GAUSS

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