[GiNaC-list] differentiating with respect to a variable in a list

[Sheplyakov Alexei]

On Sat, May 21, 2005 at 01:15:18PM -0400, Karen Yeats wrote:
> I'd like to make a function with a list as one argument and be able to
> take derivatives with respect to the variables encased in the list.

You don't want to do this, since such a function will break GiNaC's
implementation of the chain rule. Probably, you need to define a
function with variable number of arguments. Here is an example:

/**
  * @file uniform_demo.cpp 
	* Define a function, which is uniform w.r.t each argument.
  */

#include <iostream>
#include <stdexcept>
#include <ginac/ginac.h>
using namespace std;
using namespace GiNaC;

/**
 * (dummy) function for symbolic evaluation
 */
static ex uniform_eval(const exvector& ev)
{
	return uniform(ev).hold();
}

/** 
 * differentiate uniform function
 *
 * @param ev - arguments, as a std::vector<GiNaC::ex>
 * @return the partial derivative w.r.t. diff_param-th argument
 */
static ex uniform_deriv(const exvector& ev, unsigned diff_param)
{
 assert(diff_param < ev.size());
 // d/dx_i f(x_1, ..., x_n) = x_i * f(x_1, ..., x_n)
 return ev[diff_param]*uniform(ev);
}

/** 
 * Some cruft to make our function known to GiNaC.
 */
class uniform_SERIAL
{
  public:
	 static unsigned serial;
};

/** 
 * More cruft to make our function known to GiNaC.
 */
unsigned uniform_SERIAL::serial = function::register_new(
		function_options("uniform").
		eval_func(uniform_eval).
		derivative_func(uniform_deriv));

/**
 * Just a convenient wrapper. 
 */
inline function uniform(const exvector& ev)
{
  return function(uniform_SERIAL::serial, ev);
}


/**
 * just demonstrate how it works
 */
int main(int argc, char** argv)
{
	symbol x("x");
	symbol y("y");
	symbol z("z");
	exvector ev;
	ev.push_back(x+y);
	ev.push_back(cos(x)+y);
	ev.push_back(z+x);

	ex test = uniform(ev); // f(x+y, cos(x)+y, z+x)
	ex tdiff = test.diff(x);

	cout << "d/dx (" << test << ") = " << tdiff << endl;
	return 0;
}
	

Hope this helps,
  Alexei.
 
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 189 bytes
Desc: Digital signature
Url : http://www.cebix.net/pipermail/ginac-list/attachments/20050523/68a13bfe/attachment.pgp