File r37/lisp/csl/html/r37_0595.html artifact 29b4c25b97 part of check-in 1feb677270

<A NAME=jacobian>

<TITLE>jacobian</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>JACOBIAN</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>jacobian</em>(&lt;expr\_list&gt;,&lt;variable\_list&gt;) 
<P>
<P>
<P>
&lt;expr\_list&gt; :- either a single algebraic expression or a list 
 of algebraic expressions. 
<P>
<P>
&lt;variable\_list&gt; :- either a single variable or a list of 
 variables. 
<P>
<P>
<em>jacobian</em>computes the jacobian matrix of &lt;expr\_list&gt; 
w.r.t. &lt;variable\_list&gt;. 
<P>
<P>
This is a matrix whose (i,j)'th entry is 
<A HREF=r37_0148.html>df</A>(&lt;expr\_list&gt; 
(i),&lt;variable\_list&gt;(j)). 
<P>
<P>
The matrix is n by m where n is the number of variables and m the number 
of expressions. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
 
jacobian({x^4,x*y^2,x*y*z^3},{w,x,y,z}); 


  [      3                 ]
  [0  4*x     0       0    ]
  [                        ]
  [     2                  ]
  [0   y    2*x*y     0    ]
  [                        ]
  [      3     3          2]
  [0  y*z   x*z    3*x*y*z ]

</TT></PRE><P>Related functions: 

<A HREF=r37_0593.html>hessian</A>, 
<A HREF=r37_0148.html>df</A>. 
<P>
<P>