#! /bin/sh

     ###################################### 
     ##### Model Transformation Tools #####
     ######################################

# Bourne shell script: lde2ode.r
# Reduce differential-algebraic equations to Lagranges equations
# Copyright (C) 2000 by Peter J. Gawthrop

###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

# Create the reduce output code
def2write_r $1 lde
def2write_r $1 ldeo

#Inform user
echo Creating $1_lde.r
echo Creating $1_ldeo.r

# Remove the old log file
rm -f cse2lde_r.log

# Use reduce to accomplish the transformation
$SYMBOLIC  << EOF >cse2lde_r.log

%Read the formatting function
in "$MTTPATH/trans/reduce_matrix.r";

%Read the definitions file
in "$1_def.r";

%Read the substitution file
in "$1_subs.r";

%Read the dae file
in "$1_dae.r";

% Zap bits we dont need
clear mttui, mttu, mttdu, mttx, mttdz;

%% The lagrangian eqns are those set to zero.
MTTL := mttyz;

% Create the second derivative of z
MATRIX mttddz(MTTNz,1);
FOR i := 1:MTTNz DO
BEGIN
  mttuii := mkid(mttui,i);
  mttdduii := mkid(mttddui,i);
  mttddz(i,1) :=  sub(mttuii=mttdduii,mttz(i,1));
END;
mttddz;

% Create Lagranges Equations
FOR j := 1:MTTNyz DO
BEGIN
  %% Create derivative of the equations by substituting:
  %du for u
  mttuj := mkid(mttu,j);
  mttduj := mkid(mttdu,j);
  MTTL :=  sub(mttuj=mttduj,MTTL);

  % dv for v
  mttuij := mkid(mttui,j);
  mttduij := mkid(mttdui,j);
  MTTL :=  sub(mttuij=mttduij,MTTL);

  % dx for x
  mttxj := mkid(mttx,j);
  MTTL :=  sub(mttxj=mttdx(j,1),MTTL);

  % ddz for dz
  mttdzj := mkid(mttdz,j);
  MTTL :=  sub(mttdzj=mttddz(j,1),MTTL);

END;

L = MTTL;

OFF Echo;
OFF Nat;


%Write out the  ordinary differential equations.
OUT "$1_lde.r";
write "%File: $1_lde.r";
in ("$1_lde_write.r");
write "in ""$1_ldeo.r"";";
write "END;";
SHUT "$1_lde.r";

%Write out the  output equations
OUT "$1_ldeo.r";
write "%File: $1_ldeo.r";
in ("$1_ldeo_write.r");
write "END;";
SHUT "$1_ldeo.r";
quit;
EOF

# Now invoke the standard error handling.
mtt_error_r cse2lde_r.log








