Analytical Differentiation

This example shows how Symbolic Tools uses the Maple kernel to carry out analytical differentiation, and then to create and compile a GAUSS proc that has the same functionality.  This is the basis for Automatic Differentiation.

The process of creating a proc based on symbolic code is a one line operation -   symproc. This command takes four arguments - the proc name, the input argument(s), the output required, and the code.  The code ( txt ) is GAUSS, with the gradp function overloaded to permit a symbolic second argument.  The call to symproc executes the code in the Maple kernel, creates the equivalent GAUSS proc, and compiles the proc, so that it can be called immediately - as shown below.

 library symbolic;                      // define the library
 call symstate(reset);                  // turns on symbolic processing

 proc difsin; endp;                     // dummy proc
 txt = "
        slist = {x,y};
        llf =  sin(x*y)^2;
        llfg = gradp(llf,slist);
       ";

  call  symproc("difsin","x,y","llfg",txt); // create and compile the proc
  rslt = difsin(1,2);                       // execute the proc
  "rslt\n" rslt;

The proc that is created by the  symproc command :

proc difsin(x,y);
  local t0,     t1,     t2,     t3,     t4,
      unknown;
      unknown = zeros(rows(y),2);
      t1 = x .* y;
      t2 = sin(t1);
      t3 = cos(t1);
      t4 = t2 .* t3;
      unknown[.,1+0] = 2.0 .* t4 .* y;
      unknown[.,1+1] = 2.0 .* t4 .* x;
      retp(unknown); 
endp; 

The output from this example is :

	rslt   -1.5136050 -0.75680251