DT><A name="IDX273" id="IDX273"></A> <CODE>C</CODE></DT>
    <DD><A name="IDX274" id="IDX274"></A> Standard one-port I</DD>
    <DT><A name="IDX275" id="IDX275"></A> <CODE>I</CODE></DT>
    <DD><A name="IDX276" id="IDX276"></A> Standard one-port I</DD>
    <DT><A name="IDX277" id="IDX277"></A> <CODE>SS</CODE></DT>
    <DD><A name="IDX278" id="IDX278"></A> Source-sensor</DD>
    <DT><A name="IDX279" id="IDX279"></A> <CODE>TF</CODE></DT>
    <DD><A name="IDX280" id="IDX280"></A> Transformer</DD>
    <DT><A name="IDX281" id="IDX281"></A> <CODE>GY</CODE></DT>
    <DD><A name="IDX282" id="IDX282"></A> Gyrator</DD>
    <DT><A name="IDX283" id="IDX283"></A> <CODE>AE</CODE></DT>
    <DD><A name="IDX284" id="IDX284"></A> Effort amplifier</DD>
    <DT><A name="IDX285" id="IDX285"></A> <CODE>AF</CODE></DT>
    <DD><A name="IDX286" id="IDX286"></A> Flow amplifier</DD>
    <DT><A name="IDX287" id="IDX287"></A> <CODE>CSW</CODE></DT>
    <DD><A name="IDX288" id="IDX288"></A> Switched one-port I</DD>
    <DT><A name="IDX289" id="IDX289"></A> <CODE>ISW</CODE></DT>
    <DD><A name="IDX290" id="IDX290"></A> Switched one-port I</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC62">6.4.1.6 SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple
      components - implementation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="SS components"></A></P>
  <HR size="6">
  <A name="SEC62" id="SEC62"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC63">&gt;</A>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.6 SS components</H4><!--docid::SEC62::-->
  <P><CODE>SS</CODE> components provide input and output variables for a
  system; Named SS components (see section <A href="mtt.html#SEC65">6.4.1.9
  Named SS components</A>) provide this for subsystems.</P>
  <P><A name="Simple components - implementation"></A></P>
  <HR size="6">
  <A name="SEC63" id="SEC63"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC62">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC64">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.7 Simple components - implementation</H4><!--docid::SEC63::-->
  <P>Each simple component, with name NAME, is defined by two m files:</P>
  <DL compact>
    <DT><A name="IDX291" id="IDX291"></A> <CODE>NAME_cause.m</CODE></DT>
    <DD><A name="IDX292" id="IDX292"></A> defines the possible causal
    patterns for the component</DD>
    <DT><A name="IDX293" id="IDX293"></A> <CODE>NAME_eqn.m</CODE></DT>
    <DD><A name="IDX294" id="IDX294"></A> defines the equations
    generated</DD>
  </DL>Only the experienced user would normally define simple components -
  Compound components (see section <A href="mtt.html#SEC64">6.4.1.8 Compound
  components</A>) are recommended for DIY components.
  <P><A name="Compound components"></A></P>
  <HR size="6">
  <A name="SEC64" id="SEC64"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC63">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC65">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.8 Compound components</H4><!--docid::SEC64::-->
  Compound components are systems described by bond graphs and implemented by
  MTT. They have special SS components, Named SS components (see section
  <A href="mtt.html#SEC65">6.4.1.9 Named SS components</A>), to indicate
  connections to the encapsulating system.
  <P>Like any other system, they are described by a graphical Bond Graph
  description (see section <A href="mtt.html#SEC56">6.4.1 Language fig
  (abg.fig)</A>), and a label file (see section <A href="mtt.html#SEC83">6.6
  Labels (lbl)</A>).</P>
  <P>By convention, all of the files describing a component live in a
  directory with the same name as the component.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC65">6.4.1.9 Named SS
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Named SS components"></A></P>
  <HR size="6">
  <A name="SEC65" id="SEC65"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC64">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC66">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.9 Named SS components</H4><!--docid::SEC65::-->
  <P>Named SS components provide the link from the system which
  <EM>defines</EM> compound component to the system which <EM>uses</EM> a
  compound component see section <A href="mtt.html#SEC64">6.4.1.8 Compound
  components</A>. A named SS components is of the form
  <CODE>SS:[name]</CODE>;</P>
  <P>Where `name' is a name consisting of alphanumeric characters and
  underscore; for example:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>SS:[Mechanical_1]
</PRE>
      </TD>
    </TR>
  </TABLE>Each such named SS provides one of the ports (see section <A href=
  "mtt.html#SEC8">1.6.1 Ports</A>). The direction of the named SS components.
  (see section <A href="mtt.html#SEC65">6.4.1.9 Named SS components</A>) is
  coerced (see section <A href="mtt.html#SEC66">6.4.1.10 Coerced bond
  direction</A>) to have the same direction as the bond connected to the
  corresponding port. Thus the direction of the direction of the named SS
  components has no significance unless the component is at the top level of
  a system.
  <P>If a named SS component exists at the top level (see section <A href=
  "mtt.html#SEC32">3.3.1 Top level</A>) and is treated as an ordinary SS
  component with the given direction and with the attributes specified in the
  label file (see section <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>).</P>
  <P><A name="Coerced bond direction"></A></P>
  <HR size="6">
  <A name="SEC66" id="SEC66"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC65">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC67">&gt;</A>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.10 Coerced bond direction</H4><!--docid::SEC66::-->
  Named SS components (see section <A href="mtt.html#SEC65">6.4.1.9 Named SS
  components</A>) provide the mechanism for declaring the ports (see section
  <A href="mtt.html#SEC8">1.6.1 Ports</A>) of a component. The corresponding
  bond has a direction. However, under some circumstances, it may be useful
  to reverse this direction. <STRONG>MTT</STRONG> provides a coercion
  mechanism for this: the the direction of the bond attached to the named SS
  component (see section <A href="mtt.html#SEC65">6.4.1.9 Named SS
  components</A>) is replaced by the direction of the bond attached to the
  component port.
  <P><A name="Port labels"></A></P>
  <HR size="6">
  <A name="SEC67" id="SEC67"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC66">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC68">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.11 Port labels</H4><!--docid::SEC67::-->
  Most multi-port components have ports see section <A href=
  "mtt.html#SEC8">1.6.1 Ports</A>)which display different behaviors; the
  exception to this is the junction (<CODE>0</CODE> and <CODE>1</CODE>)
  components. For this reason, <STRONG>MTT</STRONG> provides a method for
  unambiguously identifying the ports of a multi-port component by port
  labels.
  <P>A port label is indicated by a name within parentheses of the form
  <CODE>[name]</CODE>, where `name' is a name consisting of alphanumeric
  characters and underscore; for example:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>[Mechanical_1]
</PRE>
      </TD>
    </TR>
  </TABLE>This provides a label for corresponding to the component to which
  the nearest bond-end is attached.
  <P>The following rules must be be obeyed:</P>
  <UL>
    <LI>If a component has any port labels at all, there must be one for each
    port of the component.</LI>
  </UL>
  <P>Port labels may be grouped into vector port labels (see section <A href=
  "mtt.html#SEC68">6.4.1.12 Vector port labels</A>). Components with
  compatible (ie containing the same number of ports) vector ports may be
  connected by a <EM>single</EM> bond (see section <A href=
  "mtt.html#SEC6">1.5 Bonds</A>); such a bond implies the corresponding
  number of bonds (one for each element of the vector port label). All such
  bonds inherit the same direction and any <EM>explicit</EM> causal strokes
  (see section <A href="mtt.html#SEC59">6.4.1.3 Strokes</A>)</P>
  <P><A name="Vector port labels"></A></P>
  <HR size="6">
  <A name="SEC68" id="SEC68"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC67">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC69">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.12 Vector port labels</H4><!--docid::SEC68::-->
  Port labels (see section <A href="mtt.html#SEC67">6.4.1.11 Port labels</A>)
  may be grouped into vector port labels of the form
  <CODE>[name1,name2,name3]</CODE>.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>[Mechanical_1,Electrical,Hydraulic_5]
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Port label defaults"></A></P>
  <HR size="6">
  <A name="SEC69" id="SEC69"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC68">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC70">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC56">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.13 Port label defaults</H4><!--docid::SEC69::-->
  Whether impicitly or explicity, all ports of components (with the exception
  of 0 and 1 junctions) must have lables (see section <A href=
  "mtt.html#SEC67">6.4.1.11 Port labels</A>). However, these can be omitted
  from the bond graph in the following circumstances and default labels are
  supplied by <STRONG>MTT</STRONG>.
  <OL>
    <LI>A single unlabled inport defaults to [in]</LI>
    <LI>A single unlabled outport defaults to [out]</LI>
  </OL>
  <P>These defaults may, in turn be aliases (see section <A href=
  "mtt.html#SEC92">6.6.9 Aliases</A>) for port labels (see section <A href=
  "mtt.html#SEC67">6.4.1.11 Port labels</A>) or vector port labels (see
  section <A href="mtt.html#SEC68">6.4.1.12 Vector port labels</A>).
  Combining the default and alias mechanism is a powerful tool for creating
  uncluttered, yet complex, bond graph models.</P>
  <P><A name="Vector components"></A></P>
  <HR size="6">
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.14 Vector Components</H4><!--docid::SEC70::-->
  Vectors of components can be created in four cases: <CODE>0</CODE>
  junctions, <CODE>1</CODE> junctions, <CODE>SS</CODE> components and
  <CODE>SS</CODE> port components.
  <P>In each case, the presence of a vector component is indicated by a
  single port label (see section <A href="mtt.html#SEC67">6.4.1.11 Port
  labels</A>) of one of two forms:</P>
  <OL>
    <LI>containing numerals from 1 to the order of the vector. Thus a vector
    of 3 components is indicated by a port label of the form [1,2,3].</LI>
    <LI>1: followed by the order of the vector. Thus a vector of 3 components
    is indicated by a port label of the form [1:3].</LI>
  </OL>
  <P>Within the corresponding label file (see section <A href=
  "mtt.html#SEC83">6.6 Labels (lbl)</A>), the components of a vector port can
  be accessed using _i where i is the corresponding index. Thus a port
  SS:[Electrical] appearing near the port label [1,2,3] could contain the
  port alias (see section <A href="mtt.html#SEC93">6.6.9.1 Port
  aliases</A>)</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS  in Electrical_1,Electrical_2,Electrical_3
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="artwork" id="artwork"></A></P>
  <HR size="6">
  <A name="SEC71" id="SEC71"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC70">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC72">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.15 Artwork</H4><!--docid::SEC71::-->
  You are encouraged to annotate your bond graphs extensively - this makes
  them an immediately readable document whilst retaining the precise and
  unambiguous expressive power of the bond graph.
  <P>You may add any Fig (see section <A href="mtt.html#SEC160">9.1 Fig</A>)
  object to the bond graph as long as it will not be interpreted as part of
  the bond graph. The reccommended way to acheive this is to put the Bond
  Graph at depth 0,10,20 etc (ie depth modulo 10 is zero) and artwork at any
  other depth.</P>
  <P>For compatibility with earlier versions of <STRONG>MTT</STRONG>, the
  following objects are ignored even at level 0. However, their use is
  strongly discouraged.</P>
  <UL>
    <LI>Adding text is OK as long as it cannot be confused with components
    (see section <A href="mtt.html#SEC60">6.4.1.4 Components</A>). In
    particular, you can include invalid component characters such as white
    space, <CODE>"</CODE>, <CODE>'</CODE>, <CODE>!</CODE> etc.</LI>
    <LI>Adding boxes, arcs etc is always OK.</LI>
    <LI>Adding dotted or dashes lines is always OK.</LI>
  </UL>
  <P>The stripped abg file (sabg) (see section <A href="mtt.html#SEC80">6.5
  Stripped acausal bond graph (sabg)</A>) shows only those parts of the
  diagram recognised by <STRONG>MTT</STRONG> and is therefore useful for
  distinguishing artwork. <A name="Valid names"></A></P>
  <HR size="6">
  <A name="SEC72" id="SEC72"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC71">&lt;</A>
      ]</TD>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.1.16 Valid Names</H4><!--docid::SEC72::-->
  A valid name is a text string containing alphanumeric characters. It must
  <STRONG>NOT</STRONG> contain underscore `<SAMP>_</SAMP>', hyphen
  `<SAMP>-</SAMP>', `<SAMP>:</SAMP>' or `<SAMP>*</SAMP>'.
  <P>The following names should be avoided</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>if endif
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The following reserved words in reduce should also be avoided (with any
  case)</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>Commands ALGEBRAIC ANTISYMMETRIC ARRAY BYE CLEAR CLEARRULES COMMENT
CONT DECOMPOSE DEFINE DEPEND DISPLAY ED EDITDEF END EVEN FACTOR FOR
FORALL FOREACH GO GOTO IF IN INDEX INFIX INPUT INTEGER KORDER LET
LINEAR LISP LISTARGP LOAD LOAD PACKAGE MASS MATCH MATRIX MSHELL
NODEPEND NONCOM NONZERO NOSPUR ODD OFF ON OPERATOR ORDER OUT PAUSE
PRECEDENCE PRINT PRECISION PROCEDURE QUIT REAL REMFAC REMIND RETRY
RETURN SAVEAS SCALAR SETMOD SHARE SHOWTIME SHUT SPUR SYMBOLIC
SYMMETRIC VECDIM VECTOR WEIGHT WRITE WTLEVEL

Boolean Operators EVENP FIXP FREEOF NUMBERP ORDP PRIMEP

Infix Operators := = &gt;= &gt; &lt;= &lt; =&gt; + * / ^ ** . WHERE SETQ OR AND
MEMBER MEMQ EQUAL NEQ EQ GEQ GREATERP LEQ LESSP PLUS DIFFERENCE MINUS
TIMES QUOTIENT EXPT CONS Numerical Operators ABS ACOS ACOSH ACOT ACOTH
ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATANH ATAN2 COS COSH COT COTH
CSC CSCH EXP FACTORIAL FIX FLOOR HYPOT LN LOG LOGB LOG10 NEXTPRIME
ROUND SEC SECH SIN SINH SQRT TAN TANH

Prefix Operators APPEND ARGLENGTH CEILING COEFF COEFFN COFACTOR CONJ
DEG DEN DET DF DILOG EI EPS ERF FACTORIZE FIRST GCD G IMPART INT
INTERPOL LCM LCOF LENGTH LHS LINELENGTH LTERM MAINVAR MAT MATEIGEN MAX
MIN MKID NULLSPACE NUM PART PF PRECISION RANDOM RANDOM NEW SEED RANK
REDERR REDUCT REMAINDER REPART REST RESULTANT REVERSE RHS SECOND SET
SHOWRULES SIGN SOLVE STRUCTR SUB SUM THIRD TP TRACE VARNAME

Reserved Variables CARD NO E EVAL MODE FORT WIDTH HIGH POW I INFINITY
K!* LOW POW NIL PI ROOT MULTIPLICITY T

Switches ADJPREC ALGINT ALLBRANCH ALLFAC BFSPACE COMBINEEXPT
COMBINELOGS COMP COMPLEX CRAMER CREF DEFN DEMO DIV ECHO ERRCONT
EVALLHSEQP EXP EXPANDLOGS EZGCD FACTOR FORT FULLROOTS GCD IFACTOR INT
INTSTR LCM LIST LISTARGS MCD MODULAR MSG MULTIPLICITIES NAT NERO
NOSPLIT OUTPUT PERIOD PRECISE PRET PRI RAT RATARG RATIONAL RATIONALIZE
RATPRI REVPRI RLISP88 ROUNDALL ROUNDBF ROUNDED SAVESTRUCTR
SOLVESINGULAR TIME TRA TRFAC TRIGFORM TRINT

Other Reserved Ids BEGIN DO EXPR FEXPR INPUT LAMBDA LISP MACRO PRODUCT
REPEAT SMACRO SUM UNTIL WHEN WHILE WS


</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Language m (rbg.m)"></A></P>
  <HR size="6">
  <A name="SEC73" id="SEC73"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC72">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC74">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC55">Up</A>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.4.2 Language m (rbg.m)</H3><!--docid::SEC73::-->
  The raw bond graph of system `sys' is represented as an m file with
  heading:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function [rbonds, rstrokes,rcomponents,rports,n_ports] = sys_rbg
</PRE>
      </TD>
    </TR>
  </TABLE>This representation is a half-way house between the fig (see
  section <A href="mtt.html#SEC56">6.4.1 Language fig (abg.fig)</A>) and m
  (see section <A href="mtt.html#SEC75">6.4.3 Language m (abg.m)</A>)
  representations. It contains the geometric information from the fig file in
  a form digestible by Octave (see section <A href="mtt.html#SEC168">10.4
  Octave</A>).
  <P>The five outputs of this function are:</P>
  <UL>
    <LI>rbonds</LI>
    <LI>rstrokes</LI>
    <LI>rcomponents</LI>
    <LI>rports</LI>
    <LI>n_ports</LI>
  </UL>
  <P><EM>rbonds</EM> is a matrix with</P>
  <UL>
    <LI>one row for each bond (see section <A href="mtt.html#SEC58">6.4.1.2
    Bonds</A>)</LI>
    <LI>columns 1 and 2 containing the x,y coordinates for one end of the
    bond</LI>
    <LI>columns 3 and 4 containing the x,y coordinates for the corner of the
    bond</LI>
    <LI>columns 5 and 6 containing the x,y coordinates for the other end of
    the bond</LI>
  </UL>
  <P><EM>rstrokes</EM> is a matrix with (see section <A href=
  "mtt.html#SEC59">6.4.1.3 Strokes</A>)</P>
  <UL>
    <LI>one row for each stroke or half-stroke</LI>
    <LI>columns 1 and 2 containing the x,y coordinates for one end of the
    stroke</LI>
    <LI>columns 3 and 4 containing the x,y coordinates for the other end of
    the stroke</LI>
  </UL>
  <P><EM>rcomponents</EM> is a matrix with (see section <A href=
  "mtt.html#SEC60">6.4.1.4 Components</A>)</P>
  <UL>
    <LI>one row for each component</LI>
    <LI>columns 1 and 2 containing the x,y coordinates of the component</LI>
    <LI>the remaining columns containing fig file information</LI>
  </UL>
  <P><EM>rports</EM> is a matrix with (see section <A href=
  "mtt.html#SEC67">6.4.1.11 Port labels</A>)</P>
  <UL>
    <LI>one row for each component port that is explicitly labeled</LI>
    <LI>columns 1 and 2 containing the x,y coordinates of the port label</LI>
    <LI>column 3 contains the port number.</LI>
  </UL>
  <P><EM>n_ports</EM> is the number of ports associated with the system --
  i.e. the number of Named SS components (see section <A href=
  "mtt.html#SEC65">6.4.1.9 Named SS components</A>).</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC74">6.4.2.1
      Transformation abg2rbg_fig2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation abg2rbg_fig2m"></A></P>
  <HR size="6">
  <A name="SEC74" id="SEC74"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC73">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC75">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC73">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.2.1 Transformation abg2rbg_fig2m</H4><!--docid::SEC74::-->
  <P>This transformation takes the acausal bond graph as a fig file (see
  section <A href="mtt.html#SEC56">6.4.1 Language fig (abg.fig)</A>) and
  transforms it into a raw bond graph in m-file format (see section <A href=
  "mtt.html#SEC73">6.4.2 Language m (rbg.m)</A>).</P>
  <P>This transformation is implemented in GNU awk (gawk). It scans both the
  fig file (see section <A href="mtt.html#SEC56">6.4.1 Language fig
  (abg.fig)</A>) and the label file (see section <A href="mtt.html#SEC83">6.6
  Labels (lbl)</A>) and generates the rbg (see section <A href=
  "mtt.html#SEC73">6.4.2 Language m (rbg.m)</A>) with components sorted
  according to the label file. It also generates a file sys_fig.fig
  containing details of the bond graph with the components removed.</P>
  <P><A name="Language m (abg.m)"></A></P>
  <HR size="6">
  <A name="SEC75" id="SEC75"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC74">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC76">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC55">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.4.3 Language m (abg.m)</H3><!--docid::SEC75::-->
  <P>The acausal bond graph of system `sys' is represented as an m file with
  heading:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function [bonds,components,n_ports] = sys_abg
</PRE>
      </TD>
    </TR>
  </TABLE>The three outputs of this function are:
  <UL>
    <LI>bonds</LI>
    <LI>components</LI>
    <LI>n_ports</LI>
  </UL>
  <P><EM>bonds</EM> is a matrix with</P>
  <UL>
    <LI>one row for each bond</LI>
    <LI>the first column contains the arrow-orientated (see section <A href=
    "mtt.html#SEC76">6.4.3.1 Arrow-orientated causality</A>) causality of the
    <EM>effort</EM> variable.</LI>
    <LI>the second column contains the arrow-orientated (see section <A href=
    "mtt.html#SEC76">6.4.3.1 Arrow-orientated causality</A>) causality of the
    <EM>flow</EM> variable.</LI>
  </UL>
  <P><EM>components</EM> is a matrix with</P>
  <UL>
    <LI>one row for each component</LI>
    <LI>one column for each bond impinging on the component. The
    <EM>magnitude</EM> of each entry corresponds to the bond number (the
    appropriate row index of` bonds'); the sign is positive if the bond arrow
    points into the component and negative otherwise.</LI>
  </UL>
  <P><EM>n_ports</EM> is the number of ports associated with the system --
  i.e. the number of Named SS components (see section <A href=
  "mtt.html#SEC65">6.4.1.9 Named SS components</A>).</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC76">6.4.3.1
      Arrow-orientated causality</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC77">6.4.3.2
      Component-orientated causality</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC78">6.4.3.3
      Transformation rbg2abg_m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Arrow-orientated causality"></A></P>
  <HR size="6">
  <A name="SEC76" id="SEC76"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC75">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC77">&gt;</A>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.3.1 Arrow-orientated causality</H4><!--docid::SEC76::-->
  <P>The arrow-orientated causality convention assigns -1, 0 or 1 to both the
  effort and flow (see section <A href="mtt.html#SEC5">1.4 Variables</A>)
  sides of a bond to represent the causal stroke (see section <A href=
  "mtt.html#SEC59">6.4.1.3 Strokes</A>) as follows:</P>
  <DL compact>
    <DT><A name="IDX295" id="IDX295"></A> <CODE>0</CODE></DT>
    <DD><A name="IDX296" id="IDX296"></A> if there is no causality set.</DD>
    <DT><A name="IDX297" id="IDX297"></A> <CODE>1</CODE></DT>
    <DD><A name="IDX298" id="IDX298"></A> if the causal stroke is at the
    arrow end of the bond.</DD>
    <DT><A name="IDX299" id="IDX299"></A> <CODE>-1</CODE></DT>
    <DD><A name="IDX300" id="IDX300"></A> if the causal stroke is at the
    other end of the bond.</DD>
  </DL>see section <A href="mtt.html#SEC77">6.4.3.2 Component-orientated
  causality</A>.
  <P><A name="Component-orientated causality"></A></P>
  <HR size="6">
  <A name="SEC77" id="SEC77"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.3.2 Component-orientated causality</H4><!--docid::SEC77::-->
  <P>The component-orientated causality convention assigns -1, 0 or 1 to both
  the effort and flow (see section <A href="mtt.html#SEC5">1.4 Variables</A>)
  sides of a bond to represent the causal stroke (see section <A href=
  "mtt.html#SEC59">6.4.1.3 Strokes</A>) as follows:</P>
  <DL compact>
    <DT><A name="IDX301" id="IDX301"></A> <CODE>0</CODE></DT>
    <DD><A name="IDX302" id="IDX302"></A> if there is no causality set.</DD>
    <DT><A name="IDX303" id="IDX303"></A> <CODE>1</CODE></DT>
    <DD><A name="IDX304" id="IDX304"></A> if the causal stroke is at the
    component end of the bond.</DD>
    <DT><A name="IDX305" id="IDX305"></A> <CODE>-1</CODE></DT>
    <DD><A name="IDX306" id="IDX306"></A> if the causal stroke is at the
    other end of the bond.</DD>
  </DL>see section <A href="mtt.html#SEC76">6.4.3.1 Arrow-orientated
  causality</A>.
  <P><A name="Transformation rbg2abg_m"></A></P>
  <HR size="6">
  <A name="SEC78" id="SEC78"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC77">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC79">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC75">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.4.3.3 Transformation rbg2abg_m</H4><!--docid::SEC78::-->
  This transformation takes the raw bond graph and, by doing some geometrical
  computation, determines the topology of the bond graph -- ie what is close
  to what.
  <P><A name="Language tex (abg.tex)"></A></P>
  <HR size="6">
  <A name="SEC79" id="SEC79"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC78">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC80">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC55">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.4.4 Language tex (abg.tex)</H3><!--docid::SEC79::-->
  <P>For the purpose of producing a report (see section <A href=
  "mtt.html#SEC144">6.16 Report (rep)</A>), <STRONG>MTT</STRONG> generates a
  LaTeX (see section <A href="mtt.html#SEC173">10.5 LaTeX</A>) file
  describing the bond graph and its subsystems. Additional information may be
  supplied using the description representation (see section <A href=
  "mtt.html#SEC158">8.2.2 Detailed on-line documentation</A>).</P>
  <P><A name="Stripped acausal bond graph (sabg)"></A></P>
  <HR size="6">
  <A name="SEC80" id="SEC80"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC79">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC81">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.5 Stripped acausal bond graph (sabg)</H2><!--docid::SEC80::-->
  The stripped acausal bond graph is the acausal bond graph representation
  (see section <A href="mtt.html#SEC55">6.4 Acausal bond graph (abg)</A>)
  without the artwork (see section <A href="mtt.html#SEC71">6.4.1.15
  Artwork</A>). It is useful to check for mistakes by showing precisely what
  is recognised by <STRONG>MTT</STRONG>.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC81">6.5.1 Language
      fig (sabg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC82">6.5.2 Stripped
      acausal bond graph (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Language fig (sabg.fig)"></A></P>
  <HR size="6">
  <A name="SEC81" id="SEC81"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC80">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC82">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC80">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.5.1 Language fig (sabg.fig)</H3><!--docid::SEC81::-->
  The stripped acausal bond graph can be generated as a fig (see section
  <A href="mtt.html#SEC160">9.1 Fig</A>) file using
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt syst sabg fig
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Stripped acausal bond graph (view)"></A></P>
  <HR size="6">
  <A name="SEC82" id="SEC82"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC81">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC83">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC80">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.5.2 Stripped acausal bond graph (view)</H3><!--docid::SEC82::-->
  This representation has the standard text view (see section <A href=
  "mtt.html#SEC165">10.1 Views</A>).
  <P><A name="Labels (lbl)"></A></P>
  <HR size="6">
  <A name="SEC83" id="SEC83"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC82">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC84">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.6 Labels (lbl)</H2><!--docid::SEC83::-->
  Bond graph components have optional labels. These provide pointers to
  further information relating to the component; this avoids clutter on the
  bond graph.
  <P>The label file contains the following non-blank lines (blank lines are
  ignored)</P>
  <UL>
    <LI>Summary - lines beginning with #SUMMARY</LI>
    <LI>Description - lines beginning with #DESCRIPTION</LI>
    <LI>Alias - lines beginning with #ALIAS</LI>
    <LI>Comments - lines beginning with #</LI>
    <LI>Labels - other non-blank lines</LI>
  </UL>
  <P>Note, for compatability with old versions, % may be used in place of #;
  but the use of % is deprecated. Each lable contains three fields (in the
  following order) separated by white space and on one line:</P>
  <OL>
    <LI>The component name see section <A href="mtt.html#SEC86">6.6.3
    Component names</A>. This must be a valid name (see section <A href=
    "mtt.html#SEC72">6.4.1.16 Valid Names</A>.</LI>
    <LI>The component constitutive relationship see section <A href=
    "mtt.html#SEC87">6.6.4 Component constitutive relationship</A></LI>
    <LI>The component arguments see section <A href="mtt.html#SEC88">6.6.5
    Component arguments</A></LI>
  </OL>
  <P>Not each component see section <A href="mtt.html#SEC60">6.4.1.4
  Components</A> needs a label, only those which are explicitly labeled on
  the Bond Graph see section <A href="mtt.html#SEC55">6.4 Acausal bond graph
  (abg)</A>. <STRONG>MTT</STRONG> checks whether all components labelled on
  the bond graph have labels and vice versa.</P>
  <P>If no lbl file exists, <STRONG>MTT</STRONG> will create a valid one for
  you; including a default set of arguments and crs for both simplae and
  compound components.</P>
  <P>If wish to create one to edit yourself, type</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system_name lbl txt
</PRE>
      </TD>
    </TR>
  </TABLE>An example lbl file (for the RC system is):
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%% Label file for system RC (RC_lbl.txt)
%SUMMARY RC
%DESCRIPTION &lt;Detailed description here&gt;
% Port aliases
%ALIAS  in      in
%ALIAS  out     out

% Argument aliases
%ALIAS  $1      c
%ALIAS  $2      r

%% Each line should be of one of the following forms:
%            a comment (ie starting with %)
%            component-name     cr_name arg1,arg2,..argn
%            blank

% ---- Component labels ----

% Component type C
        c               lin     effort,c

% Component type R
        r               lin     flow,r

% Component type SS
        [in]    SS              external,external
        [out]   SS              external,external

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The old-style lbl files (see section <A href="mtt.html#SEC98">6.6.11
  Old-style labels (lbl)</A>) are NO LONGER supported -- you are encouraged
  to convert them ASAP.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC84">6.6.1 SS
      component labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC85">6.6.2 Other
      component labels</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC86">6.6.3 Component
      names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC87">6.6.4 Component
      constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC88">6.6.5 Component
      arguments</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC89">6.6.6 Parameter
      declarations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC90">6.6.7 Units
      declarations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC91">6.6.8 Interface
      Control Definition</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC92">6.6.9
      Aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC97">6.6.10 Parameter
      passing</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style
      labels (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC102">6.6.12 Language
      tex (desc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="SS component labels"></A></P>
  <HR size="6">
  <A name="SEC84" id="SEC84"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC83">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC85">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC83">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.6.1 SS component labels</H3><!--docid::SEC84::-->
  In addition to the label there are two information fields, see section
  <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>. The first must be `SS', the
  second contains two information fields of the form
  info_field_1,info_field_2.
  <P>These two information fields correspond to the effort and flow variables
  of the of the SS components as follows</P>
  <DL compact>
    <DT><A name="IDX307" id="IDX307"></A> <CODE>info_field_1</CODE></DT>
    <DD><A name="IDX308" id="IDX308"></A> effort</DD>
    <DT><A name="IDX309" id="IDX309"></A> <CODE>info_field_2</CODE></DT>
    <DD><A name="IDX310" id="IDX310"></A> flow</DD>
  </DL>Each of these two fields contains one of the following
  <EM>attributes</EM>:
  <DL compact>
    <DT><A name="IDX311" id="IDX311"></A> <CODE>external</CODE></DT>
    <DD><A name="IDX312" id="IDX312"></A> indicates that the corresponding
    variable is a system input or output</DD>
    <DT><A name="IDX313" id="IDX313"></A> <CODE>internal</CODE></DT>
    <DD><A name="IDX314" id="IDX314"></A> indicates that the variable does
    not appear as a system output; it is an error to label an input in this
    way.</DD>
    <DT><A name="IDX315" id="IDX315"></A> <CODE>a number</CODE></DT>
    <DD><A name="IDX316" id="IDX316"></A> the value of the input; or the
    value of the (imposed) output</DD>
    <DT><A name="IDX317" id="IDX317"></A> <CODE>a symbol</CODE></DT>
    <DD><A name="IDX318" id="IDX318"></A> the symbolic value of the input; or
    the value of the (imposed) output</DD>
    <DT><A name="IDX319" id="IDX319"></A> <CODE>unknown</CODE></DT>
    <DD><A name="IDX320" id="IDX320"></A> used for the SS method of solving
    algebraic loops. This indicates that the corresponding system input (SS
    output) is to be chosen to set the corresponding system output (SS input)
    to zero.</DD>
    <DT><A name="IDX321" id="IDX321"></A> <CODE>zero</CODE></DT>
    <DD><A name="IDX322" id="IDX322"></A> used for the SS method of solving
    algebraic loops. This indicates that the corresponding system output (SS
    input) is to be set to zero using the variable indicted by the
    corresponding `unknown' label.</DD>
  </DL>
  <P>Some examples are:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%% ss1 is both a source and sensor
ss1     SS              external,external
%% ss1 acts as a flow sensor - it imposes zero effort.
ss2     SS              0,external
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Other component labels"></A></P>
  <HR size="6">
  <A name="SEC85" id="SEC85"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC84">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC86">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC83">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.6.2 Other component labels</H3><!--docid::SEC85::-->
  <P>In addition to the label there are two information fields, see section
  <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>. They correspond to the
  constitutive relationship (see see section <A href="mtt.html#SEC9">1.6.2
  Constitutive relationship</A> and arguments of the component as follows</P>
  <DL compact>
    <DT><A name="IDX323" id="IDX323"></A> <CODE>info_field_1</CODE></DT>
    <DD><A name="IDX324" id="IDX324"></A> constitutive relationship</DD>
    <DT><A name="IDX325" id="IDX325"></A> <CODE>info_field_2</CODE></DT>
    <DD><A name="IDX326" id="IDX326"></A> parameters</DD>
  </DL>
  <P>Some examples are:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%Armature resistance
r_a     lin     effort,r_a

%Gearbox ratio
n       lin     effort,n
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><STRONG>MTT</STRONG> supports parameter-passing to (see section <A href=
  "mtt.html#SEC97">6.6.10 Parameter passing</A>) subsystems.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC86">6.6.3 Component
      names</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC87">6.6.4 Component
      constitutive relationship</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC88">6.6.5 Component
      arguments</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC92">6.6.9
      Aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC97">6.6.10 Parameter
      passing</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style
      labels (lbl)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Component names"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>6.6.3 Component names</H3><!--docid::SEC86::-->
  The component name field must contain a valid name (see section <A href=
  "mtt.html#SEC72">6.4.1.16 Valid Names</A> corresponding to the name (the
  bit after the :) of each named component (see section <A href=
  "mtt.html#SEC60">6.4.1.4 Components</A>) on the bond graph (see section
  <A href="mtt.html#SEC55">6.4 Acausal bond graph (abg)</A>).
  <P><A name="Component constitutive relationship"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>6.6.4 Component constitutive relationship</H3><!--docid::SEC87::-->
  The constitutive relationship field contains the name of a constitutive
  relationship for the component. There are three sorts of constitutive
  relationship recognised by <STRONG>MTT</STRONG>:
  <OL>
    <LI>A generic constitutive relationship such as <VAR>lin</VAR> (the
    generic linear constitutive relationship.</LI>
    <LI>A local constitutive relationship with the same name as the component
    type</LI>
    <LI>The <VAR>SS</VAR> constitutive relationship reserved for
    <VAR>SS</VAR> components. All labels for <VAR>SS</VAR> components must
    contain SS in this field.</LI>
  </OL>
  <P><A name="Component arguments"></A></P>
  <HR size="6">
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  <H3>6.6.5 Component arguments</H3><!--docid::SEC88::-->
  <P><A name="Parameter declarations"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>6.6.6 Parameter declarations</H3><!--docid::SEC89::-->
  <P>It is sometimes useful to use parameters (in addition to those implied
  by the Component arguments see section <A href="mtt.html#SEC88">6.6.5
  Component arguments</A>) to compute values in, for example the numpar file.
  These can be declared in the label file; for examples , the two parameters
  par1 and par 2 can be declared as:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>#PAR par1
#PAR par2
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>On the other hand, some CR arguments (eg foo and bar) may not correspond
  to parameters. These can be excluded from the sympar list using the NOTPAR
  declaration</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>#NOTPAR foo
#NOTPAR bar
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>For comapability with old code, VAR may be used in place of PAR, but
  this usage is deprecated.</P>
  <P><A name="Units declarations"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>6.6.7 Units declarations</H3><!--docid::SEC90::-->
  The units and domains of ports (see section <A href="mtt.html#SEC8">1.6.1
  Ports</A>) are declared as:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>#UNITS Port_name domain effort_units flow_units
</PRE>
      </TD>
    </TR>
  </TABLE>where "Port_name" is the name of the port, domain is one of:
  <DL compact>
    <DT><A name="IDX327" id="IDX327"></A> <CODE>electrical</CODE></DT>
    <DD><A name="IDX328" id="IDX328"></A> the electrical domain</DD>
    <DT><A name="IDX329" id="IDX329"></A> <CODE>translational</CODE></DT>
    <DD><A name="IDX330" id="IDX330"></A> the translational mechanical
    domain</DD>
    <DT><A name="IDX331" id="IDX331"></A> <CODE>rotational</CODE></DT>
    <DD><A name="IDX332" id="IDX332"></A> the rotational mechanical
    domain</DD>
    <DT><A name="IDX333" id="IDX333"></A> <CODE>fluid</CODE></DT>
    <DD><A name="IDX334" id="IDX334"></A> the fluid domain</DD>
    <DT><A name="IDX335" id="IDX335"></A> <CODE>thermal</CODE></DT>
    <DD><A name="IDX336" id="IDX336"></A> the thermal domain</DD>
  </DL>and effort_units and flow_units are corresponding units for the effort
  and the flow.
  <P>Allowed units are those defined in the <STRONG>units</STRONG>
  package.</P>
  <P><STRONG>MTT</STRONG> checks that units are</P>
  <UL>
    <LI>defined consistently with the domain</LI>
    <LI>the same for connected ports when both ports have defined units.</LI>
  </UL>No checks are done if one or both ends of a bond are not connected to
  a port with defined units.
  <P><A name="Interface Control Definition"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>6.6.8 Interface Control Definition</H3><!--docid::SEC91::-->
  It is sometimes useful to be able to automatically generate a set of
  assignments mapping <STRONG>MTT</STRONG> inputs and outputs to an external
  interface definition. This can be achieved with use of the <EM>#ICD</EM>
  directive.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>#ICD    PressureSensor         PUMP1_PRESSURE_SENSOR,Pa;null,none
#ICD    Electrical              PUMP1_VOLTAGE,volt;PUMP1_CURRENT,amp

% Component type De
        PressureSensor  SS      external

% Component type SS
        Electrical      SS      external,external
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The ICD directive consists of 3 whitespace delimited fields:</P>
  <OL>
    <LI>[%|#]ICD</LI>
    <LI>component name</LI>
    <LI>Four comma (,) or semi-colon (;) delimited fields:
      <OL>
        <LI>name of effort parameter</LI>
        <LI>unit of effort parameter</LI>
        <LI>name of flow parameter</LI>
        <LI>unit of flow parameter</LI>
      </OL>
    </LI>
  </OL>
  <P>If no parameter name is required, a value of "null" should be used. If
  the parameter does not have any units, a value of "none" should be
  used.</P>
  <P>ICD parameters may be aliased see section <A href="mtt.html#SEC92">6.6.9
  Aliases</A> in the same way as normal parameters, thus it is possible to
  define some or all of the ICD in higher level components.</P>
  <P>The command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys ICD txt
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>will generate a text file containing a list of mappings:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>## Interface Control Definition for System sys
## sys_ICD.txt: Generated by MTT Thu Jul 12 21:21:21 CDT 2001

Input:  PUMP1_VOLTAGE           sys_P1_1_Electrical      Causality: Effort   Units: volt
Output: PUMP1_CURRENT           sys_P1_1_Electrical      Causality: Flow     Units: amp
Output: PUMP1_PRESSURE_SENSOR   sys_P1_1_PressureSensor  Causality: Effort   Units: Pa
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>A set of assignments can be generated with the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys ICD m
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>resulting in:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE># Interface Control Definition mappings for system sys
# sys_ICD.m: Generated by MTT Thu Jul 12 21:26:56 CDT 2001

# Inputs

        mttu(1) = PUMP1_VOLTAGE;

# Outputs

        PUMP1_CURRENT                  = mtty(1);
        PUMP1_PRESSURE_SENSOR          = mtty(2);
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>A similar file will be generated by the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys ICD cc
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Aliases" id="Aliases"></A></P>
  <HR size="6">
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  <H3>6.6.9 Aliases</H3><!--docid::SEC92::-->
  <P>Aliases provide a convenient mechanism for relabelling words appearing
  in the label file (see section <A href="mtt.html#SEC83">6.6 Labels
  (lbl)</A>). There are three contexts in which the alias mechanism is
  used:</P>
  <OL>
    <LI>renaming ports (see section <A href="mtt.html#SEC93">6.6.9.1 Port
    aliases</A>),</LI>
    <LI>renaming parameters (see section <A href="mtt.html#SEC94">6.6.9.2
    Parameter aliases</A>) and</LI>
    <LI>renaming components (see section <A href="mtt.html#SEC96">6.6.9.4
    Component aliases</A>).</LI>
  </OL>
  <P>All three mechanisms use the same form of statement within the label
  file</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS short_label       real_label
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><STRONG>MTT</STRONG> distinguishes between the three forms as
  follows:</P>
  <UL>
    <LI>Parameter aliases: `short_label' starts with a `$'</LI>
    <LI>Component aliases: `real_label' contains the directory separator
    `/'</LI>
    <LI>Port aliases: neither of the above</LI>
  </UL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC93">6.6.9.1 Port
      aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC94">6.6.9.2
      Parameter aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC95">6.6.9.3 CR
      aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC96">6.6.9.4
      Component aliases</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Port aliases"></A></P>
  <HR size="6">
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    </TR>
  </TABLE>
  <H4>6.6.9.1 Port aliases</H4><!--docid::SEC93::-->
  Aliases provide a way of refering to (see section <A href=
  "mtt.html#SEC67">6.4.1.11 Port labels</A>) or vector port labels (see
  section <A href="mtt.html#SEC68">6.4.1.12 Vector port labels</A>) on the
  bond graph using a short-hand notation. With in a component label file (see
  section <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>) statements of the
  following forms can occur
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS short_label       real_label
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>When the component is used within another component, the short_lable may
  be used in place of the real_label. More than one alias per label can be
  used, for example</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS short_label_1       real_label
%ALIAS short_label_2       real_label
%ALIAS short_label_3       real_label
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The port can then be refered to in four ways: as real_label,
  short_label_1, short_label_2 or short_label_3. An alternative notation for
  the ALIAS statement in this case is</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS short_label_1|short_label_2|short_label_3       real_label
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The alias feature is particularly powerful in conjunction with vector
  port labels (see section <A href="mtt.html#SEC68">6.4.1.12 Vector port
  labels</A>) and the port label default (see section <A href=
  "mtt.html#SEC69">6.4.1.13 Port label defaults</A>) mechanisms. For example,
  a component with 5 ports appearing in the lbl file as:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>        [Hydraulic_in]  external        external
        [Hydraulic_out] external        external
        [Power_Shaft]           external        external
        [Thermal_in]    external        external
        [Thermal_out]   external        external
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>together with the following statements in the label file:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS  in              Thermal_in,Hyydraulic_in
%ALIAS  out             Thermal_out,Hydraulic_out
%ALIAS  shaft|power     Power_Shaft
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>can appear in the bond graph containing that component with one bond
  labeled either [shaft] or [power] or [Power_Shaft], one unlabeled vector
  bond pointing in and one unlabeled vector bond pointing out.</P>
  <P><A name="Parameter aliases"></A></P>
  <HR size="6">
  <A name="SEC94" id="SEC94"></A>
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  </TABLE>
  <H4>6.6.9.2 Parameter aliases</H4><!--docid::SEC94::-->
  <P>Parameter aliases are of the form</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS $n       actual parameter
</PRE>
      </TD>
    </TR>
  </TABLE>where n is an integer (unique within the label file). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS  $1              c_v
%ALIAS  $2              density,ideal_gas,r
%ALIAS  $3              alpha
%ALIAS  $4              flow,k_p
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Assigns four symbolic parameters to the corresponding strings These four
  parameters (<CODE>$1</CODE>--<CODE>$4</CODE>) can then be used for
  parameter passing(see section <A href="mtt.html#SEC97">6.6.10 Parameter
  passing</A>).</P>
  <P><A name="CR aliases"></A></P>
  <HR size="6">
  <A name="SEC95" id="SEC95"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      <TD valign="middle" align="left"></TD>
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    </TR>
  </TABLE>
  <H4>6.6.9.3 CR aliases</H4><!--docid::SEC95::-->
  <P>CR aliases are of the form</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS $an       actual parameter
</PRE>
      </TD>
    </TR>
  </TABLE>where n is an integer (unique within the label file). For example
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS  $a1  lin           
</PRE>
      </TD>
    </TR>
  </TABLE>assigns the symbolic parameter to be lin. This parameter
  <CODE>$1</CODE> can then be used for passing a diofferent cr to the
  component (see section <A href="mtt.html#SEC97">6.6.10 Parameter
  passing</A>).
  <P><A name="Component aliases"></A></P>
  <HR size="6">
  <A name="SEC96" id="SEC96"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.6.9.4 Component aliases</H4><!--docid::SEC96::-->
  <P>Component aliases are of the form</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%ALIAS Component_name   Component_location       
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>An example appears in the following label file fragment</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>...
%ALIAS  wPipe   CompressibleFlow/wPipe
%ALIAS  Poly    CompressibleFlow/Poly
....

</PRE>
      </TD>
    </TR>
  </TABLE>The two components `wPipe' and `Poly' are both to be found within
  the library `Compressible flow' and the respective subdirectories. This
  follows the <STRONG>MTT</STRONG> convention that compound components (see
  section <A href="mtt.html#SEC64">6.4.1.8 Compound components</A>) live
  within a directory of the same name.
  <P><A name="Parameter passing"></A></P>
  <HR size="6">
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      <TD valign="middle" align="left"></TD>
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    </TR>
  </TABLE>
  <H3>6.6.10 Parameter passing</H3><!--docid::SEC97::-->
  <STRONG>MTT</STRONG> supports parameter-passing to subsystems within label
  files (see section <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>). Within a
  subsystem, explicit constitutive relationships and parameters (or groups
  thereof) can be replaced by postitional parameters such as <CODE>$1</CODE>,
  <CODE>$2</CODE> etc. Although this can be done directly, it is recommended
  that this is done via the alias mechanism (see section <A href=
  "mtt.html#SEC94">6.6.9.2 Parameter aliases</A>).
  <P>In a subsystem <CODE>$i</CODE>, is replaced by the ith field of a colon
  <CODE>;</CODE> separated field in the calling label file. This field may
  include commas <CODE>,</CODE> and the four arithmetic operators
  <CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE> and <CODE>/</CODE>.</P>
  <P>For example, consider the following example label file fragment
  (associated with a component called Pump:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>...

%ALIAS  $1              c_v
%ALIAS  $2              density,ideal_gas,r
%ALIAS  $3              alpha
%ALIAS  $4              flow,k_p

%ALIAS  wPipe   CompressibleFlow/wPipe
%ALIAS  Poly    CompressibleFlow/Poly

% Component type wPipe
        pipe    none                    c_v;density,ideal_gas,r

% Component type Poly
        poly            Poly            alpha

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The 4 parameters <CODE>$1</CODE>, <CODE>$2</CODE>, <CODE>$3</CODE>, and
  <CODE>$4</CODE> can be passed from a higher level component as in the
  following label file fragment:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>% Component type Pump
        comp            none            c_v;rho,ideal_gas,r;alpha;effort,k_c
        turb            none            c_v;rho,ideal_gas,r;alpha;effort,k_t
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Thus in component `comp':</P>
  <UL>
    <LI><CODE>$1</CODE> is replaced by c_v</LI>
    <LI><CODE>$2</CODE> is replaced by rho,ideal_gas</LI>
    <LI><CODE>$3</CODE> is replaced by alpha</LI>
    <LI><CODE>$4</CODE> is replaced by effort,k_c</LI>
  </UL>whereas in component `turb' the first three parameters are the same
  but
  <UL>
    <LI><CODE>$4</CODE> is replaced by effort,k_t</LI>
  </UL>
  <P><A name="Old-style labels (lbl)"></A></P>
  <HR size="6">
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  <TABLE cellpadding="1" cellspacing="1" border="0">
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.6.11 Old-style labels (lbl)</H3><!--docid::SEC98::-->
  <P>Old syle labels (mtt version 2.x) are supported by mtt version 3.x.
  However, you are advised to use the new form (see section <A href=
  "mtt.html#SEC83">6.6 Labels (lbl)</A>).</P>
  <P>Each line of the <CODE>_label.txt</CODE> file is of one of three
  forms:</P>
  <OL>
    <LI>Contains three fields (separated by white space) of the form
      <TABLE>
        <TR>
          <TD></TD>
          <TD class="example">
            <PRE>label   field_1   field_2
</PRE>
          </TD>
        </TR>
      </TABLE>
    </LI>
    <LI>Blank</LI>
    <LI>Preceded by %</LI>
  </OL>Only the first is noticed by <STRONG>MTT</STRONG>; the second and
  third are for providing helpful commenting.
  <P>The role of the two information fields depends on the component with the
  corresponding label. In particular the classes of components are:</P>
  <UL>
    <LI>SS components, see section <A href="mtt.html#SEC62">6.4.1.6 SS
    components</A>.</LI>
    <LI>Other components, see section <A href="mtt.html#SEC60">6.4.1.4
    Components</A>.</LI>
  </UL>Named SS component, see section <A href="mtt.html#SEC65">6.4.1.9 Named
  SS components</A> never have labels.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC99">6.6.11.1 SS
      component labels (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC100">6.6.11.2 Other
      component labels (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC101">6.6.11.3
      Parameter passing (old-style)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="SS component labels (old-style)"></A></P>
  <HR size="6">
  <A name="SEC99" id="SEC99"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      "mtt.html#SEC_Top">Top</A>]</TD>
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    </TR>
  </TABLE>
  <H4>6.6.11.1 SS component labels (old-style)</H4><!--docid::SEC99::-->
  In addition to the label there are two information fields, see section
  <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>. They correspond to the
  effort and flow of the components as follows
  <DL compact>
    <DT><A name="IDX337" id="IDX337"></A> <CODE>info_field_1</CODE></DT>
    <DD><A name="IDX338" id="IDX338"></A> effort</DD>
    <DT><A name="IDX339" id="IDX339"></A> <CODE>info_field_2</CODE></DT>
    <DD><A name="IDX340" id="IDX340"></A> flow</DD>
  </DL>Each of these two fields contains one of the following
  <EM>attributes</EM>:
  <DL compact>
    <DT><A name="IDX341" id="IDX341"></A></DT>
    <DD><A name="IDX342" id="IDX342"></A> external indicates that the
    corresponding variable is a system input or output</DD>
    <DT><A name="IDX343" id="IDX343"></A> <CODE>internal</CODE></DT>
    <DD><A name="IDX344" id="IDX344"></A> indicates that the variable does
    not appear as a system output; it is an error to label an input in this
    way.</DD>
    <DT><A name="IDX345" id="IDX345"></A> <CODE>a number</CODE></DT>
    <DD><A name="IDX346" id="IDX346"></A> the value of the input; or the
    value of the (imposed) output</DD>
    <DT><A name="IDX347" id="IDX347"></A> <CODE>a symbol</CODE></DT>
    <DD><A name="IDX348" id="IDX348"></A> the symbolic value of the input; or
    the value of the (imposed) output</DD>
    <DT><A name="IDX349" id="IDX349"></A> <CODE>unknown</CODE></DT>
    <DD><A name="IDX350" id="IDX350"></A> used for the SS method of solving
    algebraic loops. This indicates that the corresponding system input (SS
    output) is to be chosen to set the corresponding system output (SS input)
    to zero.</DD>
    <DT><A name="IDX351" id="IDX351"></A> <CODE>zero</CODE></DT>
    <DD><A name="IDX352" id="IDX352"></A> used for the SS method of solving
    algebraic loops. This indicates that the corresponding system output (SS
    input) is to be set to zero using the variable indicted by the
    corresponding `unknown' label.</DD>
  </DL>
  <P>Some examples are:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%Label  field1          field2
ss1     external        external
ss2     0               external
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Other component labels (old-style)"></A></P>
  <HR size="6">
  <A name="SEC100" id="SEC100"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC99">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC101">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC98">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.6.11.2 Other component labels (old-style)</H4><!--docid::SEC100::-->
  <P>In addition to the label there are two information fields, see section
  <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>. They correspond to the
  constitutive relationship (see see section <A href="mtt.html#SEC9">1.6.2
  Constitutive relationship</A> and arguments of the component as follows</P>
  <DL compact>
    <DT><A name="IDX353" id="IDX353"></A> <CODE>info_field_1</CODE></DT>
    <DD><A name="IDX354" id="IDX354"></A> constitutive relationship</DD>
    <DT><A name="IDX355" id="IDX355"></A> <CODE>info_field_2</CODE></DT>
    <DD><A name="IDX356" id="IDX356"></A> parameters</DD>
  </DL>
  <P>Some examples are:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%Armature resistance
r_a     lin     effort,r_a

%Gearbox ratio
n       lin     effort,n
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><STRONG>MTT</STRONG> supports parameter-passing to (see section <A href=
  "mtt.html#SEC101">6.6.11.3 Parameter passing (old-style)</A>)
  subsystems.</P>
  <P><A name="Parameter passing (old-style)"></A></P>
  <HR size="6">
  <A name="SEC101" id="SEC101"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC100">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC102">&gt;</A>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.6.11.3 Parameter passing (old-style)</H4><!--docid::SEC101::-->
  <STRONG>MTT</STRONG> supports parameter-passing to (see section <A href=
  "mtt.html#SEC101">6.6.11.3 Parameter passing (old-style)</A>) subsystems
  within label files (see section <A href="mtt.html#SEC83">6.6 Labels
  (lbl)</A>). Within a subsystem, explicit constitutive relationships and
  parameters (or groups thereof) can be replaced by <CODE>$1</CODE>,
  <CODE>$2</CODE>, etc.
  <P>In a subsystem <CODE>$i</CODE>, is replaced by the ith field of a colon
  <CODE>;</CODE> separated field in the calling label file. This field may
  include commas <CODE>,</CODE>.</P>
  <P>For example subsystem ROD contains the following lines in the label
  file:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>
%DESCRIPTION    Parameter 1:    length from end 1 to mass centre
%DESCRIPTION    Parameter 2:    length from end 2 to mass centre
%DESCRIPTION    Parameter 3:    inertia about mass centre
%DESCRIPTION    Parameter 4:    mass
%DESCRIPTION    See Section 10.2 of "Metamodelling"


%Inertias
J       lin     flow,$3
m_x     lin     flow,$4
m_y     lin     flow,$4

%Integrate angular velocity to get angle
th

%Modulated transformers
s1      lsin    flow,$1
s2      lsin    flow,$2
c1      lcos    flow,$1
c2      lcos    flow,$2

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>This can be used in a higher-level lbl (see section <A href=
  "mtt.html#SEC83">6.6 Labels (lbl)</A>) file as:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%SUMMARY Pendulum example from Section 10.3 of "Metamodelling"

%Rod parameters
rod     none    l;l;j;m

</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC102">6.6.12 Language
      tex (desc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Language tex (desc.tex)"></A></P>
  <HR size="6">
  <A name="SEC102" id="SEC102"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC101">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC103">&gt;</A>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC83">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.6.12 Language tex (desc.tex)</H3><!--docid::SEC102::-->
  This file may contain any LaTeX compatible commands. Any mathematics should
  conform to the AMSmath package.
  <P><A name="Structure (struc)"></A></P>
  <HR size="6">
  <A name="SEC103" id="SEC103"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC102">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC104">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.7 Structure (struc)</H2><!--docid::SEC103::-->
  <P>The causal bond graph implies a set of equations describing the system.
  The Structure (struc) representation describes the structure of these
  equations in terms of the input, outputs, states and non-states of the
  system.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC104">6.7.1 Language
      txt (struc.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC105">6.7.2 Language
      tex (struc.tex)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC106">6.7.3 Language
      tex (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Language txt (struc.txt)"></A></P>
  <HR size="6">
  <A name="SEC104" id="SEC104"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC103">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC105">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC103">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.7.1 Language txt (struc.txt)</H3><!--docid::SEC104::-->
  This text tile contains a description of the system structure (see section
  <A href="mtt.html#SEC103">6.7 Structure (struc)</A> with 5 tab-separated
  columns containing the following information:
  <DL compact>
    <DT><A name="IDX357" id="IDX357"></A> <CODE>type</CODE></DT>
    <DD><A name="IDX358" id="IDX358"></A> input, output state or
    nonstate</DD>
    <DT><A name="IDX359" id="IDX359"></A></DT>
    <DD><A name="IDX360" id="IDX360"></A> index an integer corresponding to
    the array index</DD>
    <DT><A name="IDX361" id="IDX361"></A></DT>
    <DD><A name="IDX362" id="IDX362"></A> component name the name of the
    component corresponding to the variable</DD>
    <DT><A name="IDX363" id="IDX363"></A> <CODE>system name</CODE></DT>
    <DD><A name="IDX364" id="IDX364"></A> the name of the system containing
    the component</DD>
    <DT><A name="IDX365" id="IDX365"></A> <CODE>repetition</CODE></DT>
    <DD><A name="IDX366" id="IDX366"></A> an integer corresponding to the
    repetition of a repeated subsystem.</DD>
  </DL>
  <P>An example of such a file (corresponding to rc) (see section <A href=
  "mtt.html#SEC29">3.1 Quick start</A>) is:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>input           1       e1      rc      1
output          1       e2      rc      1
state           1       c       rc      1
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Language tex (struc.tex)"></A></P>
  <HR size="6">
  <A name="SEC105" id="SEC105"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC104">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC106">&gt;</A>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.7.2 Language tex (struc.tex)</H3><!--docid::SEC105::-->
  This LaTeX (see section <A href="mtt.html#SEC173">10.5 LaTeX</A>) file
  contains a description of the system structure (see section <A href=
  "mtt.html#SEC103">6.7 Structure (struc)</A> in <CODE>longtable</CODE>
  format. It is a useful item to include in a report(see section <A href=
  "mtt.html#SEC144">6.16 Report (rep)</A>).
  <P><A name="Structure (view)"></A></P>
  <HR size="6">
  <A name="SEC106" id="SEC106"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC105">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC107">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC103">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.7.3 Language tex (view)</H3><!--docid::SEC106::-->
  This representation has the standard text view (see section <A href=
  "mtt.html#SEC165">10.1 Views</A>).
  <P><A name="Constitutive Relationship (cr)"></A></P>
  <HR size="6">
  <A name="SEC107" id="SEC107"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC106">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC108">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.8 Constitutive relationship (cr)</H2><!--docid::SEC107::-->
  <P>The constitutive relationship (see section <A href="mtt.html#SEC9">1.6.2
  Constitutive relationship</A>) of a simple component (see section <A href=
  "mtt.html#SEC61">6.4.1.5 Simple components</A> is defined in the symbolic
  algebra language Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>). The constitutive relationship of a compound components (see
  section <A href="mtt.html#SEC64">6.4.1.8 Compound components</A>) is
  implied by the constitutive relationships of its constituent
  components.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC108">6.8.1
      Predefined constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC111">6.8.2 DIY
      constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC112">6.8.3
      Unresolved constitutive relationships</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC113">6.8.4
      Unresolved constitutive relationships - Octave</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC114">6.8.5
      Unresolved constitutive relationships - c++</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Predefined constitutive relationships"></A></P>
  <HR size="6">
  <A name="SEC108" id="SEC108"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC109">&gt;</A>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H3>6.8.1 Predefined constitutive relationships</H3><!--docid::SEC108::-->
  <P>Some common cr's are predefined by MTT; these are:</P>
  <DL compact>
    <DT><A name="IDX367" id="IDX367"></A> <CODE>lin</CODE></DT>
    <DD><A name="IDX368" id="IDX368"></A> a linear constitutive
    relationship</DD>
    <DT><A name="IDX369" id="IDX369"></A> <CODE>exotherm</CODE></DT>
    <DD><A name="IDX370" id="IDX370"></A> an exothermic reaction</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC109">6.8.1.1
      lin</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC110">6.8.1.2
      exotherm</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="lin" id="lin"></A></P>
  <HR size="6">
  <A name="SEC109" id="SEC109"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC108">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC110">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC108">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H4>6.8.1.1 lin</H4><!--docid::SEC109::-->
  The constitutive relationship <CODE>lin</CODE> is predefined for the
  following components.
  <DL compact>
    <DT><A name="IDX371" id="IDX371"></A> <CODE>R</CODE></DT>
    <DD><A name="IDX372" id="IDX372"></A> (one-port) R component</DD>
    <DT><A name="IDX373" id="IDX373"></A> <CODE>TF</CODE></DT>
    <DD><A name="IDX374" id="IDX374"></A> transformer</DD>
    <DT><A name="IDX375" id="IDX375"></A> <CODE>GY</CODE></DT>
    <DD><A name="IDX376" id="IDX376"></A> gyrator</DD>
    <DT><A name="IDX377" id="IDX377"></A> <CODE>MTF</CODE></DT>
    <DD><A name="IDX378" id="IDX378"></A> modulated transformer</DD>
    <DT><A name="IDX379" id="IDX379"></A> <CODE>MGY</CODE></DT>
    <DD><A name="IDX380" id="IDX380"></A> modulated gyrator</DD>
    <DT><A name="IDX381" id="IDX381"></A> <CODE>FMR</CODE></DT>
    <DD><A name="IDX382" id="IDX382"></A> flow-modulated resistor</DD>
  </DL>Lin takes two arguments in the form causality,gain
  <DL compact>
    <DT><A name="IDX383" id="IDX383"></A> <CODE>causality</CODE></DT>
    <DD><A name="IDX384" id="IDX384"></A> the causality (effort or flow) of
    the <EM>input</EM> to the constitutive relationship</DD>
    <DT><A name="IDX385" id="IDX385"></A> <CODE>gain</CODE></DT>
    <DD><A name="IDX386" id="IDX386"></A> the gain of the component when the
    input causality is as specified in the first argument.</DD>
  </DL>For example the arguments
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>flow,r
</PRE>
      </TD>
    </TR>
  </TABLE>given to an R component corresponds to
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>e = rf
</PRE>
      </TD>
    </TR>
  </TABLE>if if the input causality is flow or
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>f = e/r
</PRE>
      </TD>
    </TR>
  </TABLE>if if the input causality is effort.
  <P><A name="exotherm" id="exotherm"></A></P>
  <HR size="6">
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  <H4>6.8.1.2 exotherm</H4><!--docid::SEC110::-->
  <P><A name="DIY constitutive relationships"></A></P>
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  <H3>6.8.2 DIY constitutive relationships</H3><!--docid::SEC111::-->
  You can write your own constitutive relationships using Reduce (see section
  <A href="mtt.html#SEC162">9.3 Reduce</A>). This requires some understanding
  as to how <STRONG>MTT</STRONG> represent the elementary system equations
  (see section <A href="mtt.html#SEC124">6.11 Elementary system equations
  (ese)</A>). Looking at the predefined constitutive relationships is a good
  way to get started (see section <A href="mtt.html#SEC186">11.5 File
  structure</A>).
  <P><A name="Unresolved constitutive relationships"></A></P>
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  <H3>6.8.3 Unresolved constitutive relationships</H3><!--docid::SEC112::-->
  <P>Consider the following CR file.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>FOR ALL rho,g,vol,h,topt,bott,flowin,press
LET tktf2(rho,g,vol,h,topt,bott,effort,2,press,effort,1)
        = tank(rho,g,vol,h,topt,bott,press);      
</PRE>
      </TD>
    </TR>
  </TABLE>Assuming that `tank' is not defined in a reduce file, MTT will
  leave it unresolved when generating m or c code.
  <P>The resulting function can then be expressed as octave (see section
  <A href="mtt.html#SEC113">6.8.4 Unresolved constitutive relationships -
  Octave</A>) or c++ code as (see section <A href="mtt.html#SEC114">6.8.5
  Unresolved constitutive relationships - c++</A>) appropriate.</P>
  <P><A name="Unresolved constitutive relationships - Octave"></A></P>
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  <H3>6.8.4 Unresolved constitutive relationships - Octave</H3>
  <!--docid::SEC113::-->
  Following the example of the previous section, the unresolved CR `tank' can
  be expressed as an Octave m-file. For example:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function p = tank (rho,g,vol,h,topt,bott,press)

  ## usage:  p = tank (vol,h,topt,bott,press)
  ##
  ## 

   val = press; zt = topt; zb = bott; 
   zval = 0.5*(abs(zb+(zt-zb)*val-h)+(zb+(zt-zb)*val-h));

   p = rho*g*zval + 0.5*(1+tanh((press-0.98)*500))*100000;

endfunction
</PRE>
      </TD>
    </TR>
  </TABLE>This will be automatically loaded into octave.
  <P><A name="Unresolved constitutive relationships - c++"></A></P>
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  <H3>6.8.5 Unresolved constitutive relationships - c++</H3>
  <!--docid::SEC114::-->
  Following the example of the previous section, the unresolved CR `tank' can
  be expressed in c++ code. For example:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>inline double tank(const double rho, 
                   const double g, 
                   const double vol, 
                   const double h, 
                   const double topt, 
                   const double bott, 
                   const double press)


  /*  ## usage:  p = tank (vol,h,topt,bott,press)
    ##
    ##
  */
  double p, val, zval, zt, zb;

  val = press;
  zt = topt;
  zb = bott;
  zval = 0.5 * (abs(zb + (zt - zb) * val - h) + zb + (zt - zb) * val - h);

  p = rho * g * zval + 0.5 * (1 + tanh((press - 0.98) * 500)) * 100000L;

  return p;

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>To make sure that this is used in system `model', the model_cr.h file
  must be as follows:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>// CR headers for system model
#include "tank.c"
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Parameters" id="Parameters"></A></P>
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  <H2>6.9 Parameters</H2><!--docid::SEC115::-->
  <P>In general, lbl (see section <A href="mtt.html#SEC83">6.6 Labels
  (lbl)</A>) files contain symbolic parameters. <STRONG>MTT</STRONG> provides
  three ways of substituting for these parameters:</P>
  <UL>
    <LI>symbolic substitution</LI>
    <LI>symbolic substitution for simplification of displayed equations</LI>
    <LI>numeric</LI>
  </UL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC116">6.9.1 Symbolic
      parameters (subs.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC117">6.9.2 Symbolic
      parameters for simplification (simp.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric
      parameters (numpar)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Symbolic parameters (subs.r)"></A></P>
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  <H3>6.9.1 Symbolic parameters (subs.r)</H3><!--docid::SEC116::-->
  This file contains reduce statements to symbolically change the expressions
  describing the system. For example, a useful set of trig substitutions is:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>LET cos(~x)*cos(~y) = (cos(x+y)+cos(x-y))/2;
LET cos(~x)*sin(~y) = (sin(x+y)-sin(x-y))/2;
LET sin(~x)*sin(~y) = (cos(x-y)-cos(x+y))/2;
LET cos(~x)^2       = (1+cos(2*x))/2;
LET sin(~x)^2       = (1-cos(2*x));
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Symbolic parameters for simplification (simp.r)"></A></P>
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  <H3>6.9.2 Symbolic parameters for simplification (simp.r)</H3>
  <!--docid::SEC117::-->
  This file contains reduce statements to symbolically change the expressions
  describing the system. Unlike the subs.r file (see section <A href=
  "mtt.html#SEC116">6.9.1 Symbolic parameters (subs.r)</A>) it does not
  affect all system transformations; only those converting to LaTeX form.
  <P><A name="Numeric parameters (numpar)"></A></P>
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  <H3>6.9.3 Numeric parameters (numpar)</H3><!--docid::SEC118::-->
  <P>When computing time and frequency responses; or when evaluating
  functions in Octave (see section <A href="mtt.html#SEC168">10.4
  Octave</A>); symbolic parameters need numerical instantiations.</P>
  <P>The numpar representation provides the relevant <EM>numerical</EM>
  information. It comes in a number of languages:</P>
  <DL compact>
    <DT><A name="IDX387" id="IDX387"></A> <CODE>txt</CODE></DT>
    <DD><A name="IDX388" id="IDX388"></A> a textual description of the
    parameter values -- this is the defining representation (see section
    <A href="mtt.html#SEC53">6.2 Defining representations</A>).</DD>
    <DT><A name="IDX389" id="IDX389"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX390" id="IDX390"></A> readable by <CODE>octave</CODE> a
    high-level interactive language for numerical computation -- translated
    by <STRONG>mtt</STRONG> from the txt version.</DD>
    <DT><A name="IDX391" id="IDX391"></A> <CODE>c</CODE></DT>
    <DD><A name="IDX392" id="IDX392"></A> readable by <CODE>gcc</CODE> a c
    compiler -- translated by <STRONG>mtt</STRONG> from the txt version.</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text
      form (numpar.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Text form (numpar.txt)"></A></P>
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  <H4>6.9.3.1 Text form (numpar.txt)</H4><!--docid::SEC119::-->
  This is the textual form of the numerical parameters representation (see
  section <A href="mtt.html#SEC118">6.9.3 Numeric parameters (numpar)</A>).
  Lines are either
  <DL compact>
    <DT><A name="IDX393" id="IDX393"></A> <CODE>assignment
    statements</CODE></DT>
    <DD><A name="IDX394" id="IDX394"></A> variable = value</DD>
    <DT><A name="IDX395" id="IDX395"></A> <CODE>comments</CODE></DT>
    <DD><A name="IDX396" id="IDX396"></A> lines beginning with #</DD>
    <DT><A name="IDX397" id="IDX397"></A> <CODE>commented assignment
    statements</CODE></DT>
    <DD><A name="IDX398" id="IDX398"></A> variable = value # comments</DD>
  </DL>An example file is:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE># Numerical parameter file (rc_numpar.txt)
# Generated by MTT at Mon Jun 16 15:10:17 BST 1997

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id: mtt.texi,v 1.18 2003/09/07 20:41:19 geraint Exp $
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# %% *** empty log message ***
# %%
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# %% Added legal appendices
# %%
# %% Revision 1.14  2003/08/06 14:50:56  gawthrop
# %% Describe the alias mechanism for invoking mtt options
# %%
# %% Revision 1.13  2002/12/13 10:07:07  gawthrop
# %% Added example in sh section of DIY reps
# %%
# %% Revision 1.12  2002/09/19 08:09:31  gawthrop
# %% Updated documentation documentation
# %%
# %% Revision 1.11  2002/08/20 15:51:17  gawthrop
# %% Update to work with ident DIY rep
# %%
# %% Revision 1.10  2002/07/22 10:45:22  geraint
# %% Fixed gnuplot rep so that it correctly re-runs the simulation if input files have changed.
# %%
# %% Revision 1.9  2002/07/05 13:29:34  geraint
# %% Added notes about generating dynamically linked functions for Octave and Matlab.
# %%
# %% Revision 1.8  2002/07/04 21:34:12  geraint
# %% Updated gnuplot view description to describe Tcl/Tk interface instead of obsolete txt method.
# %%
# %% Revision 1.7  2002/04/23 09:51:54  gawthrop
# %% Changed incorrect statement about searching for components.
# %%
# %% Revision 1.6  2001/10/15 14:29:50  gawthrop
# %% Added documentaton on  [1:N] style port labels
# %%
# %% Revision 1.5  2001/07/23 03:35:29  geraint
# %% Updated file structure (mtt/bin).
# %%
# %% Revision 1.4  2001/07/23 03:25:02  geraint
# %% Added notes on -ae hybrd, rk4, ode2odes.cc, .oct dependencies.
# %%
# %% Revision 1.3  2001/07/13 03:02:38  geraint
# %% Added notes on #ICD, gnuplot.txt and odes.sg rep.
# %%
# %% Revision 1.2  2001/07/03 22:59:10  gawthrop
# %% Fixed problems with argument passing for CRs
# %%
# %% Revision 1.1  2001/06/04 08:18:52  gawthrop
# %% Putting documentation under CVS
# %%
# %% Revision 1.66  2000/12/05 14:20:55  peterg
# %% Added the c++  anf m CR info.
# %%
# %% Revision 1.65  2000/11/27 15:36:15  peterg
# %% NOPAR --&gt; NOTPAR
# %%
# %% Revision 1.64  2000/11/16 14:22:48  peterg
# %% added UNITS declaration
# %%
# %% Revision 1.63  2000/11/03 14:41:08  peterg
# %% Added PAR and NOTPAR stuff
# %%
# %% Revision 1.62  2000/10/17 17:53:34  peterg
# %% Added some simulation details
# %%
# %% Revision 1.61  2000/09/14 17:13:06  peterg
# %% New options table
# %%
# %% Revision 1.60  2000/09/14 17:09:20  peterg
# %% Tidied up valid name sections
# %% Tidied up defining represnetations table
# %% Verion 4.6
# %%
# %% Revision 1.59  2000/08/30 13:09:00  peterg
# %% Updated option table
# %%
# %% Revision 1.58  2000/08/01 13:30:19  peterg
# %% Version 4.4
# %% updated STEPFACTOR info
# %% describes octave and OCST interfaces
# %%
# %% Revision 1.57  2000/07/20 07:55:44  peterg
# %% Version 4.3
# %%
# %% Revision 1.56  2000/05/19 17:49:17  peterg
# %% Extended the user defined representation section -- new nppp rep.
# %%
# %% Revision 1.55  2000/03/16 13:53:31  peterg
# %% Correct date
# %%
# %% Revision 1.54  2000/03/15 21:22:57  peterg
# %% Updated to 4.1 -- old style SS no longer supported
# %%
# %% Revision 1.53  1999/12/22 05:33:10  peterg
# %% Updated for 4.0
# %%
# %% Revision 1.52  1999/11/23 00:25:11  peterg
# %% Added the sensitivity reps
# %%
# %% Revision 1.51  1999/11/16 04:43:47  peterg
# %% Added start of sensitivity section
# %%
# %% Revision 1.50  1999/11/16 00:30:35  peterg
# %% Updated simulation section
# %% Added vector components
# %%
# %% Revision 1.49  1999/07/20 23:44:58  peterg
# %% V 3.8
# %%
# %% Revision 1.48  1999/07/19 03:08:33  peterg
# %% Added documentation for (new) SS lbl fields
# %%
# %% Revision 1.47  1999/03/09 01:42:22  peterg
# %% Rearranged the User interface section
# %%
# %% Revision 1.46  1999/03/09 01:18:01  peterg
# %% Updated for 3.5 including xmtt
# %%
# %% Revision 1.45  1999/03/03 02:39:26  peterg
# %% Minor updates
# %%
# %% Revision 1.44  1999/02/17 06:52:14  peterg
# %% New level formula dor artwork
# %%
# %% Revision 1.43  1998/11/25 16:49:24  peterg
# %% Put in subs.r documentation (was called params.r)
# %%
# %% Revision 1.42  1998/11/24 12:24:59  peterg
# %% Added section on simulation output
# %% Version 3.4
# %%
# %% Revision 1.41  1998/09/02 12:04:15  peterg
# %% Version 3.2
# %%
# %% Revision 1.40  1998/08/27 08:36:39  peterg
# %% Removed in. methods except Euler anf implicit
# %%
# %% Revision 1.39  1998/08/18 10:44:28  peterg
# %% Typo
# %%
# %% Revision 1.38  1998/08/18 09:16:38  peterg
# %% Version 3.1
# %%
# %% Revision 1.37  1998/08/17 16:14:30  peterg
# %% Version 3.1 - includes documentation on METHOD=IMPLICIT
# %%
# %% Revision 1.36  1998/07/30 17:33:15  peterg
# %% VERSION 3.0
# %%
# %% Revision 1.35  1998/07/22 11:00:53  peterg
# %% Correct date!
# %%
# %% Revision 1.34  1998/07/22 11:00:13  peterg
# %% Version to BAe
# %%
# %% Revision 1.33  1998/07/17 19:32:19  peterg
# %% Added more about aliases
# %%
# %% Revision 1.32  1998/07/05 14:21:56  peterg
# %% Further additions (Carlisle-Glasgow)
# %%
# %% Revision 1.31  1998/07/04 11:35:57  peterg
# %% Strarted new lbl description
# %%
# %% Revision 1.30  1998/07/02 18:39:20  peterg
# %% Started 3.0
# %% Added alias and default sections.
# %%
# %% Revision 1.29  1998/05/19 19:46:58  peterg
# %% Added the odess description
# %%
# %% Revision 1.28  1998/05/14 09:17:22  peterg
# %% Added METHOD variable to the simpar file
# %%
# %% Revision 1.27  1998/05/13 10:03:09  peterg
# %% Added unknown/zero SS label documentation.
# %%
# %% Revision 1.26  1998/04/29 15:12:46  peterg
# %% Version 2.9.
# %%
# %% Revision 1.25  1998/04/12 17:00:26  peterg
# %% Added new port features: coerced direction and top-level behaviour.
# %%
# %% Revision 1.24  1998/04/05 18:27:20  peterg
# %% This was the 2.6 version
# %%
# Revision 1.23  1997/08/24  11:17:51  peterg
# This is the released  version 2.5
#
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

# Parameters
c =     1.0; # Default value
r =     1.0; # Default value
# Initial states
x(1) =  0.0; # Initial state for rc (c)
</PRE>
      </TD>
    </TR>
  </TABLE>As usual, <STRONG>MTT</STRONG> provides a default text file to be
  edited by the user (see section <A href="mtt.html#SEC167">10.3 Text
  editors</A>).
  <P><A name="Causal bond graph (cbg)"></A></P>
  <HR size="6">
  <A name="SEC120" id="SEC120"></A>
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  </TABLE>
  <H2>6.10 Causal bond graph (cbg)</H2><!--docid::SEC120::-->
  The causal bond graph is the causally complete version of the Acausal bond
  graph (see section <A href="mtt.html#SEC55">6.4 Acausal bond graph
  (abg)</A>).
  <P>To create the causal bond graph of system `sys' in language fig
  type:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys cbg fig
</PRE>
      </TD>
    </TR>
  </TABLE>To create the causal bond graph of system `sys' in language m type:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys cbg m
</PRE>
      </TD>
    </TR>
  </TABLE>To view the causal bond graph of system `sys' type:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys cbg view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC121">6.10.1 Language
      fig (cbg.fig)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC122">6.10.2 Language
      m (cbg.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Language fig (cbg.fig)"></A></P>
  <HR size="6">
  <A name="SEC121" id="SEC121"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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    </TR>
  </TABLE>
  <H3>6.10.1 Language fig (cbg.fig)</H3><!--docid::SEC121::-->
  The fig file is created by <STRONG>MTT</STRONG>. It is identical to the
  corresponding acausal representation (see section <A href=
  "mtt.html#SEC56">6.4.1 Language fig (abg.fig)</A>) except that
  <UL>
    <LI>the new causal strokes are added (using a double thickness line in
    blue)</LI>
    <LI>components that are undercausal are bold and green</LI>
    <LI>components that are overcausal are bold and red</LI>
  </UL>
  <P><A name="Language m (cbg.m)"></A></P>
  <HR size="6">
  <A name="SEC122" id="SEC122"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC121">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC123">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC120">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H3>6.10.2 Language m (cbg.m)</H3><!--docid::SEC122::-->
  <P>The causal bond graph of system `sys' is represented as an m file with
  heading:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function [cbonds,status] = sys_cbg
</PRE>
      </TD>
    </TR>
  </TABLE>The two outputs of this function are:
  <UL>
    <LI>cbonds</LI>
    <LI>status</LI>
  </UL>
  <P><EM>cbonds</EM> is a matrix with</P>
  <UL>
    <LI>one row for each bond</LI>
    <LI>the first column contains the arrow-orientated (see section <A href=
    "mtt.html#SEC76">6.4.3.1 Arrow-orientated causality</A>) causality of the
    <EM>effort</EM> variable.</LI>
    <LI>the second column contains the arrow-orientated (see section <A href=
    "mtt.html#SEC76">6.4.3.1 Arrow-orientated causality</A>) causality of the
    <EM>flow</EM> variable.</LI>
  </UL>
  <P><EM>status</EM> is a matrix with</P>
  <UL>
    <LI>one row for each component</LI>
    <LI>the first column contains 1 if the component is overcausal; 0 if the
    component is causally complete and -1 if the component is
    undercausal.</LI>
  </UL>A successful model would therefore have all zeros in the status
  matrix.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC123">6.10.2.1
      Transformation abg2cbg_m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation abg2cbg_m"></A></P>
  <HR size="6">
  <A name="SEC123" id="SEC123"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC122">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC124">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC122">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.10.2.1 Transformation abg2cbg_m</H4><!--docid::SEC123::-->
  <P>This transformation takes the acausal bond graph as an m file (see
  section <A href="mtt.html#SEC75">6.4.3 Language m (abg.m)</A>) and
  transforms it into a causal bond graph in m-file format (see section
  <A href="mtt.html#SEC122">6.10.2 Language m (cbg.m)</A>).</P>
  <P>It is based on the m-function abg2cbg.m which iteratively tries to
  complete causality whilst recursively searching the bond graph structure.
  If causality is incomplete, it picks the first acausal dynamic (C or I)
  component, asserts integral causality, and tries again.</P>
  <P>This is essentially the sequential causality assignment procedure of
  Karnopp and Rosenberg.</P>
  <P>The transformation informs the user of the final status in terms of the
  percentage of causally complete components; a successful model will yield
  100% here.</P>
  <P><A name="Elementary system equations"></A></P>
  <HR size="6">
  <A name="SEC124" id="SEC124"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
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      <TD valign="middle" align="left"></TD>
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  </TABLE>
  <H2>6.11 Elementary system equations (ese)</H2><!--docid::SEC124::-->
  <P>The elementary system equations are a complete set of assignment
  statements describing the dynamic system corresponding to the bond graph.
  They are in the Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) language.</P>
  <P>Because these are based on a causally complete system, these assignment
  statements are directly soluble by substitution.</P>
  <P>Unlike early versions of <STRONG>MTT</STRONG>, <STRONG>MTT</STRONG> does
  <EM>not</EM> sort the equations in order of solution, but rather leaves
  them sorted by component and subsystem.</P>
  <P>These are not supposed to be read by the user, so there is no view
  facility as such. However, you may read these with your favourite text
  editor and, to this end, helpful comment lines have been added.</P>
  <P>Wherever components have an explicit constitutive relationship, the
  corresponding RHS of the equation has a standard form.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>cr(arguments,out_causality,outport,
        input_1, causality_1, port_1,
        ....
        input_i, causality_i, port_i,
        ....
        input_n, causality_n, port_n
        );
</PRE>
      </TD>
    </TR>
  </TABLE>where the symbols have the following meaning
  <DL compact>
    <DT><A name="IDX399" id="IDX399"></A> <CODE>arguments</CODE></DT>
    <DD><A name="IDX400" id="IDX400"></A> the constitutive relationship
    arguments</DD>
    <DT><A name="IDX401" id="IDX401"></A> <CODE>out_causality</CODE></DT>
    <DD><A name="IDX402" id="IDX402"></A> the causality (effort or flow) of
    the output variable (see section <A href="mtt.html#SEC5">1.4
    Variables</A>)</DD>
    <DT><A name="IDX403" id="IDX403"></A> <CODE>outport</CODE></DT>
    <DD><A name="IDX404" id="IDX404"></A> the number (integer) of the output
    port of the system</DD>
    <DT><A name="IDX405" id="IDX405"></A> <CODE>input_i</CODE></DT>
    <DD><A name="IDX406" id="IDX406"></A> the ith input to the component</DD>
    <DT><A name="IDX407" id="IDX407"></A> <CODE>causality_i</CODE></DT>
    <DD><A name="IDX408" id="IDX408"></A> the causality (effort or flow) of
    the ith input variable (see section <A href="mtt.html#SEC5">1.4
    Variables</A>)</DD>
    <DT><A name="IDX409" id="IDX409"></A> <CODE>port_i</CODE></DT>
    <DD><A name="IDX410" id="IDX410"></A> the number (integer) of the ith
    input port of the system</DD>
  </DL>
  <P>An example for a resistor with linear constitutive relationship is:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>rc_1_bond4_flow := lin(flow,r,flow,1,
        rc_1_bond4_effort,effort,1
        );
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC125">6.11.0.1
      Transformation cbg2ese_m2r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation cbg2ese_m2r"></A></P>
  <HR size="6">
  <A name="SEC125" id="SEC125"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC124">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC126">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC124">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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  </TABLE>
  <H4>6.11.0.1 Transformation cbg2ese_m2r</H4><!--docid::SEC125::-->
  This transformation takes the causal bond graph as an m file (see section
  <A href="mtt.html#SEC122">6.10.2 Language m (cbg.m)</A>) and transforms it
  into elementary system equations in Reduce (see section <A href=
  "mtt.html#SEC162">9.3 Reduce</A>) form.
  <P>It is based on the m-function cbg2ese.m which iteratively traverses the
  causal bond graph writing equations as it goes.</P>
  <P>It also writes out the system structure as the file
  `<TT>sys_def.r</TT>'.</P>
  <P><A name="Differential-Algebraic Equations"></A></P>
  <HR size="6">
  <A name="SEC126" id="SEC126"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC125">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC127">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.12 Differential-Algebraic Equations (dae)</H2><!--docid::SEC126::-->
  <P>The system differential algebraic equations describe the system dynamics
  together together with any algebraic constraints.</P>
  <P>They are generated in language <CODE>lang</CODE> for system
  <CODE>sys</CODE> by:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys dae lang
</PRE>
      </TD>
    </TR>
  </TABLE>Valid languages are:
  <DL compact>
    <DT><A name="IDX411" id="IDX411"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX412" id="IDX412"></A> reduce (see section <A href=
    "mtt.html#SEC162">9.3 Reduce</A>).</DD>
    <DT><A name="IDX413" id="IDX413"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX414" id="IDX414"></A> m (see section <A href=
    "mtt.html#SEC161">9.2 m</A>).</DD>
    <DT><A name="IDX415" id="IDX415"></A> <CODE>view</CODE></DT>
    <DD><A name="IDX416" id="IDX416"></A> reduce (see section <A href=
    "mtt.html#SEC165">10.1 Views</A>).</DD>
  </DL>
  <P>There are five sets of variables describing the system:</P>
  <DL compact>
    <DT><A name="IDX417" id="IDX417"></A> <CODE>x</CODE></DT>
    <DD><A name="IDX418" id="IDX418"></A> the system states (corresponding to
    C and I components with integral causality.</DD>
    <DT><A name="IDX419" id="IDX419"></A> <CODE>z</CODE></DT>
    <DD><A name="IDX420" id="IDX420"></A> the system nonstates (corresponding
    to C and I components with derivative causality.</DD>
    <DT><A name="IDX421" id="IDX421"></A> <CODE>u</CODE></DT>
    <DD><A name="IDX422" id="IDX422"></A> the system inputs (corresponding to
    SS components with external attribute).</DD>
    <DT><A name="IDX423" id="IDX423"></A> <CODE>ui</CODE></DT>
    <DD><A name="IDX424" id="IDX424"></A> the <EM>internal</EM> system inputs
    (corresponding to SS components with internal attribute) used to solve
    algebraic loops (see section <A href="mtt.html#SEC12">1.7 Algebraic
    loops</A>).</DD>
    <DT><A name="IDX425" id="IDX425"></A> <CODE>y</CODE></DT>
    <DD><A name="IDX426" id="IDX426"></A> the system outputs (corresponding
    to SS components with external attribute).</DD>
  </DL>
  <P>In general there are four sets of equations. The right-hand side of each
  is a function of x, dz/dt, u and ui and the left hand sides are:</P>
  <OL>
    <LI>the derivative of x (dx/dt)</LI>
    <LI>z</LI>
    <LI>w=0 (the algebraic equations)</LI>
    <LI>y</LI>
  </OL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC127">6.12.1 Language
      reduce (dae.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC129">6.12.2 Language
      m (dae.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Differential-Algebraic Equations (reduce)"></A></P>
  <HR size="6">
  <A name="SEC127" id="SEC127"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC126">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC128">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC126">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.12.1 Language reduce (dae.r)</H3><!--docid::SEC127::-->
  <P>The system DAEs (see section <A href="mtt.html#SEC126">6.12
  Differential-Algebraic Equations (dae)</A>) are represented in the reduce
  (see section <A href="mtt.html#SEC162">9.3 Reduce</A>) language as arrays
  containing the algebraic expressions for the right hand sides of each set
  of equations. The arrays are:</P>
  <DL compact>
    <DT><A name="IDX427" id="IDX427"></A> <CODE>MTTx</CODE></DT>
    <DD><A name="IDX428" id="IDX428"></A> x -- the system states
    (corresponding to C and I components with integral causality.</DD>
    <DT><A name="IDX429" id="IDX429"></A> <CODE>MTTz</CODE></DT>
    <DD><A name="IDX430" id="IDX430"></A> z -- the system nonstates
    (corresponding to C and I components with derivative causality.</DD>
    <DT><A name="IDX431" id="IDX431"></A> <CODE>MTTu</CODE></DT>
    <DD><A name="IDX432" id="IDX432"></A> u -- the system inputs
    (corresponding to SS components with external attribute).</DD>
    <DT><A name="IDX433" id="IDX433"></A> <CODE>mttv</CODE></DT>
    <DD><A name="IDX434" id="IDX434"></A> ui -- the <EM>internal</EM> system
    inputs (corresponding to SS components with internal attribute) used to
    solve algebraic loops (see section <A href="mtt.html#SEC12">1.7 Algebraic
    loops</A>).</DD>
    <DT><A name="IDX435" id="IDX435"></A> <CODE>MTTy</CODE></DT>
    <DD><A name="IDX436" id="IDX436"></A> y -- the system outputs
    (corresponding to SS components with external attribute).</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC128">6.12.1.1
      Transformation ese2dae_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation ese2dae_r"></A></P>
  <HR size="6">
  <A name="SEC128" id="SEC128"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC127">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC129">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC127">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.12.1.1 Transformation ese2dae_r</H4><!--docid::SEC128::-->
  <P>This transformation (see section <A href="mtt.html#SEC3">1.2 What is a
  transformation?</A>) uses Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) to combine the elementary system equations (see section
  <A href="mtt.html#SEC124">6.11 Elementary system equations (ese)</A>) with
  the constitutive relationships (see section <A href="mtt.html#SEC9">1.6.2
  Constitutive relationship</A>) and simplify the result.</P>
  <P><A name="Differential-Algebraic Equations (m)"></A></P>
  <HR size="6">
  <A name="SEC129" id="SEC129"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC128">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC130">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC126">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.12.2 Language m (dae.m)</H3><!--docid::SEC129::-->
  The system DAEs (see section <A href="mtt.html#SEC126">6.12
  Differential-Algebraic Equations (dae)</A>) are represented in the m (see
  section <A href="mtt.html#SEC161">9.2 m</A>) language as two m-functions of
  the form:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function resid = sys_dae(dx,x,t)
function y  = sys_dae(dx,x,t)
</PRE>
      </TD>
    </TR>
  </TABLE>Where x is the dae <EM>descriptor</EM> vector and dx its time
  derivative; t is the time. The first function is of a form suitable for
  solution by DASSL; the second function can then be used to find the
  coresponding system output.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC130">6.12.2.1
      Transformation dae_r2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation dae_r2m"></A></P>
  <HR size="6">
  <A name="SEC130" id="SEC130"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC129">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC131">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC129">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.12.2.1 Transformation dae_r2m</H4><!--docid::SEC130::-->
  <P>This transformation (see section <A href="mtt.html#SEC3">1.2 What is a
  transformation?</A>) uses Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) to rewrite the elementary system equations (see section
  <A href="mtt.html#SEC124">6.11 Elementary system equations (ese)</A>) in
  m-file format (see section <A href="mtt.html#SEC161">9.2 m</A>) . Numerical
  parameters are declared as global.</P>
  <P><A name="Constrained-state Equations"></A></P>
  <HR size="6">
  <A name="SEC131" id="SEC131"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC130">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC132">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.13 Constrained-state Equations (cse)</H2><!--docid::SEC131::-->
  <P>The system constrained-state equations describe the system dynamics for
  a special class of systems (see the book for details). The resuting
  equations are of the form:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>E(x) dx/dt = f(x,u)
y = g(x,u)
</PRE>
      </TD>
    </TR>
  </TABLE>They typically occure where two or more states are constrained to
  be equal, or proportional, to each other. For example, two capacitors in
  parallel or two inertias connected by a stiff shaft.
  <P>They are generated in language <CODE>lang</CODE> for system
  <CODE>sys</CODE> by:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys cse lang
</PRE>
      </TD>
    </TR>
  </TABLE>Valid languages are:
  <DL compact>
    <DT><A name="IDX437" id="IDX437"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX438" id="IDX438"></A> reduce (see section <A href=
    "mtt.html#SEC162">9.3 Reduce</A>).</DD>
    <DT><A name="IDX439" id="IDX439"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX440" id="IDX440"></A> m (see section <A href=
    "mtt.html#SEC161">9.2 m</A>).</DD>
    <DT><A name="IDX441" id="IDX441"></A> <CODE>view</CODE></DT>
    <DD><A name="IDX442" id="IDX442"></A> reduce (see section <A href=
    "mtt.html#SEC165">10.1 Views</A>).</DD>
  </DL>
  <P>There are three sets of variables describing the system:</P>
  <DL compact>
    <DT><A name="IDX443" id="IDX443"></A> <CODE>x</CODE></DT>
    <DD><A name="IDX444" id="IDX444"></A> the system states (corresponding to
    C and I components with integral causality.</DD>
    <DT><A name="IDX445" id="IDX445"></A> <CODE>u</CODE></DT>
    <DD><A name="IDX446" id="IDX446"></A> the system inputs (corresponding to
    SS components with external attribute).</DD>
    <DT><A name="IDX447" id="IDX447"></A> <CODE>y</CODE></DT>
    <DD><A name="IDX448" id="IDX448"></A> the system outputs (corresponding
    to SS components with external attribute).</DD>
  </DL>
  <P>In general there are two sets of equations. The right-hand side of each
  is a function of x and u and the left hand sides are:</P>
  <OL>
    <LI>the derivative of x (dx/dt) y</LI>
  </OL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC132">6.13.1 Language
      reduce (cse.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC134">6.13.2 Language
      m (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Constrained-state Equations (reduce)"></A></P>
  <HR size="6">
  <A name="SEC132" id="SEC132"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC131">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC133">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC131">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.13.1 Language reduce (cse.r)</H3><!--docid::SEC132::-->
  <P>The system CSEs (see section <A href="mtt.html#SEC131">6.13
  Constrained-state Equations (cse)</A>) are represented in the reduce (see
  section <A href="mtt.html#SEC162">9.3 Reduce</A>) language as arrays
  containing the algebraic expressions for the right hand sides of each set
  of equations. The arrays are:</P>
  <DL compact>
    <DT><A name="IDX449" id="IDX449"></A> <CODE>MTTx</CODE></DT>
    <DD><A name="IDX450" id="IDX450"></A> x -- the system states
    (corresponding to C and I components with integral causality.</DD>
    <DT><A name="IDX451" id="IDX451"></A> <CODE>MTTu</CODE></DT>
    <DD><A name="IDX452" id="IDX452"></A> u -- the system inputs
    (corresponding to SS components with external attribute).</DD>
    <DT><A name="IDX453" id="IDX453"></A> <CODE>MTTy</CODE></DT>
    <DD><A name="IDX454" id="IDX454"></A> y -- the system outputs
    (corresponding to SS components with external attribute).</DD>
  </DL>together with the array containing the elements of the E matrix.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC133">6.13.1.1
      Transformation dae2cse_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation dae2cse_r"></A></P>
  <HR size="6">
  <A name="SEC133" id="SEC133"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC132">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC134">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC132">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.13.1.1 Transformation dae2cse_r</H4><!--docid::SEC133::-->
  <P>This transformation (see section <A href="mtt.html#SEC3">1.2 What is a
  transformation?</A>) Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) to find various Jacobians which are combined to find the E
  matrix and the constrained-state equations (see section <A href=
  "mtt.html#SEC131">6.13 Constrained-state Equations (cse)</A>).</P>
  <P><A name="Constrained-state Equations (view)"></A></P>
  <HR size="6">
  <A name="SEC134" id="SEC134"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC133">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC135">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC131">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.13.2 Language m (view)</H3><!--docid::SEC134::-->
  This representation has the standard text view (see section <A href=
  "mtt.html#SEC165">10.1 Views</A>).
  <P><A name="Ordinary Differential Equations"></A></P>
  <HR size="6">
  <A name="SEC135" id="SEC135"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC134">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC136">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.14 Ordinary Differential Equations</H2><!--docid::SEC135::-->
  <P>The system ordinary differential equations describe the system
  dynamics.</P>
  <P>They are generated in language <CODE>lang</CODE> for system
  <CODE>sys</CODE> by:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys ode lang
</PRE>
      </TD>
    </TR>
  </TABLE>Valid languages are:
  <DL compact>
    <DT><A name="IDX455" id="IDX455"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX456" id="IDX456"></A> reduce (see section <A href=
    "mtt.html#SEC162">9.3 Reduce</A>).</DD>
    <DT><A name="IDX457" id="IDX457"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX458" id="IDX458"></A> m (see section <A href=
    "mtt.html#SEC161">9.2 m</A>).</DD>
    <DT><A name="IDX459" id="IDX459"></A> <CODE>view</CODE></DT>
    <DD><A name="IDX460" id="IDX460"></A> reduce (see section <A href=
    "mtt.html#SEC165">10.1 Views</A>).</DD>
  </DL>
  <P>There are three sets of variables describing the system:</P>
  <DL compact>
    <DT><A name="IDX461" id="IDX461"></A> <CODE>x</CODE></DT>
    <DD><A name="IDX462" id="IDX462"></A> the system states (corresponding to
    C and I components with integral causality.</DD>
    <DT><A name="IDX463" id="IDX463"></A> <CODE>u</CODE></DT>
    <DD><A name="IDX464" id="IDX464"></A> the system inputs (corresponding to
    SS components with external attribute).</DD>
    <DT><A name="IDX465" id="IDX465"></A> <CODE>y</CODE></DT>
    <DD><A name="IDX466" id="IDX466"></A> the system outputs (corresponding
    to SS components with external attribute).</DD>
  </DL>
  <P>In general there are two sets of equations. The right-hand side of each
  is a function of x and u and the left hand sides are:</P>
  <OL>
    <LI>the derivative of x (dx/dt) y</LI>
  </OL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC136">6.14.1 Language
      reduce (ode.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC138">6.14.2 Language
      m (ode.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC140">6.14.3 Language
      m (view)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Ordinary Differential Equations (reduce)"></A></P>
  <HR size="6">
  <A name="SEC136" id="SEC136"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC135">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC137">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC135">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.14.1 Language reduce (ode.r)</H3><!--docid::SEC136::-->
  <P>The system ODEs (see section <A href="mtt.html#SEC135">6.14 Ordinary
  Differential Equations</A>) are represented in the reduce (see section
  <A href="mtt.html#SEC162">9.3 Reduce</A>) language as arrays containing the
  algebraic expressions for the right hand sides of each set of equations.
  The arrays are:</P>
  <DL compact>
    <DT><A name="IDX467" id="IDX467"></A> <CODE>MTTx</CODE></DT>
    <DD><A name="IDX468" id="IDX468"></A> x -- the system states
    (corresponding to C and I components with integral causality.</DD>
    <DT><A name="IDX469" id="IDX469"></A> <CODE>MTTu</CODE></DT>
    <DD><A name="IDX470" id="IDX470"></A> u -- the system inputs
    (corresponding to SS components with external attribute).</DD>
    <DT><A name="IDX471" id="IDX471"></A> <CODE>MTTy</CODE></DT>
    <DD><A name="IDX472" id="IDX472"></A> y -- the system outputs
    (corresponding to SS components with external attribute).</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC137">6.14.1.1
      Transformation cse2ode_r</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation cse2ode_r"></A></P>
  <HR size="6">
  <A name="SEC137" id="SEC137"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC136">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC138">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC136">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.14.1.1 Transformation cse2ode_r</H4><!--docid::SEC137::-->
  <P>This transformation (see section <A href="mtt.html#SEC3">1.2 What is a
  transformation?</A>) uses Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) to invert the E matrix of the constrained-state equations (see
  section <A href="mtt.html#SEC131">6.13 Constrained-state Equations
  (cse)</A>) and simplify the result.</P>
  <P><A name="Ordinary Differential Equations (m)"></A></P>
  <HR size="6">
  <A name="SEC138" id="SEC138"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC137">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC139">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC135">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.14.2 Language m (ode.m)</H3><!--docid::SEC138::-->
  The system ODEs (see section <A href="mtt.html#SEC135">6.14 Ordinary
  Differential Equations</A>) are represented in the m (see section <A href=
  "mtt.html#SEC161">9.2 m</A>) language as two m-functions of the form:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function dx = sys_ODE(x,t)
function y  = sys_ODE(dx,x,t)
</PRE>
      </TD>
    </TR>
  </TABLE>Where x is the ODE <EM>state</EM> vector and dx its time
  derivative; t is the time. The first function is of a form suitable for
  solution by odesol; the second function can then be used to find the
  corresponding system output.
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC139">6.14.2.1
      Transformation ode_r2m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Transformation ode_r2m"></A></P>
  <HR size="6">
  <A name="SEC139" id="SEC139"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC138">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC140">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC138">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H4>6.14.2.1 Transformation ode_r2m</H4><!--docid::SEC139::-->
  <P>This transformation (see section <A href="mtt.html#SEC3">1.2 What is a
  transformation?</A>) uses Reduce (see section <A href="mtt.html#SEC162">9.3
  Reduce</A>) to rewrite the ordinary differential equations (see section
  <A href="mtt.html#SEC135">6.14 Ordinary Differential Equations</A>) in
  m-file format (see section <A href="mtt.html#SEC161">9.2 m</A>) . Numerical
  parameters are declared as global.</P>
  <P><A name="Ordinary Differential Equations (view)"></A></P>
  <HR size="6">
  <A name="SEC140" id="SEC140"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC139">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC141">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC135">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.14.3 Language m (view)</H3><!--docid::SEC140::-->
  This representation has the standard text view (see section <A href=
  "mtt.html#SEC165">10.1 Views</A>).
  <P><A name="Descriptor matrices"></A></P>
  <HR size="6">
  <A name="SEC141" id="SEC141"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC140">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC142">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC51">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>6.15 Descriptor matrices (dm)</H2><!--docid::SEC141::-->
  <P>The system descriptor matrices A, B, C, D and E describe the
  <EM>linearised</EM> system dynamics in the form</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>E dx/dt = Ax + Bu
y = Cx + Du
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>They are generated in language <CODE>lang</CODE> for system
  <CODE>sys</CODE> by:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys dm lang
</PRE>
      </TD>
    </TR>
  </TABLE>Valid languages are:
  <DL compact>
    <DT><A name="IDX473" id="IDX473"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX474" id="IDX474"></A> reduce (see section <A href=
    "mtt.html#SEC162">9.3 Reduce</A>).</DD>
    <DT><A name="IDX475" id="IDX475"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX476" id="IDX476"></A> m (see section <A href=
    "mtt.html#SEC161">9.2 m</A>).</DD>
    <DT><A name="IDX477" id="IDX477"></A> <CODE>view</CODE></DT>
    <DD><A name="IDX478" id="IDX478"></A> reduce (see section <A href=
    "mtt.html#SEC165">10.1 Views</A>).</DD>
  </DL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC142">6.15.1 Language
      reduce (dm.r)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC143">6.15.2 Language
      m (dm.m)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Descriptor matrices (reduce)"></A></P>
  <HR size="6">
  <A name="SEC142" id="SEC142"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC141">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC143">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC141">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.15.1 Language reduce (dm.r)</H3><!--docid::SEC142::-->
  <P>The system descriptor matrices (see section <A href=
  "mtt.html#SEC141">6.15 Descriptor matrices (dm)</A>) are represented in the
  reduce (see section <A href="mtt.html#SEC162">9.3 Reduce</A>) language as
  arrays containing the four matrices. The arrays are:</P>
  <DL compact>
    <DT><A name="IDX479" id="IDX479"></A> <CODE>MTTA</CODE></DT>
    <DD><A name="IDX480" id="IDX480"></A> A</DD>
    <DT><A name="IDX481" id="IDX481"></A> <CODE>MTTB</CODE></DT>
    <DD><A name="IDX482" id="IDX482"></A> B</DD>
    <DT><A name="IDX483" id="IDX483"></A> <CODE>MTTA</CODE></DT>
    <DD><A name="IDX484" id="IDX484"></A> C</DD>
    <DT><A name="IDX485" id="IDX485"></A> <CODE>MTTD</CODE></DT>
    <DD><A name="IDX486" id="IDX486"></A> D</DD>
    <DT><A name="IDX487" id="IDX487"></A> <CODE>MTTE</CODE></DT>
    <DD><A name="IDX488" id="IDX488"></A> E</DD>
  </DL>
  <P><A name="Descriptor matrices (m)"></A></P>
  <HR size="6">
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.15.2 Language m (dm.m)</H3><!--docid::SEC143::-->
  The system descriptor matrices (see section <A href="mtt.html#SEC141">6.15
  Descriptor matrices (dm)</A>) are represented in the m (see section
  <A href="mtt.html#SEC161">9.2 m</A>) language as an m-function of the form:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>function [A,B,C,D,E] = sys_dm
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>System numeric parameters (see section <A href="mtt.html#SEC11">1.6.4
  Numeric parameters</A>) are passed via global variables defined in the
  _numpar.m file. Thus the system descriptor matrices are typically generated
  in Octave (see section <A href="mtt.html#SEC168">10.4 Octave</A>) as
  follows:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>sys_numpar
[A,B,C,D,E] = sys_dm
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Parameters can be changed from their default values by entering their
  values directly into Octave (see section <A href="mtt.html#SEC168">10.4
  Octave</A>) and then invoking <CODE>sys_dm</CODE>; for example</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>sys_numpar
par_1 = 25
par_2 = par_1 + 3
[A,B,C,D,E] = sys_dm
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Report" id="Report"></A></P>
  <HR size="6">
  <A name="SEC144" id="SEC144"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
    </TR>
  </TABLE>
  <H2>6.16 Report (rep)</H2><!--docid::SEC144::-->
  <P><STRONG>MTT</STRONG> has a report-generator feature. The user specifies
  the report contents in a text file (see section <A href=
  "mtt.html#SEC145">6.16.1 Language text (rep.txt)</A>) using an appropriate
  text editor (see section <A href="mtt.html#SEC167">10.3 Text
  editors</A>).</P>
  <P>For example, the report can be viewed by typing</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt system rep view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC145">6.16.1 Language
      text (rep.txt)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC146">6.16.2 Language
      view</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Report (text)"></A></P>
  <HR size="6">
  <A name="SEC145" id="SEC145"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC144">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC146">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC144">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.16.1 Language text (rep.txt)</H3><!--docid::SEC145::-->
  <P>The user specifies the report contents in a text file (see section
  <A href="mtt.html#SEC145">6.16.1 Language text (rep.txt)</A>) using an
  appropriate text editor (see section <A href="mtt.html#SEC167">10.3 Text
  editors</A>). The text file contains lines which are either comments
  (indicated by %) or valid <STRONG>MTT</STRONG> commands. The report will
  then contain appropriate sections. The following languages are supported by
  the report generator:</P>
  <DL compact>
    <DT><A name="IDX489" id="IDX489"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX490" id="IDX490"></A> <CODE>octave</CODE> a high-level
    interactive language for numerical computation.</DD>
    <DT><A name="IDX491" id="IDX491"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX492" id="IDX492"></A> <CODE>reduce</CODE> a high-level
    interactive language for symbolic computation.</DD>
    <DT><A name="IDX493" id="IDX493"></A> <CODE>tex</CODE></DT>
    <DD><A name="IDX494" id="IDX494"></A> <CODE>latex</CODE> a text
    processor.</DD>
    <DT><A name="IDX495" id="IDX495"></A> <CODE>ps</CODE></DT>
    <DD><A name="IDX496" id="IDX496"></A> <CODE>ghostview</CODE> another
    document viewer.</DD>
    <DT><A name="IDX497" id="IDX497"></A> <CODE>c</CODE></DT>
    <DD><A name="IDX498" id="IDX498"></A> <CODE>gcc</CODE> a c compiler.</DD>
  </DL>For example:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt rc abg tex
mtt rc cbg ps
mtt rc struc tex
mtt rc ode tex
mtt rc sro ps
mtt rc tf tex
mtt rc lmfr ps
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The acausal bond graph (abg) (see section <A href="mtt.html#SEC55">6.4
  Acausal bond graph (abg)</A>) with the tex language is handled in a special
  way: the acausal Bond Graph in fig format (see section <A href=
  "mtt.html#SEC56">6.4.1 Language fig (abg.fig)</A>), the label file (see
  section <A href="mtt.html#SEC83">6.6 Labels (lbl)</A>) the description file
  (see section <A href="mtt.html#SEC158">8.2.2 Detailed on-line
  documentation</A>), together with corresponding subsystems are included in
  the report. It is recommended that the first (non-comment line) in the file
  should be:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt &lt;system&gt; abg tex
</PRE>
      </TD>
    </TR>
  </TABLE>where <CODE>&lt;system&gt;</CODE> is the name of the (top-level)
  system.
  <P>As usual, <STRONG>MTT</STRONG> provides a default text file to be edited
  by the user (see section <A href="mtt.html#SEC167">10.3 Text
  editors</A>).</P>
  <P>In the special case that the first argument to mtt (normally the system)
  is a directory, a default text file is provided which generates a report
  for all systems to be found in that directory tree.</P>
  <P><A name="Report (view)"></A></P>
  <HR size="6">
  <A name="SEC146" id="SEC146"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC145">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC147">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC51">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC144">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>6.16.2 Language view</H3><!--docid::SEC146::-->
  This representation has the standard text view (see section <A href=
  "mtt.html#SEC165">10.1 Views</A>).
  <P><A name="Extending MTT"></A></P>
  <HR size="6">
  <A name="SEC147" id="SEC147"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      ]</TD>
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      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_Top">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H1>7. Extending MTT</H1><!--docid::SEC147::-->
  <P><STRONG>MTT</STRONG> has a number of built-in mechanisms for the user to
  extend its capabilities. As <STRONG>MTT</STRONG> is based on `Make' it is
  unsurprising that some of these involve the creation of `make files'.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC148">7.1
      Makefiles</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC149">7.2 New (DIY)
      representations</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC153">7.3 Component
      library</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Makefiles" id="Makefiles"></A></P>
  <HR size="6">
  <A name="SEC148" id="SEC148"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC147">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC149">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC147">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC147">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>7.1 Makefiles</H2><!--docid::SEC148::-->
  <P>If a file called `Makefile' exists in the current directory,
  <STRONG>MTT</STRONG> executes it using make before doing anything else.
  This is useful if one of the .txt files contains a reference to, for
  example, an octave function of which <STRONG>MTT</STRONG> unaware. Such a
  function can be created using the makefile. An example `Makefile' is</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE># Makefile for the Two link GMV example

all: msdP_tf.m TwoLinkP_obs.m TwoLinkP_sm.m twolinkp_sm.m TwoLinkGMV_numpar.m 

msdP_tf.m: msdP_abg.fig 
        mtt -q msdP tf m

TwoLinkP_obs.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
        mtt -q TwoLinkP obs m

TwoLinkP_sm.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
        mtt -q TwoLinkP sm m

twolinkp_sm.m: TwoLinkP_sm.m
        cp -v TwoLinkP_sm.m twolinkp_sm.m

TwoLinkGMV_numpar.m: TwoLinkGMV_numpar.txt
        mtt -q TwoLinkGMV numpar m
</PRE>
      </TD>
    </TR>
  </TABLE>All of the files in the line stating `all:' are created when
  <STRONG>MTT</STRONG> is executed (if they don't already exist).
  <P><A name="New (DIY) representations"></A></P>
  <HR size="6">
  <A name="SEC149" id="SEC149"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC148">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC150">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>7.2 New (DIY) representations</H2><!--docid::SEC149::-->
  <P>It may be convenient to create new representations for
  <STRONG>MTT</STRONG>; in particular, it is nice to be able to include the
  result of some numerical or symbolic computations within an
  <STRONG>MTT</STRONG> report (see section <A href="mtt.html#SEC144">6.16
  Report (rep)</A>). Therefore <STRONG>MTT</STRONG> provides a mechanism for
  doing this.</P>
  <P>Future extensions of <STRONG>MTT</STRONG> will use such representations
  stored in $MTT_REP.</P>
  <P>There are three parts to creating a DIY representation called myrep</P>
  <OL>
    <LI>Creating a make file in Make format called myrep_rep.make</LI>
    <LI>Optionally creating a shell script called myrep_rep.sh</LI>
    <LI>Optionally creating a documentation file in LaTeX format called
    myrep_rep.tex</LI>
  </OL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC150">7.2.1
      Makefile</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC151">7.2.2
      Shell-script</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC152">7.2.3
      Documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Makefile (DIY representations)"></A></P>
  <HR size="6">
  <A name="SEC150" id="SEC150"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC149">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC151">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC149">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>7.2.1 Makefile</H3><!--docid::SEC150::-->
  <P>To create a new representation `myrep' in a language `mylang', create a
  file with the name</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>myrep_rep.make
</PRE>
      </TD>
    </TR>
  </TABLE>This file must contain text in `make' syntax. It is executed by
  <STRONG>MTT</STRONG> and the two arguments `SYS' (the system name) and
  `LANG' (the language) are passed to it by <STRONG>MTT</STRONG>. Note that
  <STRONG>MTT</STRONG> cannot know of any prerequisites, but these can be
  explicitly included in the makefile (which may include execution of
  <STRONG>MTT</STRONG> itself.
  <P>The following example declares the new representation `ident' which is
  created in conjunction with the shell-script ident_rep.sh (see section
  <A href="mtt.html#SEC151">7.2.2 Shell-script</A>).</P>
  <P>@verbatim # -*-makefile-*-</P>
  <P>#SUMMARY Identification #DESCRIPTION Partially know system
  identification using #DESCRIPTION using bond graphs</P>
  <P># Makefile for representation ident # File ident_rep.make</P>
  <P>#Copyright (C) 2000,2001,2002 by Peter J. Gawthrop</P>
  <P>## Model targets model_reps = ${SYS}_sympar.m ${SYS}_simpar.m
  ${SYS}_state.m model_reps += ${SYS}_numpar.m ${SYS}_input.m
  ${SYS}_ode2odes.m model_reps += ${SYS}_def.m</P>
  <P>## Prepend s to get the sensitivity targets sensitivity_reps =
  ${model_reps:%=s%}</P>
  <P>## Model prerequisites model_pre = ${SYS}_abg.fig ${SYS}_lbl.txt
  model_pre += ${SYS}_rdae.r ${SYS}_numpar.txt</P>
  <P>## Prepend s to get the sensitivity targets sensitivity_pre =
  ${model_pre:%=s%}</P>
  <P>## Simulation targets sims = ${SYS}_sim.m s${SYS}_ssim.m</P>
  <P>## m-files needed for ident ident_m = ${SYS}_ident.m
  ${SYS}_ident_numpar.m</P>
  <P>## Targets for the ident simulation ident_reps = ${ident_m} ${sims}
  ${model_reps} ${sensitivity_reps}</P>
  <P>## ps output files etc psfiles = ${SYS}_ident.ps
  ${SYS}_ident.comparison.ps figfiles = ${psfiles:%.ps=%.fig} gdatfiles =
  ${psfiles:%.ps=%.gdat} datfiles = ${psfiles:%.ps=%.dat2}</P>
  <P>## LaTeX files etc latexfiles = ${SYS}_ident_par.tex</P>
  <P>all: ${SYS}_ident.${LANG}</P>
  <P>echo: echo "sims: ${sims}" echo "model_reps: ${model_reps}" echo
  "sensitivity_reps: ${sensitivity_reps}" echo "ident_reps:
  ${ident_reps}"</P>
  <P>${SYS}_ident.view: ${psfiles} ident_rep.sh ${SYS} view</P>
  <P>${psfiles}: ${figfiles} ident_rep.sh ${SYS} ps</P>
  <P>${figfiles}: ${gdatfiles} ident_rep.sh ${SYS} fig</P>
  <P>${gdatfiles}: ${datfiles} ident_rep.sh ${SYS} gdat</P>
  <P>${datfiles} ${latexfiles}: ${ident_reps} ident_rep.sh ${SYS} dat2</P>
  <P>${SYS}_ident.m: ident_rep.sh ${SYS} m</P>
  <P>${SYS}_ident_numpar.m: ident_rep.sh ${SYS} numpar.m</P>
  <P>## System model reps ## Generic txt files ${SYS}_%.txt: mtt ${OPTS} -q
  -stdin ${SYS} $* txt</P>
  <P>## Specific m files ${SYS}_ode2odes.m: ${model_pre} mtt -q -stdin
  ${OPTS} ${SYS} ode2odes m</P>
  <P>${SYS}_sim.m: ${SYS}_ode2odes.m mtt ${OPTS} -q -stdin ${SYS} sim m</P>
  <P>## Numpar files ${SYS}_numpar.m: mtt ${SYS} numpar m</P>
  <P>## Sympar files ${SYS}_sympar.m: mtt ${SYS} sympar m</P>
  <P>## Generic txt to m ${SYS}_%.m: ${SYS}_%.txt mtt ${OPTS} -q -stdin
  ${SYS} $* m</P>
  <P>## r files ${SYS}_def.r: ${SYS}_abg.fig mtt ${OPTS} -q -stdin ${SYS} def
  r</P>
  <P>${SYS}_rdae.r: mtt ${OPTS} -q -stdin ${SYS} rdae r</P>
  <P>## Sensitivity model reps ## Generic txt files s${SYS}_%.txt: mtt
  ${OPTS} -q -stdin -s s${SYS} $* txt</P>
  <P>## Specific m files ## Numpar files s${SYS}_numpar.m: mtt -s s${SYS}
  numpar m</P>
  <P>## Sympar files s${SYS}_sympar.m: mtt -s s${SYS} sympar m</P>
  <P>s${SYS}_ode2odes.m: ${sensitivity_pre} mtt -q -stdin ${OPTS} -s s${SYS}
  ode2odes m</P>
  <P>s${SYS}_ssim.m: mtt -q -stdin ${OPTS} -s s${SYS} ssim m</P>
  <P>s${SYS}_def.m: mtt -q -stdin ${OPTS} -s s${SYS} def m</P>
  <P>## Generic txt to m s${SYS}_%.m: s${SYS}_%.txt mtt ${OPTS} -q -stdin
  s${SYS} $* m</P>
  <P>## r files s${SYS}_rdae.r: mtt ${OPTS} -q -stdin -s s${SYS} rdae r</P>
  <P><A name="Shell-script (DIY representations)"></A></P>
  <HR size="6">
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      ]</TD>
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  </TABLE>
  <H3>7.2.2 Shell-script</H3><!--docid::SEC151::-->
  <P>For more complex DIY representations, it is convenient to define new
  commands to be used by the Makefile (see section <A href=
  "mtt.html#SEC150">7.2.1 Makefile</A>).</P>
  <P>The following example shows this in the context of the DIY
  representation `ident' used as an example in the previous section (see
  section <A href="mtt.html#SEC150">7.2.1 Makefile</A>).</P>
  <P>@verbatim #! /bin/sh</P>
  <P>## ident_rep.sh ## DIY representation "ident" for mtt # Copyright (C)
  2002 by Peter J. Gawthrop</P>
  <P>ps=ps</P>
  <P>sys=$1 rep=ident lang=$2 mtt_parameters=$3 rep_parameters=$4</P>
  <P>## Some names target=${sys}_${rep}.${lang} def_file=${sys}_def.r
  dat2_file=${sys}_ident.dat2 dat2s_file=${sys}_idents.dat2
  ident_numpar_file=${sys}_ident_numpar.m
  option_file=${sys}_ident_mtt_options.txt</P>
  <P>## Get system information if [ -f "${def_file}" ]; then echo Using
  ${def_file} else mtt -q ${sys} def r fi</P>
  <P>ny=`mtt_getsize $1 y` nu=`mtt_getsize $1 u`</P>
  <P>check_new_options() { if [ -f "${option_file}" ]; then old_options=`cat
  ${option_file}` if [ "${mtt_options}" != "${old_options}" ]; then echo
  ${mtt_options} &gt; ${option_file} fi else echo ${mtt_options} &gt;
  ${option_file} fi }</P>
  <P>## Make the _ident.m file make_ident() { filename=${sys}_${rep}.m
  date=`date` echo Creating ${filename}</P>
  <P>cat &gt; ${filename} &lt;&lt;EOF function [epar,Y] = ${sys}_ident
  (y,u,t,par_names,Q,extras)</P>
  <P>## usage: [epar,Y] = ${sys}_ident (y,u,t,par_names,Q,extras) ## ## last
  last time in run ## ppp_names Column vector of names of ppp params ##
  par_names Column vector of names of estimated params ## extras Structure
  containing additional info ## ## Created by MTT on ${date} ## Sensitivity
  system name system_name = "s${sys}"</P>
  <P>##Sanity check if nargin&lt;3 printf("Usage: [y,u,t] =
  ${sys}_ident(y,u,t,par_names,Q,extras);"); return endif</P>
  <P>if nargin&lt;6 ## Set up optional parameters extras.criterion = 1e-3;
  extras.emulate_timing = 0; extras.max_iterations = 10; extras.simulate = 2;
  extras.v = 1e-2; extras.verbose = 1; extras.visual = 1; endif ## System
  info [n_x,n_y,n_u,n_z,n_yz] = ${sys}_def; sympar = ${sys}_sympar; simpar =
  ${sys}_simpar; sympars = s${sys}_sympar; simpars = s${sys}_simpar;</P>
  <P>## Parameter indices i_par = ppp_indices (par_names,sympar,sympars);</P>
  <P>## Initial model state x_0 = zeros(2*n_x,1);</P>
  <P>## Initial model parameters par_0 = s${sys}_numpar;</P>
  <P>## Reset simulation parameters [n_data,m_data] = size(y); dt =
  t(2)-t(1); simpars.last = (n_data-1)*dt; simpars.dt = dt;</P>
  <P>## Identification [epar,Par,Error,Y,iterations,x] =
  ppp_optimise(system_name,x_0,par_0,simpars,u,y,i_par,Q,extras); ## Do some
  plots figure(1); title("Comparison of data"); xlabel("t"); ylabel("y");
  [N,M] = size(Y); plot(t,Y(:,M-n_y+1:M),"1;Estimated;", t,y,"3;Actual;");
  figfig("${sys}_ident_comparison");</P>
  <P>## Create a table of the parameters [n_par,m_par] = size(i_par); fid =
  fopen("${sys}_ident_par.tex", "w");
  fprintf(fid,"\\\\begin{table}[htbp]\\n"); fprintf(fid," \\\\centering\\n");
  fprintf(fid," \\\\begin{tabular}{|l|l|}\\n"); fprintf(fid," \\\\hline\\n");
  fprintf(fid," Name &amp; Value \\\\\\\\ \\n"); fprintf(fid,"
  \\\\hline\\n"); for i = 1:n_par fprintf(fid,"$%s$ &amp; %4.2f \\\\\\\\
  \\n", par_names(i,:), epar(i_par(i,1))); endfor fprintf(fid,"
  \\\\hline\\n"); fprintf(fid,"\\\\end{tabular}\\n");
  fprintf(fid,"\\\\caption{Estimated Parameters}\\n");
  fprintf(fid,"\\\\end{table}\\n"); fclose(fid);</P>
  <P>endfunction EOF }</P>
  <P>make_ident_numpar() { echo Creating ${ident_numpar_file} cat &gt;
  ${sys}_ident_numpar.m &lt;&lt;EOF function [y,u,t,par_names,Q,extras] =
  ${sys}_ident_numpar;</P>
  <P>## usage: [y,u,t,par_names,Q,extras] = ${sys}_ident_numpar; ## Edit for
  your own requirements ## Created by MTT on ${date}</P>
  <P>## This section sets up the data source ## simulate = 0 Real data (you
  supply ${sys}_ident_data.dat) ## simulate = 1 Real data input, simulated
  output ## simulate = 2 Unit step input, simulated output simulate = 2;</P>
  <P>## System info [n_x,n_y,n_u,n_z,n_yz] = ${sys}_def; simpars =
  s${sys}_simpar;</P>
  <P>## Access or create data if (simulate&lt;2) # Get the real data if
  (exist("${sys}_ident_data.dat")==2) printf("Loading
  ${sys}_ident_data.dat\n"); load ${sys}_ident_data.dat else printf("Please
  create a loadable file ${sys}_ident_data.dat containing y,u and t\n");
  return endif else switch simulate case 2 # Step simulation t =
  [0:simpars.dt:simpars.last]'; u = ones(size(t)); otherwise
  error(sprintf("simulate = %i not implemented", simulate)); endswitch endif
  if (simulate&gt;0) par = ${sys}_numpar(); x_0 = ${sys}_state(par); dt =
  t(2)-t(1); simpars.dt = dt; simpars.last = t(length(t)); y =
  ${sys}_sim(zeros(n_x,1), par, simpars, u); endif</P>
  <P>## Default parameter names - Put in your own here sympar =
  ${sys}_sympar; # Symbolic params as structure par_names = struct_elements
  (sympar); # Symbolic params as strings [n,m] = size(par_names); # Size the
  string list</P>
  <P>## Sort by index for [i,name] = sympar par_names(i,:) =
  sprintf("%s%s",name, blanks(m-length(name))); endfor ## Output weighting
  vector Q = ones(n_y,1); ## Extra parameters extras.criterion = 1e-5;
  extras.emulate_timing = 0; extras.max_iterations = 10; extras.simulate =
  simulate; extras.v = 1e-2; extras.verbose = 1; extras.visual = 1;</P>
  <P>endfunction EOF }</P>
  <P>make_dat2() {</P>
  <P>## Inform user echo Creating ${dat2_file}</P>
  <P>## Use octave to generate the data octave -q &lt;&lt;EOF
  [y,u,t,par_names,Q,extras] = ${sys}_ident_numpar; [epar,Y] = ${sys}_ident
  (y,u,t,par_names,Q,extras); [N,M] = size(Y); y_est = Y(:,M); data =
  [t,y_est,u]; save -ascii ${dat2_file} data EOF</P>
  <P>## Tidy up the latex stuff - convert foo_123 to foo_{123} cat
  ${sys}_ident_par.tex &gt; mtt_junk sed -e "s/_\([a-z0-9,]*\)/_{\1}/g" &lt;
  mtt_junk &gt;${sys}_ident_par.tex rm mtt_junk }</P>
  <P>case ${lang} in numpar.m) ## Make the numpar stuff make_ident_numpar; ;;
  m) ## Make the code make_ident; ;; dat2) ## The dat2 language (output data)
  &amp; fig file make_dat2; ;; gdat) cp ${dat2_file} ${dat2s_file} dat22dat
  ${sys} ${rep} dat2gdat ${sys} ${rep} ;; fig) gdat2fig ${sys}_${rep} ;; ps)
  figs=`ls ${sys}_ident*.fig | sed -e 's/\.fig//'` for fig in ${figs}; do
  fig2dev -Leps ${fig}.fig &gt; ${fig}.ps done texs=`ls ${sys}_ident*.tex |
  sed -e 's/\.tex//'` for tex in ${texs}; do makedoc "" "${sys}" "ident_par"
  "tex" "" "" "$ps" doc2$ps ${sys}_ident_par "$documenttype" done ;; view)
  pss=`ls ${sys}_ident*.ps` echo Viewing ${pss} for ps in ${pss}; do gv
  ${ps}&amp; done ;; *) echo Language ${lang} not supported by ${rep}
  representation exit 3 esac</P>
  <P><A name="Documentation (DIY representations)"></A></P>
  <HR size="6">
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  <H3>7.2.3 Documentation</H3><!--docid::SEC152::-->
  <P><A name="Component library"></A></P>
  <HR size="6">
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  </TABLE>
  <H2>7.3 Component library</H2><!--docid::SEC153::-->
  <P>If <STRONG>MTT</STRONG> does not recognise a component (eg named
  MyComponent) as a simple component (see section <A href=
  "mtt.html#SEC61">6.4.1.5 Simple components</A>) or as already existing, it
  searches the library search path $MTT_COMPONENTS (see section <A href=
  "mtt.html#SEC182">11.4.2 $MTT_COMPONENTS</A>) for a directory called
  MyComponent containing MyComponent_lbl.txt. It then copies the
  <EM>entire</EM> directory into the current working directory. Thus, for
  example, the directory could contain MyComponent_desc.tex
  MyComponent_abg.fig MyComponent_lbl.txt and MyComponent_cr.r in addition to
  MyComponent_lbl.txt.</P>
  <P><A name="Documentation" id="Documentation"></A></P>
  <HR size="6">
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  <H1>8. Documentation</H1><!--docid::SEC154::-->
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC155">8.1
      Manual</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Manual (Documentation)"></A></P>
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  </TABLE>
  <H2>8.1 Manual</H2><!--docid::SEC155::-->
  <P>MTT is documented in this manual. The manual can be invoked in various
  ways:</P>
  <DL compact>
    <DT><A name="IDX499" id="IDX499"></A> <CODE>mtt manual</CODE></DT>
    <DD><A name="IDX500" id="IDX500"></A> Brings up a pdf version of the
    manual</DD>
    <DT><A name="IDX501" id="IDX501"></A> <CODE>mtt info</CODE></DT>
    <DD><A name="IDX502" id="IDX502"></A> Brings up an xterm containing an
    info version of the manual</DD>
    <DT><A name="IDX503" id="IDX503"></A> <CODE>mtt hinfo</CODE></DT>
    <DD><A name="IDX504" id="IDX504"></A> Brings up an html browser
    containing the manual</DD>
    <DT><A name="IDX505" id="IDX505"></A> <CODE>emacs</CODE></DT>
    <DD><A name="IDX506" id="IDX506"></A> type ^h^i followed by mmtt in the
    command window</DD>
    <DT><A name="IDX507" id="IDX507"></A> <CODE>browser</CODE></DT>
    <DD><A name="IDX508" id="IDX508"></A> point browser to mtt.sf.netb</DD>
  </DL>
  <P><A name="On-line documentation"></A></P>
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  <H2>8.2 On-line documentation</H2><!--docid::SEC156::-->
  <P><STRONG>MTT</STRONG> components, constitutive relations, examples and
  representations in libraries (see section <A href="mtt.html#SEC153">7.3
  Component library</A>) are documented in two ways:</P>
  <OL>
    <LI>brief</LI>
    <LI>verbose</LI>
  </OL>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC157">8.2.1 Brief
      on-line documentation</A></TD>
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    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC158">8.2.2 Detailed
      on-line documentation</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
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  </TABLE>
  <P><A name="Brief" id="Brief"></A></P>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC154">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC156">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>8.2.1 Brief on-line documentation</H3><!--docid::SEC157::-->
  <P>Documentation of DIY components, examples, constitutive relationships
  and representations is provides by the programmer by inserting code of the
  form</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>#SUMMARY     One line summary
#DESCRIPTION Multi-line
#DESCRIPTION More detailed description
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>within the appropriate file (usually at or near the top):</P>
  <DL compact>
    <DT><A name="IDX509" id="IDX509"></A> <CODE>components</CODE></DT>
    <DD><A name="IDX510" id="IDX510"></A> _lbl.txt (see section <A href=
    "mtt.html#SEC83">6.6 Labels (lbl)</A>)</DD>
    <DT><A name="IDX511" id="IDX511"></A> <CODE>examples</CODE></DT>
    <DD><A name="IDX512" id="IDX512"></A> _lbl.txt (see section <A href=
    "mtt.html#SEC83">6.6 Labels (lbl)</A>)</DD>
    <DT><A name="IDX513" id="IDX513"></A> <CODE>constitutive
    relations</CODE></DT>
    <DD><A name="IDX514" id="IDX514"></A> _cr.r (see section <A href=
    "mtt.html#SEC111">6.8.2 DIY constitutive relationships</A>)</DD>
    <DT><A name="IDX515" id="IDX515"></A> <CODE>representations</CODE></DT>
    <DD><A name="IDX516" id="IDX516"></A> _rep.make (see section <A href=
    "mtt.html#SEC150">7.2.1 Makefile</A>)</DD>
  </DL>
  <P>This documentation is accessed by the user in various ways</P>
  <DL compact>
    <DT><A name="IDX517" id="IDX517"></A> <CODE>mtt help name</CODE></DT>
    <DD><A name="IDX518" id="IDX518"></A> prints basic information on the
    screen</DD>
    <DT><A name="IDX519" id="IDX519"></A> <CODE>mtt system lbl
    view</CODE></DT>
    <DD><A name="IDX520" id="IDX520"></A> gives formatted information about
    the component or example</DD>
    <DT><A name="IDX521" id="IDX521"></A> <CODE>Including mtt system abg tex
    in the _rep.txt file</CODE></DT>
    <DD><A name="IDX522" id="IDX522"></A> gives formatted information about
    the component or example within the report</DD>
  </DL>
  <P><A name="Detailed" id="Detailed"></A></P>
  <HR size="6">
  <A name="SEC158" id="SEC158"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC157">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC154">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC156">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>8.2.2 Detailed on-line documentation</H3><!--docid::SEC158::-->
  <P>DIY components, examples, constitutive relationships can be described
  textually in LaTeX (.tex) description file; this is the only language for
  this representation. This representation is used by the LaTeX language
  version (see section <A href="mtt.html#SEC79">6.4.4 Language tex
  (abg.tex)</A>) of the acausal bond graph representation (see section
  <A href="mtt.html#SEC55">6.4 Acausal bond graph (abg)</A>).</P>
  <P>The file may contain any LaTeX commands valis for the "article" document
  type but must <STRONG>not</STRONG> contain:</P>
  <UL>
    <LI>documentclass commands</LI>
    <LI>document environments</LI>
  </UL>
  <P><A name="Languages" id="Languages"></A></P>
  <HR size="6">
  <A name="SEC159" id="SEC159"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC158">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC160">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC154">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_Top">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H1>9. Languages</H1><!--docid::SEC159::-->
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC160">9.1
      Fig</A></TD>
      <TD></TD>
      <TD align="left" valign="top">r</TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC161">9.2 m</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC162">9.3
      Reduce</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC163">9.4 c</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P>These are a number of languages used by <STRONG>MTT</STRONG> to
  implement the various representations. Each has associated Language tools
  (see section <A href="mtt.html#SEC164">10. Language tools</A>) to
  manipulate and/or view the representation.</P>
  <DL compact>
    <DT><A name="IDX523" id="IDX523"></A> <CODE>fig</CODE></DT>
    <DD><A name="IDX524" id="IDX524"></A> <CODE>Fig</CODE> a graphical
    description language.</DD>
    <DT><A name="IDX525" id="IDX525"></A> <CODE>m</CODE></DT>
    <DD><A name="IDX526" id="IDX526"></A> <CODE>octave</CODE> a high-level
    interactive language for numerical computation.</DD>
    <DT><A name="IDX527" id="IDX527"></A> <CODE>r</CODE></DT>
    <DD><A name="IDX528" id="IDX528"></A> <CODE>reduce</CODE> a high-level
    interactive language for symbolic computation.</DD>
    <DT><A name="IDX529" id="IDX529"></A> <CODE>tex</CODE></DT>
    <DD><A name="IDX530" id="IDX530"></A> <CODE>latex</CODE> a text
    processor.</DD>
    <DT><A name="IDX531" id="IDX531"></A> <CODE>dvi</CODE></DT>
    <DD><A name="IDX532" id="IDX532"></A> <CODE>xdvi</CODE> a document
    viewer.</DD>
    <DT><A name="IDX533" id="IDX533"></A> <CODE>ps</CODE></DT>
    <DD><A name="IDX534" id="IDX534"></A> <CODE>ghostview</CODE> another
    document viewer.</DD>
    <DT><A name="IDX535" id="IDX535"></A> <CODE>gdat</CODE></DT>
    <DD><A name="IDX536" id="IDX536"></A> <CODE>gnuplot</CODE> a data
    viewer.</DD>
    <DT><A name="IDX537" id="IDX537"></A> <CODE>c</CODE></DT>
    <DD><A name="IDX538" id="IDX538"></A> <CODE>gcc</CODE> a c compiler.</DD>
    <DT><A name="IDX539" id="IDX539"></A> <CODE>sg</CODE></DT>
    <DD><A name="IDX540" id="IDX540"></A> <CODE>scigraphica</CODE> a plotting
    package.</DD>
  </DL>
  <P>These tools are automatically invoked as appropriate by
  <STRONG>MTT</STRONG>; but for more advanced use, these tools can be used
  directly on files (with the appropriate suffix) generated by
  <STRONG>MTT</STRONG>.</P>
  <P><A name="Fig" id="Fig"></A></P>
  <HR size="6">
  <A name="SEC160" id="SEC160"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC161">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>9.1 Fig</H2><!--docid::SEC160::-->
  Please see xfig documentation.
  <P><A name="m" id="m"></A></P>
  <HR size="6">
  <A name="SEC161" id="SEC161"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC160">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC162">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>9.2 m</H2><!--docid::SEC161::-->
  Please see Octave documentation &lt;A
  HREF="http://www.che.wisc.edu/octave/"&gt;Octave&lt;/A&gt; documentation.
  &lt;A HREF="http://www.mathworks.com/homepage.html"&gt;Matlab&lt;/A&gt;
  documentation.
  <P><A name="Reduce" id="Reduce"></A></P>
  <HR size="6">
  <A name="SEC162" id="SEC162"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC161">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC163">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>9.3 Reduce</H2><!--docid::SEC162::-->
  Please see the reduce documentation.
  <P><A name="c" id="c"></A></P>
  <HR size="6">
  <A name="SEC163" id="SEC163"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC162">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC164">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC159">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>9.4 c</H2><!--docid::SEC163::-->
  Please see the gcc documentation. <A name="Language tools"></A>
  <HR size="6">
  <A name="SEC164" id="SEC164"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC163">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC165">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC159">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_Top">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC174">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H1>10. Language tools</H1><!--docid::SEC164::-->
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC165">10.1
      Views</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC166">10.2
      Xfig</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC167">10.3 Text
      editors</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC168">10.4
      Octave</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC173">10.5
      LaTeX</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Views" id="Views"></A></P>
  <HR size="6">
  <A name="SEC165" id="SEC165"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC164">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC166">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC164">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC174">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>10.1 Views</H2><!--docid::SEC165::-->
  <P>A number of representations (see section <A href="mtt.html#SEC51">6.
  Representations</A>) have a language representation which is particularly
  useful for viewing by the user. These views are invoked, where appropriate
  by the command:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>mtt sys rep view
</PRE>
      </TD>
    </TR>
  </TABLE>where <CODE>sys</CODE> is the system name and <CODE>rep</CODE> a
  corresponding representation.
  <P><A name="Xfig" id="Xfig"></A></P>
  <HR size="6">
  <A name="SEC166" id="SEC166"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC165">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC167">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC164">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC174">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>10.2 Xfig</H2><!--docid::SEC166::-->
  <P><A name="Text editors"></A></P>
  <HR size="6">
  <A name="SEC167" id="SEC167"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC166">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC168">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC164">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC164">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC174">&gt;&gt;</A> ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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    </TR>
  </TABLE>
  <H2>10.3 Text editors</H2><!--docid::SEC167::-->
  All representations live in text files and thus may be edited using your
  favourite text editor; however, the Fig (see section <A href=
  "mtt.html#SEC160">9.1 Fig</A>) representation is pretty meaningless in this
  form and so you should use Xfig (see section <A href="mtt.html#SEC166">10.2
  Xfig</A>) for representation in this language.
  <P>Its up to you which text editor to use. I recommend emacs, but simpler
  (and less powerful) editors such as xedit, textedit and vi are also ok.</P>
  <P>I usually run <STRONG>MTT</STRONG> out of an emacs shell window and keep
  the rest of the files in emacs buffers.</P>
  <P><A name="Octave" id="Octave"></A></P>
  <HR size="6">
  <A name="SEC168" id="SEC168"></A>
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  </TABLE>
  <H2>10.4 Octave</H2><!--docid::SEC168::-->
  <P>Octave is a numerical matrix-based language See section `Octave' in
  <CITE>Octave</CITE>. It is similar to Matlab in many ways. In most cases,
  m-files generated by <STRONG>MTT</STRONG> can be understood by both Matlab
  and Octave (and no doubt other Matlab lookalikes).</P>
  <P><STRONG>MTT</STRONG> provides the octave function <CODE>mtt</CODE>. The
  octave command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>help mtt
</PRE>
      </TD>
    </TR>
  </TABLE>gives the following information:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE> usage:  mtt (system[,representation,language])

 Invokes mtt from octave to generate system_representation.language
 Ie equivalent to "mtt system representation language" at the shell
 Representation and language defualt to "sm" and "m" respectively

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Thus for example, if octave is in the directory containing the system rc
  the following session generates the state matrices of the system "rc" with
  the defaut capacitance but resitance r=0.1.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>octave&gt; mtt("rc");
Creating rc_rbg.m
Creating rc_cmp.m
Creating rc_fig.fig
Creating rc_sabg.fig
Creating rc_alias.txt
Creating rc_alias.m
Creating rc_sub.sh
Creating rc_abg.m
Creating rc_cbg.m (maximise integral causality)
Creating rc_type.sh
Creating rc_ese.r
Creating rc_def.r
Creating rc_struc.txt
Creating rc_rdae.r
Creating rc_subs.r
Creating rc_cr.txt
Creating rc_cr.r
Copying CR SS to here from
Copying CR lin to here from
Creating rc_dae.r
Creating rc_sympar.txt
Creating rc_sympar.r
Creating rc_cse.r
Creating rc_sspar.r
Creating rc_csm.r
Creating rc_ode.r
Creating rc_ss.r
Creating rc_sm.r
Creating rc_switch.txt
0 switches found
Creating rc_sympars.txt
Creating rc_sm.m
Copying rc_sm.m
octave&gt; mtt("rc","numpar");
Creating rc_numpar.txt
Creating rc_numpar.m
Copying rc_numpar.m
octave&gt; mtt("rc","sympar");
Creating rc_sympar.m
Copying rc_sympar.m
octave&gt; par = rc_numpar
par =

  1
  1

octave&gt; sym = rc_sympar;

octave&gt; par(sym.r) = 0.1;
octave&gt; [A,B,C,D] = rc_sm(par)
A = -10

B = 10

C = 1

D = 0

octave&gt; 
</PRE>
      </TD>
    </TR>
  </TABLE>generates the data structure rc corresponding the the bond graph of
  the system called `rc'. The following octave commands then generate the
  step reponse and bode diagram respectively:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>step(rc);
bode(rc);
</PRE>
      </TD>
    </TR>
  </TABLE>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC169">10.4.1 Octave
      control system toolbox (OCST)</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC170">10.4.2 Creating
      GNU Octave .oct files</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC171">10.4.3 Creating
      Matlab .mex files</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC172">10.4.4
      Embedding MTT models in Simulink</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Octave control system toolbox (OCST)"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>10.4.1 Octave control system toolbox (OCST)</H3><!--docid::SEC169::-->
  <P><STRONG>MTT</STRONG> provides an interface to the Octave control system
  toolbox (OCST) using the mfile <CODE>mtt2sys</CODE>. the octave command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>help mtt2sys
</PRE>
      </TD>
    </TR>
  </TABLE>gives the following information.
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE> usage:  sys = mtt2sys (Name[,par])

 Creates a sys structure for the Octave Control Systems Toolbox
 from an MTT system with name "Name"
 Optional second argument is system parameter list
 Assumes that Name_sm.m, Name_struc.m and Name_numpar.m exist
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Thus for example, if octave is in the directory containing the system
  rc:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>rc = mtt2sys("rc");
</PRE>
      </TD>
    </TR>
  </TABLE>generates the data structure rc corresponding the the bond graph of
  the system called `rc'. The following octave commands then generate the
  step reponse and bode diagram respectively:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>step(rc);
bode(rc);
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Creating GNU Octave .oct files"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>10.4.2 Creating GNU Octave .oct files</H3><!--docid::SEC170::-->
  <P>GNU Octave dynamically loaded functions (.oct files) can be created by
  instructing <STRONG>MTT</STRONG> to create the "oct" representation:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt [options] sys ode oct
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>This will cause <STRONG>MTT</STRONG> to create the C++ representation of
  the system (sys_ode.cc) and to then compile it as a shared object suitable
  for use within Octave. The resultant file may be used in an identical
  manner to the equivalent, but generally slower, interpreted .m file.</P>
  <P>Usage information for the function may be obtained within Octave in the
  usual manner:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  octave:1&gt; help rc_ode

  rc_ode is the dynamically-linked function from the file
  /home/mttuser/rc/rc_ode.oct

  Usage: [mttdx] = rc_ode(mttx,mttu,mttt,mttpar)
  Octave ode representation of system rc
  Generated by MTT on Fri Jul  5 11:23:08 BST 2002
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Note that the first line of output from Octave identifies whether the
  compiled or interpreted function is being used.</P>
  <P>Alternatively, standard representations may be generated using the
  Octave DLDs by use of the "-oct" switch:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt -oct rc odeso view
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>In order to successfully generate .oct files, Octave must be correctly
  configured prior to compilation and certain headers and libraries must be
  correctly installed on the system (see section <A href=
  "mtt.html#SEC179">11.3.2 .oct file dependencies</A>).</P>
  <P><A name="Creating Matlab .mex files"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>10.4.3 Creating Matlab .mex files</H3><!--docid::SEC171::-->
  <P>On GNU/Linux systems, Matlab dynamically linked executables (.mexglx
  files) can created by instructing <STRONG>MTT</STRONG> to create the
  "mexglx" representation:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt [options] sys ode mexglx
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>This will cause <STRONG>MTT</STRONG> to create the C++ representation of
  the system (sys_ode.cc) and to then compile it as a shared object suitable
  for use within Matlab.</P>
  <P>If it is necessary to compile mex files for another platform, then the
  usual C++ representation (generated with the -cc flag) can be created and
  the resultant file compiled with the -DCODEGENTARGET=MATLABMEX flag on the
  target platform.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt_machine:
  mtt -cc rc ode cc

  matlab_machine:
  matlab&gt; mex -DCODEGENTARGET=MATLABMEX rc_ode.cc
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="Embedding MTT models in Simulink"></A></P>
  <HR size="6">
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  </TABLE>
  <H3>10.4.4 Embedding MTT models in Simulink</H3><!--docid::SEC172::-->
  <P>It is possible to embed <STRONG>MTT</STRONG> functions or entire
  <STRONG>MTT</STRONG> models within Simulink simulations as Sfun blocks. If
  the zip package is installed on the system, the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt sys sfun zip
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>will create a compressed archive containing sys.mdl, which may be
  embedded into a larger Simulink model. Also contained within the archive
  will be four sys_sfun*.c files,</P>
  <UL>
    <LI>sys_sfun.c model state and output equations</LI>
    <LI>sys_sfun_ae.c model algebraic equations</LI>
    <LI>sys_sfun_input.c model inputs</LI>
    <LI>sys_sfun_interface.c interface between MTT model and Simulink</LI>
  </UL>
  <P>The last of these files must be edited to correctly map the inputs and
  outputs between the <STRONG>MTT</STRONG> and Simulink models. The two
  sections to edit are clearly marked with</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  <CODE>/* Start EDIT */</CODE>
  <CODE>....</CODE>
  <CODE>/* End EDIT */</CODE>
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>These four files should then be compiled with the Matlab "mex" compiler
  as described in the <EM>README</EM> file in the archive.</P>
  <P>If it is desired to compile the .mex files directly from within
  <STRONG>MTT</STRONG> on a machine which has the Matlab header files
  installed, this may be done with the command</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>  mtt sys sfun mexglx 
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>which will generated the four .mex files and the .mdl file. In this
  case, the user must ensure that <EM>sys_sfun_interface.c</EM> has been
  correctly edited prior to compilation.</P>
  <P>Note that solution of algebraic equations within Simulink is not
  possible unless the <EM>Matlab Optimisation Toolbox</EM> is installed.</P>
  <P><A name="LaTeX" id="LaTeX"></A></P>
  <HR size="6">
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  <H2>10.5 LaTeX</H2><!--docid::SEC173::-->
  <P>LaTeX is a powerful text processor which <STRONG>MTT</STRONG> uses to
  provide visual output.</P>
  <P><A name="Administration" id="Administration"></A></P>
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  <A name="SEC174" id="SEC174"></A>
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  <H1>11. Administration</H1><!--docid::SEC174::-->
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC175">11.1 Software
      components</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC176">11.2 REDUCE
      setup</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC177">11.3 Octave
      setup</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC180">11.4
      Paths</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC186">11.5 File
      structure</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC188">A.1 GNU Free
      Documentation License</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC190">A.2 GNU GENERAL
      PUBLIC LICENSE</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="Software components"></A></P>
  <HR size="6">
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    </TR>
  </TABLE>
  <H2>11.1 Software components</H2><!--docid::SEC175::-->
  <P><STRONG>MTT</STRONG> is built from a set of readily-available software
  tools. These are:</P>
  <UL>
    <LI>General purpose software tools.</LI>
    <LI>Octave (see section <A href="mtt.html#SEC177">11.3 Octave
    setup</A>)</LI>
    <LI>REDUCE (see section <A href="mtt.html#SEC176">11.2 REDUCE
    setup</A>)</LI>
  </UL>
  <P>The General purpose tools are (these will all be available with a
  standard Linux distribution):</P>
  <DL compact>
    <DT><A name="IDX541" id="IDX541"></A> <CODE>sh</CODE></DT>
    <DD><A name="IDX542" id="IDX542"></A> Bourne shell</DD>
    <DT><A name="IDX543" id="IDX543"></A> <CODE>gmake</CODE></DT>
    <DD><A name="IDX544" id="IDX544"></A> Gnu make</DD>
    <DT><A name="IDX545" id="IDX545"></A> <CODE>gawk</CODE></DT>
    <DD><A name="IDX546" id="IDX546"></A> Gnu awk</DD>
    <DT><A name="IDX547" id="IDX547"></A> <CODE>sed</CODE></DT>
    <DD><A name="IDX548" id="IDX548"></A> Gnu sed</DD>
    <DT><A name="IDX549" id="IDX549"></A> <CODE>grep</CODE></DT>
    <DD><A name="IDX550" id="IDX550"></A> Gnu grep</DD>
    <DT><A name="IDX551" id="IDX551"></A> <CODE>comm</CODE></DT>
    <DD><A name="IDX552" id="IDX552"></A> Gnu Compare sorted files by
    line</DD>
    <DT><A name="IDX553" id="IDX553"></A> <CODE>xfig</CODE></DT>
    <DD><A name="IDX554" id="IDX554"></A> Figure editor, version 3 or
    greater.</DD>
    <DT><A name="IDX555" id="IDX555"></A> <CODE>fig2dev</CODE></DT>
    <DD><A name="IDX556" id="IDX556"></A> Fig file conversion, version 3 or
    greater.</DD>
    <DT><A name="IDX557" id="IDX557"></A> <CODE>ghostview</CODE></DT>
    <DD><A name="IDX558" id="IDX558"></A> postscript viewer</DD>
    <DT><A name="IDX559" id="IDX559"></A> <CODE>xdvi</CODE></DT>
    <DD><A name="IDX560" id="IDX560"></A> dvi viewer</DD>
    <DT><A name="IDX561" id="IDX561"></A> <CODE>dvips</CODE></DT>
    <DD><A name="IDX562" id="IDX562"></A> dvi to postscript conversion</DD>
    <DT><A name="IDX563" id="IDX563"></A> <CODE>latex</CODE></DT>
    <DD><A name="IDX564" id="IDX564"></A> the text processor (LaTeX2e
    needed)</DD>
    <DT><A name="IDX565" id="IDX565"></A> <CODE>latex2html</CODE></DT>
    <DD><A name="IDX566" id="IDX566"></A> converts latex to html</DD>
    <DT><A name="IDX567" id="IDX567"></A> <CODE>perl</CODE></DT>
    <DD><A name="IDX568" id="IDX568"></A> needed for latex2html</DD>
    <DT><A name="IDX569" id="IDX569"></A> <CODE>gnuplot</CODE></DT>
    <DD><A name="IDX570" id="IDX570"></A> a graph plotting program</DD>
    <DT><A name="IDX571" id="IDX571"></A> <CODE>gnuscape</CODE></DT>
    <DD><A name="IDX572" id="IDX572"></A> or other web/html browser such as
    netscape, Red Baron etc.</DD>
    <DT><A name="IDX573" id="IDX573"></A> <CODE>gcc</CODE></DT>
    <DD><A name="IDX574" id="IDX574"></A> GNU c compiler</DD>
  </DL>
  <P>&lt;A HREF="http://home.pages.de/~GNU/"&gt;GNU&lt;/A&gt;
  documentation.</P>
  <P><A name="REDUCE setup"></A></P>
  <HR size="6">
  <A name="SEC176" id="SEC176"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC177">&gt;</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>11.2 REDUCE setup</H2><!--docid::SEC176::-->
  <P>Symbolic algebra is performed by REDUCE, which although not free
  software is the the result of international collaboration. The version I
  use is obtained from:</P>
  <BLOCKQUOTE>
    ZIB ( http://www.zib.de )
  </BLOCKQUOTE>&lt;A
  HREF="http://www.rrz.uni-koeln.de/REDUCE/"&gt;REDUCE&lt;/A&gt;
  documentation. &lt;A HREF="http://www.zib.de"&gt;ZIB&lt;/A&gt;
  documentation.
  <P><A name="Octave setup"></A></P>
  <HR size="6">
  <A name="SEC177" id="SEC177"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      ]</TD>
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      <TD valign="middle" align="left">[ <A href=
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>11.3 Octave setup</H2><!--docid::SEC177::-->
  <P>Octave is available at various web sites including: <A href=
  "http://www.octave.org">http://www.octave.org</A></P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC178">11.3.1
      .octaverc</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC179">11.3.2 .oct
      file dependencies</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name=".octaverc" id=".octaverc"></A></P>
  <HR size="6">
  <A name="SEC178" id="SEC178"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC179">&gt;</A>
      ]</TD>
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      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC177">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.3.1 .octaverc</H3><!--docid::SEC178::-->
  <P>The `<TT>.octaverc</TT>' file should contain the following lines:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Startup file for Octave for use with MTT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

implicit_str_to_num_ok = 1;
empty_list_elements_ok = 1;

</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name=".oct file dependencies"></A></P>
  <HR size="6">
  <A name="SEC179" id="SEC179"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.3.2 .oct file dependencies</H3><!--docid::SEC179::-->
  Successful compilation of .oct code requires that Octave has been
  configured to use dynamically linked libraries and that the Octave
  libraries <CODE>liboctave</CODE>, <CODE>libcruft</CODE> and
  <CODE>liboctinterp</CODE> are available on the system.
  <P>This can be acheived by compiling Octave from the source code,
  configured with the options <CODE>--enable-shared</CODE> and
  <CODE>--enable-dl</CODE>.</P>
  <P>A number of additional libraries and headers are also required to be
  installed on a system. These include,</P>
  <UL>
    <LI><EM>ncurses</EM> and <EM>readline</EM> terminal control routines</LI>
    <LI><EM>blas</EM> or <EM>altas</EM> basic linear algebra subprograms,
    usually optimised for the specific processor</LI>
    <LI><EM>fftw</EM> fast Fourier transform routines</LI>
    <LI><EM>g2c</EM> GNU Fortran to C conversion routines</LI>
    <LI><EM>kpathsea</EM> TeX path search routines</LI>
  </UL>
  <P>Note that on many GNU/Linux distributions, the necessary headers are
  contained in development packages which must be installed in addition to
  the standard library package.</P>
  <P>Further information on configuring and installing Octave to handle
  dynamic libraries (DLDs) can be found in the <A href=
  "http://www.octave.org/docs.html">Octave documentation</A>.</P>
  <P><A name="Paths" id="Paths"></A></P>
  <HR size="6">
  <A name="SEC180" id="SEC180"></A>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>11.4 Paths</H2><!--docid::SEC180::-->
  <P>There are a number of paths that must be set correctely for
  <STRONG>MTT</STRONG> to work. These are normally set up by sourcing the
  file <CODE>mttrc</CODE> that lives in the <STRONG>MTT</STRONG> home
  directory.</P>
  <TABLE border="0" cellspacing="0">
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC181">11.4.1
      $MTTPATH</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC182">11.4.2
      $MTT_COMPONENTS</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC183">11.4.3
      $MTT_CRS</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC184">11.4.4
      $MTT_EXAMPLES</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
    <TR>
      <TD align="left" valign="top"><A href="mtt.html#SEC185">11.4.5
      $OCTAVE_PATH</A></TD>
      <TD></TD>
      <TD align="left" valign="top"></TD>
    </TR>
  </TABLE>
  <P><A name="$MTTPATH" id="$MTTPATH"></A></P>
  <HR size="6">
  <A name="SEC181" id="SEC181"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC180">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC182">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.4.1 $MTTPATH</H3><!--docid::SEC181::-->
  The environment variable $MTTPATH points to the mtt home directory. This is
  usually <CODE>/usr/local/lib/mtt</CODE>.
  <P><A name="$MTT_COMPONENTS" id="$MTT_COMPONENTS"></A></P>
  <HR size="6">
  <A name="SEC182" id="SEC182"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC183">&gt;</A>
      ]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC180">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.4.2 $MTT_COMPONENTS</H3><!--docid::SEC182::-->
  The environment variable $MTT_COMPONENTS is a colon-separated path pointing
  to directories containing components and subsystems. By default
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_COMPONENTS=.:$MTT_LIB/lib/comp/
</PRE>
      </TD>
    </TR>
  </TABLE>but you may wish to add your own component libraries:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_COMPONENTS=my_library_path:$MTT_COMPONENTS
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="$MTT_CRS" id="$MTT_CRS"></A></P>
  <HR size="6">
  <A name="SEC183" id="SEC183"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC182">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC184">&gt;</A>
      ]</TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC180">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.4.3 $MTT_CRS</H3><!--docid::SEC183::-->
  The environment variable $MTT_CRS is a colon-separated path pointing to
  directories containing constitutive relationships. By default
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_CRS=$MTTPATH/lib/cr
</PRE>
      </TD>
    </TR>
  </TABLE>but you may wish to add your own component libraries:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_CRS=my_cr_path:$MTT_CRS
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="$MTT_EXAMPLES" id="$MTT_EXAMPLES"></A></P>
  <HR size="6">
  <A name="SEC184" id="SEC184"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Contents">Contents</A>]</TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H3>11.4.4 $MTT_EXAMPLES</H3><!--docid::SEC184::-->
  The environment variable $MTT_EXAMPLES is a colon-separated path pointing
  to directories containing EXAMPLES and subsystems. By default
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_EXAMPLES=$MTTPATH/lib/examples
</PRE>
      </TD>
    </TR>
  </TABLE>but you may wish to add your own component libraries:
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>MTT_EXAMPLES=my_examples_path:$MTT_EXAMPLES
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="$OCTAVE_PATH" id="$OCTAVE_PATH"></A></P>
  <HR size="6">
  <A name="SEC185" id="SEC185"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC184">&lt;</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC186">&gt;</A>
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      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      ]</TD>
    </TR>
  </TABLE>
  <H3>11.4.5 $OCTAVE_PATH</H3><!--docid::SEC185::-->
  <P>The <CODE>$OCTAVE_PATH</CODE> path must include the relevant paths for
  mtt to work properly. In particular, it must include:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>$MTTPATH/trans/m
$MTTPATH/lib/comp/simple
$MTTPATH/lib/comp/compound
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P><A name="File structure"></A></P>
  <HR size="6">
  <A name="SEC186" id="SEC186"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC185">&lt;</A>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC187">&gt;</A>
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      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC174">Up</A>
      ]</TD>
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      <TD valign="middle" align="left"></TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>11.5 File structure</H2><!--docid::SEC186::-->
  The recommended installation of <STRONG>MTT</STRONG> uses the following
  directory structure with corresponding contents. Normally, each of the
  listed directories is a subdirectory of `<TT>/usr/local</TT>'. The
  directory <CODE>mtt</CODE> is pointed to by $MTTPATH (see section <A href=
  "mtt.html#SEC181">11.4.1 $MTTPATH</A>).
  <DL compact>
    <DT><A name="IDX575" id="IDX575"></A> `<TT>mtt/bin</TT>'</DT>
    <DD><A name="IDX576" id="IDX576"></A> This is the home directory for
    <STRONG>MTT</STRONG>. <STRONG>MTT</STRONG> itself lives here along with
    `<TT>mttrc</TT>'.</DD>
    <DT><A name="IDX577" id="IDX577"></A> `<TT>mtt/bin/trans</TT>'</DT>
    <DD><A name="IDX578" id="IDX578"></A> The transformations executed by
    <STRONG>MTT</STRONG>.</DD>
    <DT><A name="IDX579" id="IDX579"></A> `<TT>mtt/bin/trans/m</TT>'</DT>
    <DD><A name="IDX580" id="IDX580"></A> The <CODE>m-files</CODE> associated
    with the transformations.</DD>
    <DT><A name="IDX581" id="IDX581"></A> `<TT>mtt/bin/trans/awk</TT>'</DT>
    <DD><A name="IDX582" id="IDX582"></A> The <CODE>awk</CODE> scripts
    associated with the transformations.</DD>
    <DT><A name="IDX583" id="IDX583"></A> `<TT>mtt/lib</TT>'</DT>
    <DD><A name="IDX584" id="IDX584"></A> The place for components, examples
    and CRs which will be updated.</DD>
    <DT><A name="IDX585" id="IDX585"></A> `<TT>mtt/lib/comp/simple</TT>'</DT>
    <DD><A name="IDX586" id="IDX586"></A> <A name="IDX587" id="IDX587"></A>
    The <CODE>m-files</CODE> defining the simple components. <A name="IDX588"
    id="IDX588"></A></DD>
    <DT><A name="IDX589" id="IDX589"></A>
    `<TT>mtt/lib/comp/compound</TT>'</DT>
    <DD><A name="IDX590" id="IDX590"></A> The <CODE>m-files</CODE> defining
    the compound components.</DD>
    <DT><A name="IDX591" id="IDX591"></A> `<TT>mtt/lib/cr/r</TT>'</DT>
    <DD><A name="IDX592" id="IDX592"></A> constitutive relationship
    definitions</DD>
    <DT><A name="IDX593" id="IDX593"></A> `<TT>mtt/lib/examples</TT>'</DT>
    <DD><A name="IDX594" id="IDX594"></A> Some examples.</DD>
    <DT><A name="IDX595" id="IDX595"></A>
    `<TT>mtt/examples/metamodelling</TT>'</DT>
    <DD><A name="IDX596" id="IDX596"></A> Examples from the book.</DD>
    <DT><A name="IDX597" id="IDX597"></A> `<TT>mtt/doc</TT>'</DT>
    <DD><A name="IDX598" id="IDX598"></A> The documentation files for
    <STRONG>MTT</STRONG>.</DD>
    <DT><A name="IDX599" id="IDX599"></A> `<TT>mtt/doc/Examples</TT>'</DT>
    <DD><A name="IDX600" id="IDX600"></A> Examples used in the
    documentation.</DD>
  </DL>
  <HR size="6">
  <A name="SEC187" id="SEC187"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      <TD valign="middle" align="left">[ <A href=
      "mtt.html#SEC174">&lt;&lt;</A> ]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC174">Up</A>
      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H1>A. Legal stuff</H1><!--docid::SEC187::-->
  <A name="GNU Free Documentation License"></A>
  <HR size="6">
  <A name="SEC188" id="SEC188"></A>
  <TABLE cellpadding="1" cellspacing="1" border="0">
    <TR>
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      ]</TD>
      <TD valign="middle" align="left">[ <A href=
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      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left"></TD>
      <TD valign="middle" align="left">[<A href=
      "mtt.html#SEC_Top">Top</A>]</TD>
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      "mtt.html#SEC_Contents">Contents</A>]</TD>
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      "mtt.html#SEC194">Index</A>]</TD>
      <TD valign="middle" align="left">[ <A href="mtt.html#SEC_About">?</A>
      ]</TD>
    </TR>
  </TABLE>
  <H2>A.1 GNU Free Documentation License</H2><!--docid::SEC188::-->
  <P><A name="IDX601" id="IDX601"></A></P>
  <DIV class="c1">
    Version 1.2, November 2002
  </DIV>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="display">
        <PRE class=
        "c2">Copyright © 2000,2001,2002 Free Software Foundation, Inc.
59 Temple Place, Suite 330, Boston, MA  02111-1307, USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
</PRE>
      </TD>
    </TR>
  </TABLE>
  <OL>
    <LI>PREAMBLE
      <P>The purpose of this License is to make a manual, textbook, or other
      functional and useful document <EM>free</EM> in the sense of freedom:
      to assure everyone the effective freedom to copy and redistribute it,
      with or without modifying it, either commercially or noncommercially.
      Secondarily, this License preserves for the author and publisher a way
      to get credit for their work, while not being considered responsible
      for modifications made by others.</P>
      <P>This License is a kind of "copyleft", which means that derivative
      works of the document must themselves be free in the same sense. It
      complements the GNU General Public License, which is a copyleft license
      designed for free software.</P>
      <P>We have designed this License in order to use it for manuals for
      free software, because free software needs free documentation: a free
      program should come with manuals providing the same freedoms that the
      software does. But this License is not limited to software manuals; it
      can be used for any textual work, regardless of subject matter or
      whether it is published as a printed book. We recommend this License
      principally for works whose purpose is instruction or reference.</P>
    </LI>
    <LI>APPLICABILITY AND DEFINITIONS
      <P>This License applies to any manual or other work, in any medium,
      that contains a notice placed by the copyright holder saying it can be
      distributed under the terms of this License. Such a notice grants a
      world-wide, royalty-free license, unlimited in duration, to use that
      work under the conditions stated herein. The "Document", below, refers
      to any such manual or work. Any member of the public is a licensee, and
      is addressed as "you". You accept the license if you copy, modify or
      distribute the work in a way requiring permission under copyright
      law.</P>
      <P>A "Modified Version" of the Document means any work containing the
      Document or a portion of it, either copied verbatim, or with
      modifications and/or translated into another language.</P>
      <P>A "Secondary Section" is a named appendix or a front-matter section
      of the Document that deals exclusively with the relationship of the
      publishers or authors of the Document to the Document's overall subject
      (or to related matters) and contains nothing that could fall directly
      within that overall subject. (Thus, if the Document is in part a
      textbook of mathematics, a Secondary Section may not explain any
      mathematics.) The relationship could be a matter of historical
      connection with the subject or with related matters, or of legal,
      commercial, philosophical, ethical or political position regarding
      them.</P>
      <P>The "Invariant Sections" are certain Secondary Sections whose titles
      are designated, as being those of Invariant Sections, in the notice
      that says that the Document is released under this License. If a
      section does not fit the above definition of Secondary then it is not
      allowed to be designated as Invariant. The Document may contain zero
      Invariant Sections. If the Document does not identify any Invariant
      Sections then there are none.</P>
      <P>The "Cover Texts" are certain short passages of text that are
      listed, as Front-Cover Texts or Back-Cover Texts, in the notice that
      says that the Document is released under this License. A Front-Cover
      Text may be at most 5 words, and a Back-Cover Text may be at most 25
      words.</P>
      <P>A "Transparent" copy of the Document means a machine-readable copy,
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      public, that is suitable for revising the document straightforwardly
      with generic text editors or (for images composed of pixels) generic
      paint programs or (for drawings) some widely available drawing editor,
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      translation to a variety of formats suitable for input to text
      formatters. A copy made in an otherwise Transparent file format whose
      markup, or absence of markup, has been arranged to thwart or discourage
      subsequent modification by readers is not Transparent. An image format
      is not Transparent if used for any substantial amount of text. A copy
      that is not "Transparent" is called "Opaque".</P>
      <P>Examples of suitable formats for Transparent copies include plain
      ASCII without markup, Texinfo input format, LaTeX input format,
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      publicly available <SPAN class="c3">DTD</SPAN>, and standard-conforming
      simple <SPAN class="c3">HTML</SPAN>, PostScript or <SPAN class=
      "c3">PDF</SPAN> designed for human modification. Examples of
      transparent image formats include <SPAN class="c3">PNG</SPAN>,
      <SPAN class="c3">XCF</SPAN> and <SPAN class="c3">JPG</SPAN>. Opaque
      formats include proprietary formats that can be read and edited only by
      proprietary word processors, <SPAN class="c3">SGML</SPAN> or
      <SPAN class="c3">XML</SPAN> for which the <SPAN class="c3">DTD</SPAN>
      and/or processing tools are not generally available, and the
      machine-generated <SPAN class="c3">HTML</SPAN>, PostScript or
      <SPAN class="c3">PDF</SPAN> produced by some word processors for output
      purposes only.</P>
      <P>The "Title Page" means, for a printed book, the title page itself,
      plus such following pages as are needed to hold, legibly, the material
      this License requires to appear in the title page. For works in formats
      which do not have any title page as such, "Title Page" means the text
      near the most prominent appearance of the work's title, preceding the
      beginning of the body of the text.</P>
      <P>A section "Entitled XYZ" means a named subunit of the Document whose
      title either is precisely XYZ or contains XYZ in parentheses following
      text that translates XYZ in another language. (Here XYZ stands for a
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      of such a section when you modify the Document means that it remains a
      section "Entitled XYZ" according to this definition.</P>
      <P>The Document may include Warranty Disclaimers next to the notice
      which states that this License applies to the Document. These Warranty
      Disclaimers are considered to be included by reference in this License,
      but only as regards disclaiming warranties: any other implication that
      these Warranty Disclaimers may have is void and has no effect on the
      meaning of this License.</P>
    </LI>
    <LI>VERBATIM COPYING
      <P>You may copy and distribute the Document in any medium, either
      commercially or noncommercially, provided that this License, the
      copyright notices, and the license notice saying this License applies
      to the Document are reproduced in all copies, and that you add no other
      conditions whatsoever to those of this License. You may not use
      technical measures to obstruct or control the reading or further
      copying of the copies you make or distribute. However, you may accept
      compensation in exchange for copies. If you distribute a large enough
      number of copies you must also follow the conditions in section 3.</P>
      <P>You may also lend copies, under the same conditions stated above,
      and you may publicly display copies.</P>
    </LI>
    <LI>COPYING IN QUANTITY
      <P>If you publish printed copies (or copies in media that commonly have
      printed covers) of the Document, numbering more than 100, and the
      Document's license notice requires Cover Texts, you must enclose the
      copies in covers that carry, clearly and legibly, all these Cover
      Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on
      the back cover. Both covers must also clearly and legibly identify you
      as the publisher of these copies. The front cover must present the full
      title with all words of the title equally prominent and visible. You
      may add other material on the covers in addition. Copying with changes
      limited to the covers, as long as they preserve the title of the
      Document and satisfy these conditions, can be treated as verbatim
      copying in other respects.</P>
      <P>If the required texts for either cover are too voluminous to fit
      legibly, you should put the first ones listed (as many as fit
      reasonably) on the actual cover, and continue the rest onto adjacent
      pages.</P>
      <P>If you publish or distribute Opaque copies of the Document numbering
      more than 100, you must either include a machine-readable Transparent
      copy along with each Opaque copy, or state in or with each Opaque copy
      a computer-network location from which the general network-using public
      has access to download using public-standard network protocols a
      complete Transparent copy of the Document, free of added material. If
      you use the latter option, you must take reasonably prudent steps, when
      you begin distribution of Opaque copies in quantity, to ensure that
      this Transparent copy will remain thus accessible at the stated
      location until at least one year after the last time you distribute an
      Opaque copy (directly or through your agents or retailers) of that
      edition to the public.</P>
      <P>It is requested, but not required, that you contact the authors of
      the Document well before redistributing any large number of copies, to
      give them a chance to provide you with an updated version of the
      Document.</P>
    </LI>
    <LI>MODIFICATIONS
      <P>You may copy and distribute a Modified Version of the Document under
      the conditions of sections 2 and 3 above, provided that you release the
      Modified Version under precisely this License, with the Modified
      Version filling the role of the Document, thus licensing distribution
      and modification of the Modified Version to whoever possesses a copy of
      it. In addition, you must do these things in the Modified Version:</P>
      <OL>
        <LI>Use in the Title Page (and on the covers, if any) a title
        distinct from that of the Document, and from those of previous
        versions (which should, if there were any, be listed in the History
        section of the Document). You may use the same title as a previous
        version if the original publisher of that version gives
        permission.</LI>
        <LI>List on the Title Page, as authors, one or more persons or
        entities responsible for authorship of the modifications in the
        Modified Version, together with at least five of the principal
        authors of the Document (all of its principal authors, if it has
        fewer than five), unless they release you from this requirement.</LI>
        <LI>State on the Title page the name of the publisher of the Modified
        Version, as the publisher.</LI>
        <LI>Preserve all the copyright notices of the Document.</LI>
        <LI>Add an appropriate copyright notice for your modifications
        adjacent to the other copyright notices.</LI>
        <LI>Include, immediately after the copyright notices, a license
        notice giving the public permission to use the Modified Version under
        the terms of this License, in the form shown in the Addendum
        below.</LI>
        <LI>Preserve in that license notice the full lists of Invariant
        Sections and required Cover Texts given in the Document's license
        notice.</LI>
        <LI>Include an unaltered copy of this License.</LI>
        <LI>Preserve the section Entitled "History", Preserve its Title, and
        add to it an item stating at least the title, year, new authors, and
        publisher of the Modified Version as given on the Title Page. If
        there is no section Entitled "History" in the Document, create one
        stating the title, year, authors, and publisher of the Document as
        given on its Title Page, then add an item describing the Modified
        Version as stated in the previous sentence.</LI>
        <LI>Preserve the network location, if any, given in the Document for
        public access to a Transparent copy of the Document, and likewise the
        network locations given in the Document for previous versions it was
        based on. These may be placed in the "History" section. You may omit
        a network location for a work that was published at least four years
        before the Document itself, or if the original publisher of the
        version it refers to gives permission.</LI>
        <LI>For any section Entitled "Acknowledgements" or "Dedications",
        Preserve the Title of the section, and preserve in the section all
        the substance and tone of each of the contributor acknowledgements
        and/or dedications given therein.</LI>
        <LI>Preserve all the Invariant Sections of the Document, unaltered in
        their text and in their titles. Section numbers or the equivalent are
        not considered part of the section titles.</LI>
        <LI>Delete any section Entitled "Endorsements". Such a section may
        not be included in the Modified Version.</LI>
        <LI>Do not retitle any existing section to be Entitled "Endorsements"
        or to conflict in title with any Invariant Section.</LI>
        <LI>Preserve any Warranty Disclaimers.</LI>
      </OL>
      <P>If the Modified Version includes new front-matter sections or
      appendices that qualify as Secondary Sections and contain no material
      copied from the Document, you may at your option designate some or all
      of these sections as invariant. To do this, add their titles to the
      list of Invariant Sections in the Modified Version's license notice.
      These titles must be distinct from any other section titles.</P>
      <P>You may add a section Entitled "Endorsements", provided it contains
      nothing but endorsements of your Modified Version by various
      parties--for example, statements of peer review or that the text has
      been approved by an organization as the authoritative definition of a
      standard.</P>
      <P>You may add a passage of up to five words as a Front-Cover Text, and
      a passage of up to 25 words as a Back-Cover Text, to the end of the
      list of Cover Texts in the Modified Version. Only one passage of
      Front-Cover Text and one of Back-Cover Text may be added by (or through
      arrangements made by) any one entity. If the Document already includes
      a cover text for the same cover, previously added by you or by
      arrangement made by the same entity you are acting on behalf of, you
      may not add another; but you may replace the old one, on explicit
      permission from the previous publisher that added the old one.</P>
      <P>The author(s) and publisher(s) of the Document do not by this
      License give permission to use their names for publicity for or to
      assert or imply endorsement of any Modified Version.</P>
    </LI>
    <LI>COMBINING DOCUMENTS
      <P>You may combine the Document with other documents released under
      this License, under the terms defined in section 4 above for modified
      versions, provided that you include in the combination all of the
      Invariant Sections of all of the original documents, unmodified, and
      list them all as Invariant Sections of your combined work in its
      license notice, and that you preserve all their Warranty
      Disclaimers.</P>
      <P>The combined work need only contain one copy of this License, and
      multiple identical Invariant Sections may be replaced with a single
      copy. If there are multiple Invariant Sections with the same name but
      different contents, make the title of each such section unique by
      adding at the end of it, in parentheses, the name of the original
      author or publisher of that section if known, or else a unique number.
      Make the same adjustment to the section titles in the list of Invariant
      Sections in the license notice of the combined work.</P>
      <P>In the combination, you must combine any sections Entitled "History"
      in the various original documents, forming one section Entitled
      "History"; likewise combine any sections Entitled "Acknowledgements",
      and any sections Entitled "Dedications". You must delete all sections
      Entitled "Endorsements."</P>
    </LI>
    <LI>COLLECTIONS OF DOCUMENTS
      <P>You may make a collection consisting of the Document and other
      documents released under this License, and replace the individual
      copies of this License in the various documents with a single copy that
      is included in the collection, provided that you follow the rules of
      this License for verbatim copying of each of the documents in all other
      respects.</P>
      <P>You may extract a single document from such a collection, and
      distribute it individually under this License, provided you insert a
      copy of this License into the extracted document, and follow this
      License in all other respects regarding verbatim copying of that
      document.</P>
    </LI>
    <LI>AGGREGATION WITH INDEPENDENT WORKS
      <P>A compilation of the Document or its derivatives with other separate
      and independent documents or works, in or on a volume of a storage or
      distribution medium, is called an "aggregate" if the copyright
      resulting from the compilation is not used to limit the legal rights of
      the compilation's users beyond what the individual works permit. When
      the Document is included in an aggregate, this License does not apply
      to the other works in the aggregate which are not themselves derivative
      works of the Document.</P>
      <P>If the Cover Text requirement of section 3 is applicable to these
      copies of the Document, then if the Document is less than one half of
      the entire aggregate, the Document's Cover Texts may be placed on
      covers that bracket the Document within the aggregate, or the
      electronic equivalent of covers if the Document is in electronic form.
      Otherwise they must appear on printed covers that bracket the whole
      aggregate.</P>
    </LI>
    <LI>TRANSLATION
      <P>Translation is considered a kind of modification, so you may
      distribute translations of the Document under the terms of section 4.
      Replacing Invariant Sections with translations requires special
      permission from their copyright holders, but you may include
      translations of some or all Invariant Sections in addition to the
      original versions of these Invariant Sections. You may include a
      translation of this License, and all the license notices in the
      Document, and any Warranty Disclaimers, provided that you also include
      the original English version of this License and the original versions
      of those notices and disclaimers. In case of a disagreement between the
      translation and the original version of this License or a notice or
      disclaimer, the original version will prevail.</P>
      <P>If a section in the Document is Entitled "Acknowledgements",
      "Dedications", or "History", the requirement (section 4) to Preserve
      its Title (section 1) will typically require changing the actual
      title.</P>
    </LI>
    <LI>TERMINATION
      <P>You may not copy, modify, sublicense, or distribute the Document
      except as expressly provided for under this License. Any other attempt
      to copy, modify, sublicense or distribute the Document is void, and
      will automatically terminate your rights under this License. However,
      parties who have received copies, or rights, from you under this
      License will not have their licenses terminated so long as such parties
      remain in full compliance.</P>
    </LI>
    <LI>FUTURE REVISIONS OF THIS LICENSE
      <P>The Free Software Foundation may publish new, revised versions of
      the GNU Free Documentation License from time to time. Such new versions
      will be similar in spirit to the present version, but may differ in
      detail to address new problems or concerns. See <A href=
      "http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</A>.</P>
      <P>Each version of the License is given a distinguishing version
      number. If the Document specifies that a particular numbered version of
      this License "or any later version" applies to it, you have the option
      of following the terms and conditions either of that specified version
      or of any later version that has been published (not as a draft) by the
      Free Software Foundation. If the Document does not specify a version
      number of this License, you may choose any version ever published (not
      as a draft) by the Free Software Foundation.</P>
    </LI>
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  <H3>A.1.1 ADDENDUM: How to use this License for your documents</H3>
  <!--docid::SEC189::-->
  <P>To use this License in a document you have written, include a copy of
  the License in the document and put the following copyright and license
  notices just after the title page:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="smallexample">
        <PRE class=
        "c4">  Copyright (C)  <VAR>year</VAR>  <VAR>your name</VAR>.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.2
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
  replace the "with...Texts." line with this:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="smallexample">
        <PRE class=
        "c4">    with the Invariant Sections being <VAR>list their titles</VAR>, with
    the Front-Cover Texts being <VAR>list</VAR>, and with the Back-Cover Texts
    being <VAR>list</VAR>.
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>If you have Invariant Sections without Cover Texts, or some other
  combination of the three, merge those two alternatives to suit the
  situation.</P>
  <P>If your document contains nontrivial examples of program code, we
  recommend releasing these examples in parallel under your choice of free
  software license, such as the GNU General Public License, to permit their
  use in free software.</P>
  <P><A name="Copying" id="Copying"></A></P>
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  <H2>A.2 GNU GENERAL PUBLIC LICENSE</H2><!--docid::SEC190::-->
  <DIV class="c1">
    Version 2, June 1991
  </DIV>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="display">
        <PRE class="c2">Copyright © 1989, 1991 Free Software Foundation, Inc.
59 Temple Place - Suite 330, Boston, MA  02111-1307, USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
</PRE>
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  </TABLE>
  <H3>A.2.1 Preamble</H3><!--docid::SEC191::-->
  <P>The licenses for most software are designed to take away your freedom to
  share and change it. By contrast, the GNU General Public License is
  intended to guarantee your freedom to share and change free software--to
  make sure the software is free for all its users. This General Public
  License applies to most of the Free Software Foundation's software and to
  any other program whose authors commit to using it. (Some other Free
  Software Foundation software is covered by the GNU Library General Public
  License instead.) You can apply it to your programs, too.</P>
  <P>When we speak of free software, we are referring to freedom, not price.
  Our General Public Licenses are designed to make sure that you have the
  freedom to distribute copies of free software (and charge for this service
  if you wish), that you receive source code or can get it if you want it,
  that you can change the software or use pieces of it in new free programs;
  and that you know you can do these things.</P>
  <P>To protect your rights, we need to make restrictions that forbid anyone
  to deny you these rights or to ask you to surrender the rights. These
  restrictions translate to certain responsibilities for you if you
  distribute copies of the software, or if you modify it.</P>
  <P>For example, if you distribute copies of such a program, whether gratis
  or for a fee, you must give the recipients all the rights that you have.
  You must make sure that they, too, receive or can get the source code. And
  you must show them these terms so they know their rights.</P>
  <P>We protect your rights with two steps: (1) copyright the software, and
  (2) offer you this license which gives you legal permission to copy,
  distribute and/or modify the software.</P>
  <P>Also, for each author's protection and ours, we want to make certain
  that everyone understands that there is no warranty for this free software.
  If the software is modified by someone else and passed on, we want its
  recipients to know that what they have is not the original, so that any
  problems introduced by others will not reflect on the original authors'
  reputations.</P>
  <P>Finally, any free program is threatened constantly by software patents.
  We wish to avoid the danger that redistributors of a free program will
  individually obtain patent licenses, in effect making the program
  proprietary. To prevent this, we have made it clear that any patent must be
  licensed for everyone's free use or not licensed at all.</P>
  <P>The precise terms and conditions for copying, distribution and
  modification follow.</P>
  <DIV class="c1">
    TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
  </DIV>
  <OL>
    <LI>This License applies to any program or other work which contains a
    notice placed by the copyright holder saying it may be distributed under
    the terms of this General Public License. The "Program", below, refers to
    any such program or work, and a "work based on the Program" means either
    the Program or any derivative work under copyright law: that is to say, a
    work containing the Program or a portion of it, either verbatim or with
    modifications and/or translated into another language. (Hereinafter,
    translation is included without limitation in the term "modification".)
    Each licensee is addressed as "you".
      <P>Activities other than copying, distribution and modification are not
      covered by this License; they are outside its scope. The act of running
      the Program is not restricted, and the output from the Program is
      covered only if its contents constitute a work based on the Program
      (independent of having been made by running the Program). Whether that
      is true depends on what the Program does.</P>
    </LI>
    <LI>You may copy and distribute verbatim copies of the Program's source
    code as you receive it, in any medium, provided that you conspicuously
    and appropriately publish on each copy an appropriate copyright notice
    and disclaimer of warranty; keep intact all the notices that refer to
    this License and to the absence of any warranty; and give any other
    recipients of the Program a copy of this License along with the Program.
      <P>You may charge a fee for the physical act of transferring a copy,
      and you may at your option offer warranty protection in exchange for a
      fee.</P>
    </LI>
    <LI>You may modify your copy or copies of the Program or any portion of
    it, thus forming a work based on the Program, and copy and distribute
    such modifications or work under the terms of Section 1 above, provided
    that you also meet all of these conditions:
      <OL>
        <LI>You must cause the modified files to carry prominent notices
        stating that you changed the files and the date of any change.</LI>
        <LI>You must cause any work that you distribute or publish, that in
        whole or in part contains or is derived from the Program or any part
        thereof, to be licensed as a whole at no charge to all third parties
        under the terms of this License.</LI>
        <LI>If the modified program normally reads commands interactively
        when run, you must cause it, when started running for such
        interactive use in the most ordinary way, to print or display an
        announcement including an appropriate copyright notice and a notice
        that there is no warranty (or else, saying that you provide a
        warranty) and that users may redistribute the program under these
        conditions, and telling the user how to view a copy of this License.
        (Exception: if the Program itself is interactive but does not
        normally print such an announcement, your work based on the Program
        is not required to print an announcement.)</LI>
      </OL>
      <P>These requirements apply to the modified work as a whole. If
      identifiable sections of that work are not derived from the Program,
      and can be reasonably considered independent and separate works in
      themselves, then this License, and its terms, do not apply to those
      sections when you distribute them as separate works. But when you
      distribute the same sections as part of a whole which is a work based
      on the Program, the distribution of the whole must be on the terms of
      this License, whose permissions for other licensees extend to the
      entire whole, and thus to each and every part regardless of who wrote
      it.</P>
      <P>Thus, it is not the intent of this section to claim rights or
      contest your rights to work written entirely by you; rather, the intent
      is to exercise the right to control the distribution of derivative or
      collective works based on the Program.</P>
      <P>In addition, mere aggregation of another work not based on the
      Program with the Program (or with a work based on the Program) on a
      volume of a storage or distribution medium does not bring the other
      work under the scope of this License.</P>
    </LI>
    <LI>You may copy and distribute the Program (or a work based on it, under
    Section 2) in object code or executable form under the terms of Sections
    1 and 2 above provided that you also do one of the following:
      <OL>
        <LI>Accompany it with the complete corresponding machine-readable
        source code, which must be distributed under the terms of Sections 1
        and 2 above on a medium customarily used for software interchange;
        or,</LI>
        <LI>Accompany it with a written offer, valid for at least three
        years, to give any third party, for a charge no more than your cost
        of physically performing source distribution, a complete
        machine-readable copy of the corresponding source code, to be
        distributed under the terms of Sections 1 and 2 above on a medium
        customarily used for software interchange; or,</LI>
        <LI>Accompany it with the information you received as to the offer to
        distribute corresponding source code. (This alternative is allowed
        only for noncommercial distribution and only if you received the
        program in object code or executable form with such an offer, in
        accord with Subsection b above.)</LI>
      </OL>
      <P>The source code for a work means the preferred form of the work for
      making modifications to it. For an executable work, complete source
      code means all the source code for all modules it contains, plus any
      associated interface definition files, plus the scripts used to control
      compilation and installation of the executable. However, as a special
      exception, the source code distributed need not include anything that
      is normally distributed (in either source or binary form) with the
      major components (compiler, kernel, and so on) of the operating system
      on which the executable runs, unless that component itself accompanies
      the executable.</P>
      <P>If distribution of executable or object code is made by offering
      access to copy from a designated place, then offering equivalent access
      to copy the source code from the same place counts as distribution of
      the source code, even though third parties are not compelled to copy
      the source along with the object code.</P>
    </LI>
    <LI>You may not copy, modify, sublicense, or distribute the Program
    except as expressly provided under this License. Any attempt otherwise to
    copy, modify, sublicense or distribute the Program is void, and will
    automatically terminate your rights under this License. However, parties
    who have received copies, or rights, from you under this License will not
    have their licenses terminated so long as such parties remain in full
    compliance.</LI>
    <LI>You are not required to accept this License, since you have not
    signed it. However, nothing else grants you permission to modify or
    distribute the Program or its derivative works. These actions are
    prohibited by law if you do not accept this License. Therefore, by
    modifying or distributing the Program (or any work based on the Program),
    you indicate your acceptance of this License to do so, and all its terms
    and conditions for copying, distributing or modifying the Program or
    works based on it.</LI>
    <LI>Each time you redistribute the Program (or any work based on the
    Program), the recipient automatically receives a license from the
    original licensor to copy, distribute or modify the Program subject to
    these terms and conditions. You may not impose any further restrictions
    on the recipients' exercise of the rights granted herein. You are not
    responsible for enforcing compliance by third parties to this
    License.</LI>
    <LI>If, as a consequence of a court judgment or allegation of patent
    infringement or for any other reason (not limited to patent issues),
    conditions are imposed on you (whether by court order, agreement or
    otherwise) that contradict the conditions of this License, they do not
    excuse you from the conditions of this License. If you cannot distribute
    so as to satisfy simultaneously your obligations under this License and
    any other pertinent obligations, then as a consequence you may not
    distribute the Program at all. For example, if a patent license would not
    permit royalty-free redistribution of the Program by all those who
    receive copies directly or indirectly through you, then the only way you
    could satisfy both it and this License would be to refrain entirely from
    distribution of the Program.
      <P>If any portion of this section is held invalid or unenforceable
      under any particular circumstance, the balance of the section is
      intended to apply and the section as a whole is intended to apply in
      other circumstances.</P>
      <P>It is not the purpose of this section to induce you to infringe any
      patents or other property right claims or to contest validity of any
      such claims; this section has the sole purpose of protecting the
      integrity of the free software distribution system, which is
      implemented by public license practices. Many people have made generous
      contributions to the wide range of software distributed through that
      system in reliance on consistent application of that system; it is up
      to the author/donor to decide if he or she is willing to distribute
      software through any other system and a licensee cannot impose that
      choice.</P>
      <P>This section is intended to make thoroughly clear what is believed
      to be a consequence of the rest of this License.</P>
    </LI>
    <LI>If the distribution and/or use of the Program is restricted in
    certain countries either by patents or by copyrighted interfaces, the
    original copyright holder who places the Program under this License may
    add an explicit geographical distribution limitation excluding those
    countries, so that distribution is permitted only in or among countries
    not thus excluded. In such case, this License incorporates the limitation
    as if written in the body of this License.</LI>
    <LI>The Free Software Foundation may publish revised and/or new versions
    of the General Public License from time to time. Such new versions will
    be similar in spirit to the present version, but may differ in detail to
    address new problems or concerns.
      <P>Each version is given a distinguishing version number. If the
      Program specifies a version number of this License which applies to it
      and "any later version", you have the option of following the terms and
      conditions either of that version or of any later version published by
      the Free Software Foundation. If the Program does not specify a version
      number of this License, you may choose any version ever published by
      the Free Software Foundation.</P>
    </LI>
    <LI>If you wish to incorporate parts of the Program into other free
    programs whose distribution conditions are different, write to the author
    to ask for permission. For software which is copyrighted by the Free
    Software Foundation, write to the Free Software Foundation; we sometimes
    make exceptions for this. Our decision will be guided by the two goals of
    preserving the free status of all derivatives of our free software and of
    promoting the sharing and reuse of software generally.
      <DIV class="c1">
        NO WARRANTY
      </DIV>
    </LI>
    <LI>BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
    FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
    OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
    PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER
    EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
    WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE
    ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.
    SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY
    SERVICING, REPAIR OR CORRECTION.</LI>
    <LI>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
    WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
    REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR
    DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL
    DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING
    BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
    LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO
    OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS
    BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</LI>
  </OL>
  <DIV class="c1">
    END OF TERMS AND CONDITIONS
  </DIV>
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  <H3>A.2.2 Appendix: How to Apply These Terms to Your New Programs</H3>
  <!--docid::SEC192::-->
  <P>If you develop a new program, and you want it to be of the greatest
  possible use to the public, the best way to achieve this is to make it free
  software which everyone can redistribute and change under these terms.</P>
  <P>To do so, attach the following notices to the program. It is safest to
  attach them to the start of each source file to most effectively convey the
  exclusion of warranty; and each file should have at least the "copyright"
  line and a pointer to where the full notice is found.</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="smallexample">
        <PRE class=
        "c4"><VAR>one line to give the program's name and a brief idea of what it does.</VAR>
Copyright (C) <VAR>yyyy</VAR>  <VAR>name of author</VAR>

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>Also add information on how to contact you by electronic and paper
  mail.</P>
  <P>If the program is interactive, make it output a short notice like this
  when it starts in an interactive mode:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="smallexample">
        <PRE class=
        "c4">Gnomovision version 69, Copyright (C) 19<VAR>yy</VAR> <VAR>name of author</VAR>
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>The hypothetical commands `<SAMP>show w</SAMP>' and `<SAMP>show
  c</SAMP>' should show the appropriate parts of the General Public License.
  Of course, the commands you use may be called something other than
  `<SAMP>show w</SAMP>' and `<SAMP>show c</SAMP>'; they could even be
  mouse-clicks or menu items--whatever suits your program.</P>
  <P>You should also get your employer (if you work as a programmer) or your
  school, if any, to sign a "copyright disclaimer" for the program, if
  necessary. Here is a sample; alter the names:</P>
  <TABLE>
    <TR>
      <TD></TD>
      <TD class="example">
        <PRE>Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.

<VAR>signature of Ty Coon</VAR>, 1 April 1989
Ty Coon, President of Vice
</PRE>
      </TD>
    </TR>
  </TABLE>
  <P>This General Public License does not permit incorporating your program
  into proprietary programs. If your program is a subroutine library, you may
  consider it more useful to permit linking proprietary applications with the
  library. If this is what you want to do, use the GNU Library General Public
  License instead of this License.</P>
  <P><A name="Glossary" id="Glossary"></A></P>
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    <TR>
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      <TD valign="top"><A href="mtt.html#IDX137"><CODE>abg</CODE></A></TD>
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      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX138"><CODE>abg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX283"><CODE>AE</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
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      <TD valign="top"><A href="mtt.html#IDX284"><CODE>AE</CODE></A></TD>
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      <TD></TD>
      <TD valign="top"><A href=
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      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX258"><CODE>artwork</CODE></A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX393"><CODE>assignment
      statements</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
      (numpar.txt)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX394"><CODE>assignment
      statements</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
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      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX251"><CODE>bonds</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX252"><CODE>bonds</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
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    <TR>
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        <HR>
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    <TR>
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      <TD></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX273"><CODE>C</CODE></A></TD>
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      components</A></TD>
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      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX111"><CODE>c</CODE></A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX274"><CODE>C</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
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      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX112"><CODE>c</CODE></A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX391"><CODE>c</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX392"><CODE>c</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX497"><CODE>c</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX498"><CODE>c</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX537"><CODE>c</CODE></A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX139"><CODE>cbg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX140"><CODE>cbg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX113"><CODE>cc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX114"><CODE>cc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX397"><CODE>commented assignment
      statements</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
      (numpar.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX398"><CODE>commented assignment
      statements</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
      (numpar.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX395"><CODE>comments</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
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    <TR>
      <TD></TD>
      <TD valign="top"><A href=
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      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
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    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX255"><CODE>components</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX256"><CODE>components</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
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    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX141"><CODE>cr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX142"><CODE>cr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX97"><CODE>cse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX98"><CODE>cse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX143"><CODE>cse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX144"><CODE>cse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX145"><CODE>csm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX146"><CODE>csm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX287"><CODE>CSW</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX288"><CODE>CSW</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_D" id="fn_D"></A>D</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX147"><CODE>dae</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX148"><CODE>dae</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX149"><CODE>daes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX150"><CODE>daes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX151"><CODE>daeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX152"><CODE>daeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX153"><CODE>def</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX154"><CODE>def</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX155"><CODE>desc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX156"><CODE>desc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX157"><CODE>dm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX158"><CODE>dm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX531"><CODE>dvi</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX532"><CODE>dvi</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_E" id="fn_E"></A>E</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX159"><CODE>ese</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX160"><CODE>ese</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#SEC110"><CODE>exotherm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC110">6.8.1.2 exotherm</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_F" id="fn_F"></A>F</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX523"><CODE>fig</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX524"><CODE>fig</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX161"><CODE>fr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX162"><CODE>fr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_G" id="fn_G"></A>G</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX535"><CODE>gdat</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX536"><CODE>gdat</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX281"><CODE>GY</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX282"><CODE>GY</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_I" id="fn_I"></A>I</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX275"><CODE>I</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX276"><CODE>I</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX163"><CODE>input</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX164"><CODE>input</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX101"><CODE>ir</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX102"><CODE>ir</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX165"><CODE>ir</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX166"><CODE>ir</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX103"><CODE>iro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX104"><CODE>iro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX167"><CODE>iro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX168"><CODE>iro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX289"><CODE>ISW</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX290"><CODE>ISW</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_L" id="fn_L"></A>L</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX169"><CODE>lbl</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX170"><CODE>lbl</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC109"><CODE>lin</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC109">6.8.1.1 lin</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX171"><CODE>lmfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX172"><CODE>lmfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX173"><CODE>lpfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX174"><CODE>lpfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_M" id="fn_M"></A>M</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX109"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX110"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX389"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX390"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX489"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX490"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX525"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX526"><CODE>m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX85"><CODE>mtt
      &amp;lt;system&amp;gt; clean</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX86"><CODE>mtt
      &amp;lt;system&amp;gt; clean</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX121"><CODE>mtt -c -i euler system
      odeso view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX122"><CODE>mtt -c -i euler system
      odeso view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX119"><CODE>mtt -c system odeso
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX120"><CODE>mtt -c system odeso
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX87"><CODE>mtt
      clean</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX88"><CODE>mtt
      clean</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX81"><CODE>mtt copy
      &amp;lt;system&amp;gt;</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX82"><CODE>mtt copy
      &amp;lt;system&amp;gt;</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX79"><CODE>mtt
      help</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX80"><CODE>mtt
      help</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX83"><CODE>mtt rename
      &amp;lt;old_name&amp;gt; &amp;lt;new_name&amp;gt;</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX84"><CODE>mtt rename
      &amp;lt;old_name&amp;gt; &amp;lt;new_name&amp;gt;</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX115"><CODE>mtt system iro
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX116"><CODE>mtt system iro
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX89"><CODE>mtt system
      representation vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX90"><CODE>mtt system
      representation vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX93"><CODE>mtt system
      representation vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX94"><CODE>mtt system
      representation vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX117"><CODE>mtt system sro
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX118"><CODE>mtt system sro
      view</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX91"><CODE>mtt system
      vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX92"><CODE>mtt system
      vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX95"><CODE>mtt system
      vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX96"><CODE>mtt system
      vc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_N" id="fn_N"></A>N</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX291"><CODE>NAME_cause.m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple components -
      implementation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX292"><CODE>NAME_cause.m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple components -
      implementation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX293"><CODE>NAME_eqn.m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple components -
      implementation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX294"><CODE>NAME_eqn.m</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple components -
      implementation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX175"><CODE>nifr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX176"><CODE>nifr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX177"><CODE>numpar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX178"><CODE>numpar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX179"><CODE>nyfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX180"><CODE>nyfr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_O" id="fn_O"></A>O</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX181"><CODE>obs</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX182"><CODE>obs</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX99"><CODE>ode</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX100"><CODE>ode</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX183"><CODE>ode</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX184"><CODE>ode</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX123"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX124"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX185"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX186"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX187"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX188"><CODE>odes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX125"><CODE>odeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX126"><CODE>odeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX189"><CODE>odeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX190"><CODE>odeso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX191"><CODE>odess</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX192"><CODE>odess</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX193"><CODE>odesso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX194"><CODE>odesso</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_P" id="fn_P"></A>P</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX495"><CODE>ps</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX496"><CODE>ps</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX533"><CODE>ps</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX534"><CODE>ps</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_R" id="fn_R"></A>R</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX271"><CODE>R</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX491"><CODE>r</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX272"><CODE>R</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX492"><CODE>r</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX527"><CODE>r</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX528"><CODE>r</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX195"><CODE>rbg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX196"><CODE>rbg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX197"><CODE>rep</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX198"><CODE>rep</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX199"><CODE>rfe</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX200"><CODE>rfe</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_S" id="fn_S"></A>S</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX201"><CODE>sabg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX202"><CODE>sabg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX131"><CODE>scse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX132"><CODE>scse</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX135"><CODE>scsm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX136"><CODE>scsm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX539"><CODE>sg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX540"><CODE>sg</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX203"><CODE>simp</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX204"><CODE>simp</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX133"><CODE>sm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX134"><CODE>sm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX205"><CODE>sm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX206"><CODE>sm</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX209"><CODE>sms</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX210"><CODE>sms</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX211"><CODE>smss</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX212"><CODE>smss</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX207"><CODE>smx</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX208"><CODE>smx</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX105"><CODE>sr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX106"><CODE>sr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX213"><CODE>sr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX214"><CODE>sr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX107"><CODE>sro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX108"><CODE>sro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX215"><CODE>sro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX216"><CODE>sro</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX277"><CODE>SS</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX217"><CODE>ss</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX218"><CODE>ss</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX278"><CODE>SS</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX219"><CODE>sspar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX220"><CODE>sspar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX253"><CODE>strokes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX254"><CODE>strokes</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX221"><CODE>struc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX222"><CODE>struc</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX223"><CODE>sub</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX224"><CODE>sub</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX225"><CODE>sub</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX226"><CODE>sub</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX227"><CODE>sympar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX228"><CODE>sympar</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="fn_T" id="fn_T"></A>T</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX493"><CODE>tex</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX494"><CODE>tex</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX529"><CODE>tex</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX530"><CODE>tex</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX279"><CODE>TF</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX229"><CODE>tf</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX280"><CODE>TF</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX230"><CODE>tf</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX387"><CODE>txt</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX388"><CODE>txt</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX259"><CODE>type</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX260"><CODE>type</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX267"><CODE>type*n</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX268"><CODE>type*n</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX261"><CODE>type:label</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX262"><CODE>type:label</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX269"><CODE>type:label*n</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX270"><CODE>type:label*n</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX263"><CODE>type:label:cr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX264"><CODE>type:label:cr</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX265"><CODE>type:label:expression</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href=
      "mtt.html#IDX266"><CODE>type:label:expression</CODE></A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
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      <TD valign="top"><A href="mtt.html#IDX5">Bond graphs, what are
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      <TD valign="top"><A href="mtt.html#SEC163">c</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC120">Causal bond graph
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      <TD valign="top"><A href="mtt.html#SEC120">6.10 Causal bond graph
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    <TR>
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      <TD valign="top"><A href="mtt.html#SEC122">cbonds</A></TD>
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    <TR>
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      <TD valign="top"><A href="mtt.html#SEC26">Clean</A></TD>
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      <TD valign="top"><A href="mtt.html#SEC66">Coerced bond
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      <TD valign="top"><A href="mtt.html#SEC16">Command line
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      <TD valign="top"><A href="mtt.html#SEC96">component aliases</A></TD>
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    <TR>
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      <TD valign="top"><A href="mtt.html#SEC87">Component constitutive
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      <TD valign="top"><A href="mtt.html#SEC153">Component library</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC77">Component-orientated
      causality</A></TD>
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      causality</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC7">Components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC7">1.6 Components</A></TD>
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    <TR>
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      <TD valign="top"><A href="mtt.html#SEC21">components</A></TD>
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      components</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC156">Components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC60">components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC60">6.4.1.4 Components</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC75">components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC75">6.4.3 Language m
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX588">compound components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC186">11.5 File structure</A></TD>
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      <TD valign="top"><A href="mtt.html#SEC64">Compound components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC64">6.4.1.8 Compound
      components</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC9">Constitutive
      Relationship</A></TD>
      <TD valign="top"><A href="mtt.html#SEC9">1.6.2 Constitutive
      relationship</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC107">Constitutive
      relationship</A></TD>
      <TD valign="top"><A href="mtt.html#SEC107">6.8 Constitutive
      relationship (cr)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC131">Constrained-state
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC131">6.13 Constrained-state
      Equations (cse)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC132">Constrained-state Equations
      (reduce)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC132">6.13.1 Language reduce
      (cse.r)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC134">Constrained-state Equations
      (view)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC134">6.13.2 Language m
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC169">control systems</A></TD>
      <TD valign="top"><A href="mtt.html#SEC169">10.4.1 Octave control system
      toolbox (OCST)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC25">Copy</A></TD>
      <TD valign="top"><A href="mtt.html#SEC25">2.4.2 Copy</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC95">CR aliases</A></TD>
      <TD valign="top"><A href="mtt.html#SEC95">6.6.9.3 CR aliases</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC31">Creating complex
      models</A></TD>
      <TD valign="top"><A href="mtt.html#SEC31">3.3 Creating complex
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC170">Creating GNU Octave .oct
      files</A></TD>
      <TD valign="top"><A href="mtt.html#SEC170">10.4.2 Creating GNU Octave
      .oct files</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC171">Creating Matlab .mex
      files</A></TD>
      <TD valign="top"><A href="mtt.html#SEC171">10.4.3 Creating Matlab .mex
      files</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC28">Creating Models</A></TD>
      <TD valign="top"><A href="mtt.html#SEC28">3. Creating Models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC30">Creating simple
      models</A></TD>
      <TD valign="top"><A href="mtt.html#SEC30">3.2 Creating simple
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC23">crs</A></TD>
      <TD valign="top"><A href="mtt.html#SEC23">2.4.1.4 help crs</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC132">cse.r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC132">6.13.1 Language reduce
      (cse.r)</A></TD>
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    <TR>
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        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_D" id="cp_D"></A>D</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
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      <TD valign="top"><A href="mtt.html#SEC126">DAE</A></TD>
      <TD valign="top"><A href="mtt.html#SEC126">6.12 Differential-Algebraic
      Equations (dae)</A></TD>
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    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC129">dae.m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC129">6.12.2 Language m
      (dae.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC127">dae.r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC127">6.12.1 Language reduce
      (dae.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC125">def.r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC125">6.11.0.1 Transformation
      cbg2ese_m2r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC51">Defining
      representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC51">6. Representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC53">Defining
      representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC53">6.2 Defining
      representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC158">desc</A></TD>
      <TD valign="top"><A href="mtt.html#SEC158">8.2.2 Detailed on-line
      documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC158">Description</A></TD>
      <TD valign="top"><A href="mtt.html#SEC158">8.2.2 Detailed on-line
      documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC141">Descriptor matrices</A></TD>
      <TD valign="top"><A href="mtt.html#SEC141">6.15 Descriptor matrices
      (dm)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC143">Descriptor matrices
      (m)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC143">6.15.2 Language m
      (dm.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC142">Descriptor matrices
      (reduce)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC142">6.15.1 Language reduce
      (dm.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC158">Detailed
      documentation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC158">8.2.2 Detailed on-line
      documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC126">Differential-Algebraic
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC126">6.12 Differential-Algebraic
      Equations (dae)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC129">Differential-Algebraic
      Equations (m)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC129">6.12.2 Language m
      (dae.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC127">Differential-Algebraic
      Equations (reduce)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC127">6.12.1 Language reduce
      (dae.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC111">DIY constitutive
      relationships</A></TD>
      <TD valign="top"><A href="mtt.html#SEC111">6.8.2 DIY constitutive
      relationships</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC149">DIY representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC149">7.2 New (DIY)
      representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC150">DIY representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC150">7.2.1 Makefile</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC151">DIY representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC151">7.2.2 Shell-script</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC152">DIY representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC152">7.2.3 Documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC141">dm</A></TD>
      <TD valign="top"><A href="mtt.html#SEC141">6.15 Descriptor matrices
      (dm)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC143">dm.m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC143">6.15.2 Language m
      (dm.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC142">dm.r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC142">6.15.1 Language reduce
      (dm.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC152">Documentation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC152">7.2.3 Documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC154">Documentation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC154">8. Documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC156">Documentation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
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    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_E" id="cp_E"></A>E</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC124">Elementary system
      equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC124">6.11 Elementary system
      equations (ese)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC172">Embedding MTT models in
      Simulink</A></TD>
      <TD valign="top"><A href="mtt.html#SEC172">10.4.4 Embedding MTT models
      in Simulink</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC38">Euler integration</A></TD>
      <TD valign="top"><A href="mtt.html#SEC38">4.2.1 Euler
      integration</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC156">Examples</A></TD>
      <TD valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC22">examples</A></TD>
      <TD valign="top"><A href="mtt.html#SEC22">2.4.1.3 help
      examples</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC147">Extending MTT</A></TD>
      <TD valign="top"><A href="mtt.html#SEC147">7. Extending MTT</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_F" id="cp_F"></A>F</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX601">FDL, GNU Free Documentation
      License</A></TD>
      <TD valign="top"><A href="mtt.html#SEC188">A.1 GNU Free Documentation
      License</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC160">Fig</A></TD>
      <TD valign="top"><A href="mtt.html#SEC160">9.1 Fig</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC186">File structure</A></TD>
      <TD valign="top"><A href="mtt.html#SEC186">11.5 File structure</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_G" id="cp_G"></A>G</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC48">gnuplot</A></TD>
      <TD valign="top"><A href="mtt.html#SEC48">4.7.1 Viewing results with
      gnuplot</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_H" id="cp_H"></A>H</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC20">help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC20">2.4.1.1 help
      representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC19">Help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC19">2.4.1 Help</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC21">help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC21">2.4.1.2 help
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC22">help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC22">2.4.1.3 help
      examples</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC23">help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC23">2.4.1.4 help crs</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC24">help</A></TD>
      <TD valign="top"><A href="mtt.html#SEC24">2.4.1.5 help
      &lt;name&gt;</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC13">Hybrid systems</A></TD>
      <TD valign="top"><A href="mtt.html#SEC13">1.8 Switched systems</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_I" id="cp_I"></A>I</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC91">ICD (label file
      directive)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC91">6.6.8 Interface Control
      Definition</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC57">Icon</A></TD>
      <TD valign="top"><A href="mtt.html#SEC57">6.4.1.1 Icon library</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC39">Implicit integration</A></TD>
      <TD valign="top"><A href="mtt.html#SEC39">4.2.2 Implicit
      integration</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_L" id="cp_L"></A>L</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC83">Labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC83">6.6 Labels (lbl)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC56">Language fig
      (abg.fig)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC56">6.4.1 Language fig
      (abg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC121">Language fig
      (cbg.fig)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC121">6.10.1 Language fig
      (cbg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC81">Language fig
      (sabg.fig)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC81">6.5.1 Language fig
      (sabg.fig)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC75">Language m (abg.m)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC75">6.4.3 Language m
      (abg.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC122">Language m (cbg.m)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC122">6.10.2 Language m
      (cbg.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC82">Language m (view)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC82">6.5.2 Stripped acausal bond
      graph (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC79">Language tex
      (abg.tex)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC79">6.4.4 Language tex
      (abg.tex)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC102">Language tex
      (desc.tex)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC102">6.6.12 Language tex
      (desc.tex)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC105">Language tex
      (struc.tex)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC105">6.7.2 Language tex
      (struc.tex)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC164">Language tools</A></TD>
      <TD valign="top"><A href="mtt.html#SEC164">10. Language tools</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC104">Language txt
      (struc.txt)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC104">6.7.1 Language txt
      (struc.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC159">Languages</A></TD>
      <TD valign="top"><A href="mtt.html#SEC159">9. Languages</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC173">LaTeX</A></TD>
      <TD valign="top"><A href="mtt.html#SEC173">10.5 LaTeX</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC83">lbl</A></TD>
      <TD valign="top"><A href="mtt.html#SEC83">6.6 Labels (lbl)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC98">lbl</A></TD>
      <TD valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style labels
      (lbl)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC57">library</A></TD>
      <TD valign="top"><A href="mtt.html#SEC57">6.4.1.1 Icon library</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC13">logic</A></TD>
      <TD valign="top"><A href="mtt.html#SEC13">1.8 Switched systems</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_M" id="cp_M"></A>M</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC161">m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC161">9.2 m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC168">m-files</A></TD>
      <TD valign="top"><A href="mtt.html#SEC168">10.4 Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC147">Make</A></TD>
      <TD valign="top"><A href="mtt.html#SEC147">7. Extending MTT</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC150">Makefile</A></TD>
      <TD valign="top"><A href="mtt.html#SEC150">7.2.1 Makefile</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC148">Makefiles</A></TD>
      <TD valign="top"><A href="mtt.html#SEC148">7.1 Makefiles</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC155">Manual</A></TD>
      <TD valign="top"><A href="mtt.html#SEC155">8.1 Manual</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC168">Matlab</A></TD>
      <TD valign="top"><A href="mtt.html#SEC168">10.4 Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC15">Menu-driven
      interface</A></TD>
      <TD valign="top"><A href="mtt.html#SEC15">2.1 Menu-driven
      interface</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX1">MTT, purpose of</A></TD>
      <TD valign="top"><A href="mtt.html#SEC1">1. Introduction</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC168">mtt.m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC168">10.4 Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC169">mtt2sys</A></TD>
      <TD valign="top"><A href="mtt.html#SEC169">10.4.1 Octave control system
      toolbox (OCST)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC180">mttrc</A></TD>
      <TD valign="top"><A href="mtt.html#SEC180">11.4 Paths</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_N" id="cp_N"></A>N</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC75">n_ports</A></TD>
      <TD valign="top"><A href="mtt.html#SEC75">6.4.3 Language m
      (abg.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC64">Named SS</A></TD>
      <TD valign="top"><A href="mtt.html#SEC64">6.4.1.8 Compound
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC65">Named SS components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC65">6.4.1.9 Named SS
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC149">New representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC149">7.2 New (DIY)
      representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC150">New representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC150">7.2.1 Makefile</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC151">New representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC151">7.2.2 Shell-script</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC152">New representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC152">7.2.3 Documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC11">Numeric parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC11">1.6.4 Numeric
      parameters</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC118">Numeric parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC118">6.9.3 Numeric parameters
      (numpar)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC119">Numeric parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC119">6.9.3.1 Text form
      (numpar.txt)</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_O" id="cp_O"></A>O</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC169">OCST</A></TD>
      <TD valign="top"><A href="mtt.html#SEC169">10.4.1 Octave control system
      toolbox (OCST)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC168">Octave</A></TD>
      <TD valign="top"><A href="mtt.html#SEC168">10.4 Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC169">Octave</A></TD>
      <TD valign="top"><A href="mtt.html#SEC169">10.4.1 Octave control system
      toolbox (OCST)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC168">Octave interface</A></TD>
      <TD valign="top"><A href="mtt.html#SEC168">10.4 Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC177">Octave setup</A></TD>
      <TD valign="top"><A href="mtt.html#SEC177">11.3 Octave setup</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC131">ODE</A></TD>
      <TD valign="top"><A href="mtt.html#SEC131">6.13 Constrained-state
      Equations (cse)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC135">ODE</A></TD>
      <TD valign="top"><A href="mtt.html#SEC135">6.14 Ordinary Differential
      Equations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC138">ode.m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC138">6.14.2 Language m
      (ode.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC136">ode.r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC136">6.14.1 Language reduce
      (ode.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC98">Old-style labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC98">6.6.11 Old-style labels
      (lbl)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC156">On-line
      documentation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC156">8.2 On-line
      documentation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC17">options</A></TD>
      <TD valign="top"><A href="mtt.html#SEC17">2.3 Options</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC135">Ordinary Differential
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC135">6.14 Ordinary Differential
      Equations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC138">Ordinary Differential
      Equations (m)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC138">6.14.2 Language m
      (ode.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC136">Ordinary Differential
      Equations (reduce)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC136">6.14.1 Language reduce
      (ode.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC140">Ordinary Differential
      Equations (view)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC140">6.14.3 Language m
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC85">Other component
      labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC85">6.6.2 Other component
      labels</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC100">Other component labels
      (old-style)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC100">6.6.11.2 Other component
      labels (old-style)</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_P" id="cp_P"></A>P</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC94">parameter aliases</A></TD>
      <TD valign="top"><A href="mtt.html#SEC94">6.6.9.2 Parameter
      aliases</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC89">parameter
      declarations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC89">6.6.6 Parameter
      declarations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC97">Parameter passing</A></TD>
      <TD valign="top"><A href="mtt.html#SEC97">6.6.10 Parameter
      passing</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC101">Parameter passing
      (old-style)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC101">6.6.11.3 Parameter passing
      (old-style)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC115">Parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC115">6.9 Parameters</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC180">paths</A></TD>
      <TD valign="top"><A href="mtt.html#SEC180">11.4 Paths</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC93">port aliases</A></TD>
      <TD valign="top"><A href="mtt.html#SEC93">6.6.9.1 Port aliases</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC69">Port label defaults</A></TD>
      <TD valign="top"><A href="mtt.html#SEC69">6.4.1.13 Port label
      defaults</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC68">port labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC68">6.4.1.12 Vector port
      labels</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC8">ports</A></TD>
      <TD valign="top"><A href="mtt.html#SEC8">1.6.1 Ports</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC67">ports</A></TD>
      <TD valign="top"><A href="mtt.html#SEC67">6.4.1.11 Port labels</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC108">Predefined constitutive
      relationships</A></TD>
      <TD valign="top"><A href="mtt.html#SEC108">6.8.1 Predefined
      constitutive relationships</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_Q" id="cp_Q"></A>Q</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC29">Quick start</A></TD>
      <TD valign="top"><A href="mtt.html#SEC29">3.1 Quick start</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_R" id="cp_R"></A>R</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC162">Reduce</A></TD>
      <TD valign="top"><A href="mtt.html#SEC162">9.3 Reduce</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC176">REDUCE setup</A></TD>
      <TD valign="top"><A href="mtt.html#SEC176">11.2 REDUCE setup</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC144">rep</A></TD>
      <TD valign="top"><A href="mtt.html#SEC144">6.16 Report (rep)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC145">rep.txt</A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC144">Report</A></TD>
      <TD valign="top"><A href="mtt.html#SEC144">6.16 Report (rep)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC145">Report (text)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC145">6.16.1 Language text
      (rep.txt)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC146">Report (view)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC146">6.16.2 Language
      view</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC52">Representation
      summary</A></TD>
      <TD valign="top"><A href="mtt.html#SEC52">6.1 Representation
      summary</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC51">Representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC51">6. Representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC20">representations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC20">2.4.1.1 help
      representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC51">Representations,
      defining</A></TD>
      <TD valign="top"><A href="mtt.html#SEC51">6. Representations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX3">Representations, what are
      they?</A></TD>
      <TD valign="top"><A href="mtt.html#SEC2">1.1 What is a
      representation?</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_S" id="cp_S"></A>S</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC49">SciGraphica</A></TD>
      <TD valign="top"><A href="mtt.html#SEC49">4.7.2 Exporting results to
      SciGraphica</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC50">Sensitivity models</A></TD>
      <TD valign="top"><A href="mtt.html#SEC50">5. Sensitivity
      models</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC151">Shell-script</A></TD>
      <TD valign="top"><A href="mtt.html#SEC151">7.2.2 Shell-script</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC61">Simple components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC61">6.4.1.5 Simple
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#IDX587">simple components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC186">11.5 File structure</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC63">Simple components -
      implementation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC63">6.4.1.7 Simple components -
      implementation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC33">Simulation</A></TD>
      <TD valign="top"><A href="mtt.html#SEC33">4. Simulation</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC44">Simulation initial
      state</A></TD>
      <TD valign="top"><A href="mtt.html#SEC44">4.5 Simulation initial
      state</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC42">Simulation input</A></TD>
      <TD valign="top"><A href="mtt.html#SEC42">4.3 Simulation input</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC43">Simulation logic</A></TD>
      <TD valign="top"><A href="mtt.html#SEC43">4.4 Simulation logic</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC47">Simulation output</A></TD>
      <TD valign="top"><A href="mtt.html#SEC47">4.7 Simulation
      output</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC37">Simulation
      parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC37">4.2 Simulation
      parameters</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC175">Software components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC175">11.1 Software
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC84">SS component labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC84">6.6.1 SS component
      labels</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC99">SS component labels
      (old-style)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC99">6.6.11.1 SS component labels
      (old-style)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC62">SS components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC62">6.4.1.6 SS
      components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC122">status</A></TD>
      <TD valign="top"><A href="mtt.html#SEC122">6.10.2 Language m
      (cbg.m)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC34">Steady-state
      solutions</A></TD>
      <TD valign="top"><A href="mtt.html#SEC34">4.1 Steady-state
      solutions</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC35">Steady-state solutions -
      numerical</A></TD>
      <TD valign="top"><A href="mtt.html#SEC35">4.1.1 Steady-state solutions
      (odess)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC36">Steady-state solutions -
      symbolic</A></TD>
      <TD valign="top"><A href="mtt.html#SEC36">4.1.2 Steady-state solutions
      (ss)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC80">Stripped acausal bond graph
      (sabg)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC80">6.5 Stripped acausal bond
      graph (sabg)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC59">strokes</A></TD>
      <TD valign="top"><A href="mtt.html#SEC59">6.4.1.3 Strokes</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC103">struc</A></TD>
      <TD valign="top"><A href="mtt.html#SEC103">6.7 Structure
      (struc)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC103">Structure</A></TD>
      <TD valign="top"><A href="mtt.html#SEC103">6.7 Structure
      (struc)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC125">Structure</A></TD>
      <TD valign="top"><A href="mtt.html#SEC125">6.11.0.1 Transformation
      cbg2ese_m2r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC106">Structure (view)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC106">6.7.3 Language tex
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC13">Switched systems</A></TD>
      <TD valign="top"><A href="mtt.html#SEC13">1.8 Switched systems</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC10">Symbolic parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC10">1.6.3 Symbolic
      parameters</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC116">Symbolic parameters</A></TD>
      <TD valign="top"><A href="mtt.html#SEC116">6.9.1 Symbolic parameters
      (subs.r)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC117">Symbolic parameters for
      simplification</A></TD>
      <TD valign="top"><A href="mtt.html#SEC117">6.9.2 Symbolic parameters
      for simplification (simp.r)</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_T" id="cp_T"></A>T</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC167">Text editors</A></TD>
      <TD valign="top"><A href="mtt.html#SEC167">10.3 Text editors</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC169">toolbox</A></TD>
      <TD valign="top"><A href="mtt.html#SEC169">10.4.1 Octave control system
      toolbox (OCST)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC32">Top level</A></TD>
      <TD valign="top"><A href="mtt.html#SEC32">3.3.1 Top level</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC123">Transformation
      abg2cbg_m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC123">6.10.2.1 Transformation
      abg2cbg_m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC74">Transformation
      abg2rbg_fig2m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC74">6.4.2.1 Transformation
      abg2rbg_fig2m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC125">Transformation
      cbg2ese_m2r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC125">6.11.0.1 Transformation
      cbg2ese_m2r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC137">Transformation
      cse2ode_r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC137">6.14.1.1 Transformation
      cse2ode_r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC133">Transformation
      dae2cse_r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC133">6.13.1.1 Transformation
      dae2cse_r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC130">Transformation
      dae_r2m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC130">6.12.2.1 Transformation
      dae_r2m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC128">Transformation
      ese2dae_r</A></TD>
      <TD valign="top"><A href="mtt.html#SEC128">6.12.1.1 Transformation
      ese2dae_r</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC139">Transformation
      ode_r2m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC139">6.14.2.1 Transformation
      ode_r2m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC78">Transformation
      rbg2abg_m</A></TD>
      <TD valign="top"><A href="mtt.html#SEC78">6.4.3.3 Transformation
      rbg2abg_m</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC3">Transformations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC3">1.2 What is a
      transformation?</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_U" id="cp_U"></A>U</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC90">units declarations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC90">6.6.7 Units
      declarations</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC112">Unresolved constitutive
      relationships</A></TD>
      <TD valign="top"><A href="mtt.html#SEC112">6.8.3 Unresolved
      constitutive relationships</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC113">Unresolved constitutive
      relationships - Octave</A></TD>
      <TD valign="top"><A href="mtt.html#SEC113">6.8.4 Unresolved
      constitutive relationships - Octave</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC114">Unresolved constitutive
      relationships - Octave</A></TD>
      <TD valign="top"><A href="mtt.html#SEC114">6.8.5 Unresolved
      constitutive relationships - c++</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC14">User interface</A></TD>
      <TD valign="top"><A href="mtt.html#SEC14">2. User interface</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC18">Utilities</A></TD>
      <TD valign="top"><A href="mtt.html#SEC18">2.4 Utilities</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_V" id="cp_V"></A>V</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC72">valid name</A></TD>
      <TD valign="top"><A href="mtt.html#SEC72">6.4.1.16 Valid Names</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC5">Variables</A></TD>
      <TD valign="top"><A href="mtt.html#SEC5">1.4 Variables</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC70">Vector components</A></TD>
      <TD valign="top"><A href="mtt.html#SEC70">6.4.1.14 Vector
      Components</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC68">vector port labels</A></TD>
      <TD valign="top"><A href="mtt.html#SEC68">6.4.1.12 Vector port
      labels</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC54">Verbal description
      (desc)</A></TD>
      <TD valign="top"><A href="mtt.html#SEC54">6.3 Verbal description
      (desc)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC27">Version control</A></TD>
      <TD valign="top"><A href="mtt.html#SEC27">2.4.4 Version
      control</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC82">view Constrained-state
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC82">6.5.2 Stripped acausal bond
      graph (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC134">view Constrained-state
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC134">6.13.2 Language m
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC140">view Ordinary Differential
      Equations</A></TD>
      <TD valign="top"><A href="mtt.html#SEC140">6.14.3 Language m
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC146">view Report</A></TD>
      <TD valign="top"><A href="mtt.html#SEC146">6.16.2 Language
      view</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC106">view Structure</A></TD>
      <TD valign="top"><A href="mtt.html#SEC106">6.7.3 Language tex
      (view)</A></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC165">views</A></TD>
      <TD valign="top"><A href="mtt.html#SEC165">10.1 Views</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
    </TR>
    <TR>
      <TH><A name="cp_X" id="cp_X"></A>X</TH>
      <TD></TD>
      <TD></TD>
    </TR>
    <TR>
      <TD></TD>
      <TD valign="top"><A href="mtt.html#SEC166">Xfig</A></TD>
      <TD valign="top"><A href="mtt.html#SEC166">10.2 Xfig</A></TD>
    </TR>
    <TR>
      <TD colspan="3">
        <HR>
      </TD>
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  <H1>Table of Contents</H1>
  <BLOCKQUOTE>
    <A name="TOC1" href="mtt.html#SEC1" id="TOC1">1. Introduction</A><BR>
    <BLOCKQUOTE>
      <A name="TOC2" href="mtt.html#SEC2" id="TOC2">1.1 What is a
      representation?</A><BR>
      <A name="TOC3" href="mtt.html#SEC3" id="TOC3">1.2 What is a
      transformation?</A><BR>
      <A name="TOC4" href="mtt.html#SEC4" id="TOC4">1.3 What is a bond
      graph?</A><BR>
      <A name="TOC5" href="mtt.html#SEC5" id="TOC5">1.4 Variables</A><BR>
      <A name="TOC6" href="mtt.html#SEC6" id="TOC6">1.5 Bonds</A><BR>
      <A name="TOC7" href="mtt.html#SEC7" id="TOC7">1.6 Components</A><BR>
      <BLOCKQUOTE>
        <A name="TOC8" href="mtt.html#SEC8" id="TOC8">1.6.1 Ports</A><BR>
        <A name="TOC9" href="mtt.html#SEC9" id="TOC9">1.6.2 Constitutive
        relationship</A><BR>
        <A name="TOC10" href="mtt.html#SEC10" id="TOC10">1.6.3 Symbolic
        parameters</A><BR>
        <A name="TOC11" href="mtt.html#SEC11" id="TOC11">1.6.4 Numeric
        parameters</A><BR>
      </BLOCKQUOTE><A name="TOC12" href="mtt.html#SEC12" id="TOC12">1.7
      Algebraic loops</A><BR>
      <A name="TOC13" href="mtt.html#SEC13" id="TOC13">1.8 Switched
      systems</A><BR>
    </BLOCKQUOTE><A name="TOC14" href="mtt.html#SEC14" id="TOC14">2. User
    interface</A><BR>
    <BLOCKQUOTE>
      <A name="TOC15" href="mtt.html#SEC15" id="TOC15">2.1 Menu-driven
      interface</A><BR>
      <A name="TOC16" href="mtt.html#SEC16" id="TOC16">2.2 Command line
      interface</A><BR>
      <A name="TOC17" href="mtt.html#SEC17" id="TOC17">2.3 Options</A><BR>
      <A name="TOC18" href="mtt.html#SEC18" id="TOC18">2.4 Utilities</A><BR>
      <BLOCKQUOTE>
        <A name="TOC19" href="mtt.html#SEC19" id="TOC19">2.4.1 Help</A><BR>
        <BLOCKQUOTE>
          <A name="TOC20" href="mtt.html#SEC20" id="TOC20">2.4.1.1 help
          representations</A><BR>
          <A name="TOC21" href="mtt.html#SEC21" id="TOC21">2.4.1.2 help
          components</A><BR>
          <A name="TOC22" href="mtt.html#SEC22" id="TOC22">2.4.1.3 help
          examples</A><BR>
          <A name="TOC23" href="mtt.html#SEC23" id="TOC23">2.4.1.4 help
          crs</A><BR>
          <A name="TOC24" href="mtt.html#SEC24" id="TOC24">2.4.1.5 help
          &lt;name&gt;</A><BR>
        </BLOCKQUOTE><A name="TOC25" href="mtt.html#SEC25" id="TOC25">2.4.2
        Copy</A><BR>
        <A name="TOC26" href="mtt.html#SEC26" id="TOC26">2.4.3 Clean</A><BR>
        <A name="TOC27" href="mtt.html#SEC27" id="TOC27">2.4.4 Version
        control</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC28" href="mtt.html#SEC28" id="TOC28">3. Creating
    Models</A><BR>
    <BLOCKQUOTE>
      <A name="TOC29" href="mtt.html#SEC29" id="TOC29">3.1 Quick
      start</A><BR>
      <A name="TOC30" href="mtt.html#SEC30" id="TOC30">3.2 Creating simple
      models</A><BR>
      <A name="TOC31" href="mtt.html#SEC31" id="TOC31">3.3 Creating complex
      models</A><BR>
      <BLOCKQUOTE>
        <A name="TOC32" href="mtt.html#SEC32" id="TOC32">3.3.1 Top
        level</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC33" href="mtt.html#SEC33" id="TOC33">4.
    Simulation</A><BR>
    <BLOCKQUOTE>
      <A name="TOC34" href="mtt.html#SEC34" id="TOC34">4.1 Steady-state
      solutions</A><BR>
      <BLOCKQUOTE>
        <A name="TOC35" href="mtt.html#SEC35" id="TOC35">4.1.1 Steady-state
        solutions (odess)</A><BR>
        <A name="TOC36" href="mtt.html#SEC36" id="TOC36">4.1.2 Steady-state
        solutions (ss)</A><BR>
      </BLOCKQUOTE><A name="TOC37" href="mtt.html#SEC37" id="TOC37">4.2
      Simulation parameters</A><BR>
      <BLOCKQUOTE>
        <A name="TOC38" href="mtt.html#SEC38" id="TOC38">4.2.1 Euler
        integration</A><BR>
        <A name="TOC39" href="mtt.html#SEC39" id="TOC39">4.2.2 Implicit
        integration</A><BR>
        <A name="TOC40" href="mtt.html#SEC40" id="TOC40">4.2.3 Runge Kutta IV
        integration</A><BR>
        <A name="TOC41" href="mtt.html#SEC41" id="TOC41">4.2.4 Hybrd
        algebraic solver</A><BR>
      </BLOCKQUOTE><A name="TOC42" href="mtt.html#SEC42" id="TOC42">4.3
      Simulation input</A><BR>
      <A name="TOC43" href="mtt.html#SEC43" id="TOC43">4.4 Simulation
      logic</A><BR>
      <A name="TOC44" href="mtt.html#SEC44" id="TOC44">4.5 Simulation initial
      state</A><BR>
      <A name="TOC45" href="mtt.html#SEC45" id="TOC45">4.6 Simulation
      code</A><BR>
      <BLOCKQUOTE>
        <A name="TOC46" href="mtt.html#SEC46" id="TOC46">4.6.1 Dynamically
        linked functions</A><BR>
      </BLOCKQUOTE><A name="TOC47" href="mtt.html#SEC47" id="TOC47">4.7
      Simulation output</A><BR>
      <BLOCKQUOTE>
        <A name="TOC48" href="mtt.html#SEC48" id="TOC48">4.7.1 Viewing
        results with gnuplot</A><BR>
        <A name="TOC49" href="mtt.html#SEC49" id="TOC49">4.7.2 Exporting
        results to SciGraphica</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC50" href="mtt.html#SEC50" id="TOC50">5.
    Sensitivity models</A><BR>
    <A name="TOC51" href="mtt.html#SEC51" id="TOC51">6.
    Representations</A><BR>
    <BLOCKQUOTE>
      <A name="TOC52" href="mtt.html#SEC52" id="TOC52">6.1 Representation
      summary</A><BR>
      <A name="TOC53" href="mtt.html#SEC53" id="TOC53">6.2 Defining
      representations</A><BR>
      <A name="TOC54" href="mtt.html#SEC54" id="TOC54">6.3 Verbal description
      (desc)</A><BR>
      <A name="TOC55" href="mtt.html#SEC55" id="TOC55">6.4 Acausal bond graph
      (abg)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC56" href="mtt.html#SEC56" id="TOC56">6.4.1 Language fig
        (abg.fig)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC57" href="mtt.html#SEC57" id="TOC57">6.4.1.1 Icon
          library</A><BR>
          <A name="TOC58" href="mtt.html#SEC58" id="TOC58">6.4.1.2
          Bonds</A><BR>
          <A name="TOC59" href="mtt.html#SEC59" id="TOC59">6.4.1.3
          Strokes</A><BR>
          <A name="TOC60" href="mtt.html#SEC60" id="TOC60">6.4.1.4
          Components</A><BR>
          <A name="TOC61" href="mtt.html#SEC61" id="TOC61">6.4.1.5 Simple
          components</A><BR>
          <A name="TOC62" href="mtt.html#SEC62" id="TOC62">6.4.1.6 SS
          components</A><BR>
          <A name="TOC63" href="mtt.html#SEC63" id="TOC63">6.4.1.7 Simple
          components - implementation</A><BR>
          <A name="TOC64" href="mtt.html#SEC64" id="TOC64">6.4.1.8 Compound
          components</A><BR>
          <A name="TOC65" href="mtt.html#SEC65" id="TOC65">6.4.1.9 Named SS
          components</A><BR>
          <A name="TOC66" href="mtt.html#SEC66" id="TOC66">6.4.1.10 Coerced
          bond direction</A><BR>
          <A name="TOC67" href="mtt.html#SEC67" id="TOC67">6.4.1.11 Port
          labels</A><BR>
          <A name="TOC68" href="mtt.html#SEC68" id="TOC68">6.4.1.12 Vector
          port labels</A><BR>
          <A name="TOC69" href="mtt.html#SEC69" id="TOC69">6.4.1.13 Port
          label defaults</A><BR>
          <A name="TOC70" href="mtt.html#SEC70" id="TOC70">6.4.1.14 Vector
          Components</A><BR>
          <A name="TOC71" href="mtt.html#SEC71" id="TOC71">6.4.1.15
          Artwork</A><BR>
          <A name="TOC72" href="mtt.html#SEC72" id="TOC72">6.4.1.16 Valid
          Names</A><BR>
        </BLOCKQUOTE><A name="TOC73" href="mtt.html#SEC73" id="TOC73">6.4.2
        Language m (rbg.m)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC74" href="mtt.html#SEC74" id="TOC74">6.4.2.1
          Transformation abg2rbg_fig2m</A><BR>
        </BLOCKQUOTE><A name="TOC75" href="mtt.html#SEC75" id="TOC75">6.4.3
        Language m (abg.m)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC76" href="mtt.html#SEC76" id="TOC76">6.4.3.1
          Arrow-orientated causality</A><BR>
          <A name="TOC77" href="mtt.html#SEC77" id="TOC77">6.4.3.2
          Component-orientated causality</A><BR>
          <A name="TOC78" href="mtt.html#SEC78" id="TOC78">6.4.3.3
          Transformation rbg2abg_m</A><BR>
        </BLOCKQUOTE><A name="TOC79" href="mtt.html#SEC79" id="TOC79">6.4.4
        Language tex (abg.tex)</A><BR>
      </BLOCKQUOTE><A name="TOC80" href="mtt.html#SEC80" id="TOC80">6.5
      Stripped acausal bond graph (sabg)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC81" href="mtt.html#SEC81" id="TOC81">6.5.1 Language fig
        (sabg.fig)</A><BR>
        <A name="TOC82" href="mtt.html#SEC82" id="TOC82">6.5.2 Stripped
        acausal bond graph (view)</A><BR>
      </BLOCKQUOTE><A name="TOC83" href="mtt.html#SEC83" id="TOC83">6.6
      Labels (lbl)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC84" href="mtt.html#SEC84" id="TOC84">6.6.1 SS component
        labels</A><BR>
        <A name="TOC85" href="mtt.html#SEC85" id="TOC85">6.6.2 Other
        component labels</A><BR>
        <A name="TOC86" href="mtt.html#SEC86" id="TOC86">6.6.3 Component
        names</A><BR>
        <A name="TOC87" href="mtt.html#SEC87" id="TOC87">6.6.4 Component
        constitutive relationship</A><BR>
        <A name="TOC88" href="mtt.html#SEC88" id="TOC88">6.6.5 Component
        arguments</A><BR>
        <A name="TOC89" href="mtt.html#SEC89" id="TOC89">6.6.6 Parameter
        declarations</A><BR>
        <A name="TOC90" href="mtt.html#SEC90" id="TOC90">6.6.7 Units
        declarations</A><BR>
        <A name="TOC91" href="mtt.html#SEC91" id="TOC91">6.6.8 Interface
        Control Definition</A><BR>
        <A name="TOC92" href="mtt.html#SEC92" id="TOC92">6.6.9
        Aliases</A><BR>
        <BLOCKQUOTE>
          <A name="TOC93" href="mtt.html#SEC93" id="TOC93">6.6.9.1 Port
          aliases</A><BR>
          <A name="TOC94" href="mtt.html#SEC94" id="TOC94">6.6.9.2 Parameter
          aliases</A><BR>
          <A name="TOC95" href="mtt.html#SEC95" id="TOC95">6.6.9.3 CR
          aliases</A><BR>
          <A name="TOC96" href="mtt.html#SEC96" id="TOC96">6.6.9.4 Component
          aliases</A><BR>
        </BLOCKQUOTE><A name="TOC97" href="mtt.html#SEC97" id="TOC97">6.6.10
        Parameter passing</A><BR>
        <A name="TOC98" href="mtt.html#SEC98" id="TOC98">6.6.11 Old-style
        labels (lbl)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC99" href="mtt.html#SEC99" id="TOC99">6.6.11.1 SS
          component labels (old-style)</A><BR>
          <A name="TOC100" href="mtt.html#SEC100" id="TOC100">6.6.11.2 Other
          component labels (old-style)</A><BR>
          <A name="TOC101" href="mtt.html#SEC101" id="TOC101">6.6.11.3
          Parameter passing (old-style)</A><BR>
        </BLOCKQUOTE><A name="TOC102" href="mtt.html#SEC102" id=
        "TOC102">6.6.12 Language tex (desc.tex)</A><BR>
      </BLOCKQUOTE><A name="TOC103" href="mtt.html#SEC103" id="TOC103">6.7
      Structure (struc)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC104" href="mtt.html#SEC104" id="TOC104">6.7.1 Language
        txt (struc.txt)</A><BR>
        <A name="TOC105" href="mtt.html#SEC105" id="TOC105">6.7.2 Language
        tex (struc.tex)</A><BR>
        <A name="TOC106" href="mtt.html#SEC106" id="TOC106">6.7.3 Language
        tex (view)</A><BR>
      </BLOCKQUOTE><A name="TOC107" href="mtt.html#SEC107" id="TOC107">6.8
      Constitutive relationship (cr)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC108" href="mtt.html#SEC108" id="TOC108">6.8.1 Predefined
        constitutive relationships</A><BR>
        <BLOCKQUOTE>
          <A name="TOC109" href="mtt.html#SEC109" id="TOC109">6.8.1.1
          lin</A><BR>
          <A name="TOC110" href="mtt.html#SEC110" id="TOC110">6.8.1.2
          exotherm</A><BR>
        </BLOCKQUOTE><A name="TOC111" href="mtt.html#SEC111" id=
        "TOC111">6.8.2 DIY constitutive relationships</A><BR>
        <A name="TOC112" href="mtt.html#SEC112" id="TOC112">6.8.3 Unresolved
        constitutive relationships</A><BR>
        <A name="TOC113" href="mtt.html#SEC113" id="TOC113">6.8.4 Unresolved
        constitutive relationships - Octave</A><BR>
        <A name="TOC114" href="mtt.html#SEC114" id="TOC114">6.8.5 Unresolved
        constitutive relationships - c++</A><BR>
      </BLOCKQUOTE><A name="TOC115" href="mtt.html#SEC115" id="TOC115">6.9
      Parameters</A><BR>
      <BLOCKQUOTE>
        <A name="TOC116" href="mtt.html#SEC116" id="TOC116">6.9.1 Symbolic
        parameters (subs.r)</A><BR>
        <A name="TOC117" href="mtt.html#SEC117" id="TOC117">6.9.2 Symbolic
        parameters for simplification (simp.r)</A><BR>
        <A name="TOC118" href="mtt.html#SEC118" id="TOC118">6.9.3 Numeric
        parameters (numpar)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC119" href="mtt.html#SEC119" id="TOC119">6.9.3.1 Text
          form (numpar.txt)</A><BR>
        </BLOCKQUOTE>
      </BLOCKQUOTE><A name="TOC120" href="mtt.html#SEC120" id="TOC120">6.10
      Causal bond graph (cbg)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC121" href="mtt.html#SEC121" id="TOC121">6.10.1 Language
        fig (cbg.fig)</A><BR>
        <A name="TOC122" href="mtt.html#SEC122" id="TOC122">6.10.2 Language m
        (cbg.m)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC123" href="mtt.html#SEC123" id="TOC123">6.10.2.1
          Transformation abg2cbg_m</A><BR>
        </BLOCKQUOTE>
      </BLOCKQUOTE><A name="TOC124" href="mtt.html#SEC124" id="TOC124">6.11
      Elementary system equations (ese)</A><BR>
      <BLOCKQUOTE>
        <BLOCKQUOTE>
          <A name="TOC125" href="mtt.html#SEC125" id="TOC125">6.11.0.1
          Transformation cbg2ese_m2r</A><BR>
        </BLOCKQUOTE>
      </BLOCKQUOTE><A name="TOC126" href="mtt.html#SEC126" id="TOC126">6.12
      Differential-Algebraic Equations (dae)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC127" href="mtt.html#SEC127" id="TOC127">6.12.1 Language
        reduce (dae.r)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC128" href="mtt.html#SEC128" id="TOC128">6.12.1.1
          Transformation ese2dae_r</A><BR>
        </BLOCKQUOTE><A name="TOC129" href="mtt.html#SEC129" id=
        "TOC129">6.12.2 Language m (dae.m)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC130" href="mtt.html#SEC130" id="TOC130">6.12.2.1
          Transformation dae_r2m</A><BR>
        </BLOCKQUOTE>
      </BLOCKQUOTE><A name="TOC131" href="mtt.html#SEC131" id="TOC131">6.13
      Constrained-state Equations (cse)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC132" href="mtt.html#SEC132" id="TOC132">6.13.1 Language
        reduce (cse.r)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC133" href="mtt.html#SEC133" id="TOC133">6.13.1.1
          Transformation dae2cse_r</A><BR>
        </BLOCKQUOTE><A name="TOC134" href="mtt.html#SEC134" id=
        "TOC134">6.13.2 Language m (view)</A><BR>
      </BLOCKQUOTE><A name="TOC135" href="mtt.html#SEC135" id="TOC135">6.14
      Ordinary Differential Equations</A><BR>
      <BLOCKQUOTE>
        <A name="TOC136" href="mtt.html#SEC136" id="TOC136">6.14.1 Language
        reduce (ode.r)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC137" href="mtt.html#SEC137" id="TOC137">6.14.1.1
          Transformation cse2ode_r</A><BR>
        </BLOCKQUOTE><A name="TOC138" href="mtt.html#SEC138" id=
        "TOC138">6.14.2 Language m (ode.m)</A><BR>
        <BLOCKQUOTE>
          <A name="TOC139" href="mtt.html#SEC139" id="TOC139">6.14.2.1
          Transformation ode_r2m</A><BR>
        </BLOCKQUOTE><A name="TOC140" href="mtt.html#SEC140" id=
        "TOC140">6.14.3 Language m (view)</A><BR>
      </BLOCKQUOTE><A name="TOC141" href="mtt.html#SEC141" id="TOC141">6.15
      Descriptor matrices (dm)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC142" href="mtt.html#SEC142" id="TOC142">6.15.1 Language
        reduce (dm.r)</A><BR>
        <A name="TOC143" href="mtt.html#SEC143" id="TOC143">6.15.2 Language m
        (dm.m)</A><BR>
      </BLOCKQUOTE><A name="TOC144" href="mtt.html#SEC144" id="TOC144">6.16
      Report (rep)</A><BR>
      <BLOCKQUOTE>
        <A name="TOC145" href="mtt.html#SEC145" id="TOC145">6.16.1 Language
        text (rep.txt)</A><BR>
        <A name="TOC146" href="mtt.html#SEC146" id="TOC146">6.16.2 Language
        view</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC147" href="mtt.html#SEC147" id="TOC147">7.
    Extending MTT</A><BR>
    <BLOCKQUOTE>
      <A name="TOC148" href="mtt.html#SEC148" id="TOC148">7.1
      Makefiles</A><BR>
      <A name="TOC149" href="mtt.html#SEC149" id="TOC149">7.2 New (DIY)
      representations</A><BR>
      <BLOCKQUOTE>
        <A name="TOC150" href="mtt.html#SEC150" id="TOC150">7.2.1
        Makefile</A><BR>
        <A name="TOC151" href="mtt.html#SEC151" id="TOC151">7.2.2
        Shell-script</A><BR>
        <A name="TOC152" href="mtt.html#SEC152" id="TOC152">7.2.3
        Documentation</A><BR>
      </BLOCKQUOTE><A name="TOC153" href="mtt.html#SEC153" id="TOC153">7.3
      Component library</A><BR>
    </BLOCKQUOTE><A name="TOC154" href="mtt.html#SEC154" id="TOC154">8.
    Documentation</A><BR>
    <BLOCKQUOTE>
      <A name="TOC155" href="mtt.html#SEC155" id="TOC155">8.1 Manual</A><BR>
      <A name="TOC156" href="mtt.html#SEC156" id="TOC156">8.2 On-line
      documentation</A><BR>
      <BLOCKQUOTE>
        <A name="TOC157" href="mtt.html#SEC157" id="TOC157">8.2.1 Brief
        on-line documentation</A><BR>
        <A name="TOC158" href="mtt.html#SEC158" id="TOC158">8.2.2 Detailed
        on-line documentation</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC159" href="mtt.html#SEC159" id="TOC159">9.
    Languages</A><BR>
    <BLOCKQUOTE>
      <A name="TOC160" href="mtt.html#SEC160" id="TOC160">9.1 Fig</A><BR>
      <A name="TOC161" href="mtt.html#SEC161" id="TOC161">9.2 m</A><BR>
      <A name="TOC162" href="mtt.html#SEC162" id="TOC162">9.3 Reduce</A><BR>
      <A name="TOC163" href="mtt.html#SEC163" id="TOC163">9.4 c</A><BR>
    </BLOCKQUOTE><A name="TOC164" href="mtt.html#SEC164" id="TOC164">10.
    Language tools</A><BR>
    <BLOCKQUOTE>
      <A name="TOC165" href="mtt.html#SEC165" id="TOC165">10.1 Views</A><BR>
      <A name="TOC166" href="mtt.html#SEC166" id="TOC166">10.2 Xfig</A><BR>
      <A name="TOC167" href="mtt.html#SEC167" id="TOC167">10.3 Text
      editors</A><BR>
      <A name="TOC168" href="mtt.html#SEC168" id="TOC168">10.4 Octave</A><BR>
      <BLOCKQUOTE>
        <A name="TOC169" href="mtt.html#SEC169" id="TOC169">10.4.1 Octave
        control system toolbox (OCST)</A><BR>
        <A name="TOC170" href="mtt.html#SEC170" id="TOC170">10.4.2 Creating
        GNU Octave .oct files</A><BR>
        <A name="TOC171" href="mtt.html#SEC171" id="TOC171">10.4.3 Creating
        Matlab .mex files</A><BR>
        <A name="TOC172" href="mtt.html#SEC172" id="TOC172">10.4.4 Embedding
        MTT models in Simulink</A><BR>
      </BLOCKQUOTE><A name="TOC173" href="mtt.html#SEC173" id="TOC173">10.5
      LaTeX</A><BR>
    </BLOCKQUOTE><A name="TOC174" href="mtt.html#SEC174" id="TOC174">11.
    Administration</A><BR>
    <BLOCKQUOTE>
      <A name="TOC175" href="mtt.html#SEC175" id="TOC175">11.1 Software
      components</A><BR>
      <A name="TOC176" href="mtt.html#SEC176" id="TOC176">11.2 REDUCE
      setup</A><BR>
      <A name="TOC177" href="mtt.html#SEC177" id="TOC177">11.3 Octave
      setup</A><BR>
      <BLOCKQUOTE>
        <A name="TOC178" href="mtt.html#SEC178" id="TOC178">11.3.1
        .octaverc</A><BR>
        <A name="TOC179" href="mtt.html#SEC179" id="TOC179">11.3.2 .oct file
        dependencies</A><BR>
      </BLOCKQUOTE><A name="TOC180" href="mtt.html#SEC180" id="TOC180">11.4
      Paths</A><BR>
      <BLOCKQUOTE>
        <A name="TOC181" href="mtt.html#SEC181" id="TOC181">11.4.1
        $MTTPATH</A><BR>
        <A name="TOC182" href="mtt.html#SEC182" id="TOC182">11.4.2
        $MTT_COMPONENTS</A><BR>
        <A name="TOC183" href="mtt.html#SEC183" id="TOC183">11.4.3
        $MTT_CRS</A><BR>
        <A name="TOC184" href="mtt.html#SEC184" id="TOC184">11.4.4
        $MTT_EXAMPLES</A><BR>
        <A name="TOC185" href="mtt.html#SEC185" id="TOC185">11.4.5
        $OCTAVE_PATH</A><BR>
      </BLOCKQUOTE><A name="TOC186" href="mtt.html#SEC186" id="TOC186">11.5
      File structure</A><BR>
    </BLOCKQUOTE><A name="TOC187" href="mtt.html#SEC187" id="TOC187">A. Legal
    stuff</A><BR>
    <BLOCKQUOTE>
      <A name="TOC188" href="mtt.html#SEC188" id="TOC188">A.1 GNU Free
      Documentation License</A><BR>
      <BLOCKQUOTE>
        <A name="TOC189" href="mtt.html#SEC189" id="TOC189">A.1.1 ADDENDUM:
        How to use this License for your documents</A><BR>
      </BLOCKQUOTE><A name="TOC190" href="mtt.html#SEC190" id="TOC190">A.2
      GNU GENERAL PUBLIC LICENSE</A><BR>
      <BLOCKQUOTE>
        <A name="TOC191" href="mtt.html#SEC191" id="TOC191">A.2.1
        Preamble</A><BR>
        <A name="TOC192" href="mtt.html#SEC192" id="TOC192">A.2.2 Appendix:
        How to Apply These Terms to Your New Programs</A><BR>
      </BLOCKQUOTE>
    </BLOCKQUOTE><A name="TOC193" href="mtt.html#SEC193" id=
    "TOC193">Glossary</A><BR>
    <A name="TOC194" href="mtt.html#SEC194" id="TOC194">Index</A><BR>
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  <H1>Short Table of Contents</H1>
  <BLOCKQUOTE>
    <A name="TOC1" href="mtt.html#SEC1" id="TOC1">1. Introduction</A><BR>
    <A name="TOC14" href="mtt.html#SEC14" id="TOC14">2. User
    interface</A><BR>
    <A name="TOC28" href="mtt.html#SEC28" id="TOC28">3. Creating
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    <A name="TOC33" href="mtt.html#SEC33" id="TOC33">4. Simulation</A><BR>
    <A name="TOC50" href="mtt.html#SEC50" id="TOC50">5. Sensitivity
    models</A><BR>
    <A name="TOC51" href="mtt.html#SEC51" id="TOC51">6.
    Representations</A><BR>
    <A name="TOC147" href="mtt.html#SEC147" id="TOC147">7. Extending
    MTT</A><BR>
    <A name="TOC154" href="mtt.html#SEC154" id="TOC154">8.
    Documentation</A><BR>
    <A name="TOC159" href="mtt.html#SEC159" id="TOC159">9. Languages</A><BR>
    <A name="TOC164" href="mtt.html#SEC164" id="TOC164">10. Language
    tools</A><BR>
    <A name="TOC174" href="mtt.html#SEC174" id="TOC174">11.
    Administration</A><BR>
    <A name="TOC187" href="mtt.html#SEC187" id="TOC187">A. Legal
    stuff</A><BR>
    <A name="TOC193" href="mtt.html#SEC193" id="TOC193">Glossary</A><BR>
    <A name="TOC194" href="mtt.html#SEC194" id="TOC194">Index</A><BR>
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