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// Copyright (C) 2004, 2006   Michael Creel   <michael.creel@uab.es>
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  GNU General Public License for more details.
//  You should have received a copy of the GNU General Public License
//  along with this program; If not, see <http://www.gnu.org/licenses/>.

// numgradient: numeric central difference gradient

#include <oct.h>
#include <octave/parse.h>
#include <octave/lo-mappers.h>
#include <octave/Cell.h>
#include <float.h>

// argument checks
static bool
any_bad_argument(const octave_value_list& args)
      if (!args(0).is_string())
            error("numgradient: first argument must be string holding objective function name");
            return true;

      if (!args(1).is_cell())
            error("numgradient: second argument must cell array of function arguments");
            return true;

      // minarg, if provided
      if (args.length() == 3)
            int tmp = args(2).int_value();
            if (error_state)
                  error("numgradient: 3rd argument, if supplied,  must an integer\n\
that specifies the argument wrt which differentiation is done");
                  return true;
            if ((tmp > args(1).length())||(tmp < 1))
                  error("numgradient: 3rd argument must be a positive integer that indicates \n\
which of the elements of the second argument is the\n\
one to differentiate with respect to");
                  return true;
      return false;

DEFUN_DLD(numgradient, args, , "numgradient(f, {args}, minarg)\n\
Numeric central difference gradient of f with respect\n\
to argument \"minarg\".\n\
* first argument: function name (string)\n\
* second argument: all arguments of the function (cell array)\n\
* third argument: (optional) the argument to differentiate w.r.t.\n\
      (scalar, default=1)\n\
\"f\" may be vector-valued. If \"f\" returns\n\
an n-vector, and the argument is a k-vector, the gradient\n\
will be an nxk matrix\n\
function a = f(x);\n\
      a = [x'*x; 2*x];\n\
numgradient(\"f\", {ones(2,1)})\n\
ans =\n\
  2.00000  2.00000\n\
  2.00000  0.00000\n\
  0.00000  2.00000\n\
      int nargin = args.length();
      if (!((nargin == 2)|| (nargin == 3))) {
            error("numgradient: you must supply 2 or 3 arguments");
            return octave_value_list();

      // check the arguments
      if (any_bad_argument(args)) return octave_value_list();

      std::string f (args(0).string_value());
      Cell f_args_cell (args(1).cell_value());
      octave_value_list f_args, f_return;
      Matrix obj_value, obj_left, obj_right;
      double SQRT_EPS, p, delta, diff;
      int i, j, k, n, minarg, test;

      // Default values for controls
      minarg = 1; // by default, first arg is one over which we minimize

      // copy cell contents over to octave_value_list to use feval()
      k = f_args_cell.length();
      f_args(k); // resize only once
      for (i = 0; i<k; i++) f_args(i) = f_args_cell(i);

      // check which arg w.r.t which we need to differentiate
      if (args.length() == 3) minarg = args(2).int_value();
      Matrix parameter = f_args(minarg - 1).matrix_value();

      // initial function value
      f_return = feval(f, f_args);
      obj_value = f_return(0).matrix_value();

      n = obj_value.rows(); // find out dimension
      k = parameter.rows();
      Matrix derivative(n, k);
      Matrix columnj;

      for (j=0; j<k; j++) { // get 1st derivative by central difference
            p = parameter(j);

            // determine delta for finite differencing
            SQRT_EPS = sqrt(DBL_EPSILON);
            diff = exp(log(DBL_EPSILON)/3);
            test = (fabs(p) + SQRT_EPS) * SQRT_EPS > diff;
            if (test) delta = (fabs(p) + SQRT_EPS) * SQRT_EPS;
            else delta = diff;

            // right side
            parameter(j) = p + delta;
            f_args(minarg - 1) = parameter;
            f_return = feval(f, f_args);
            obj_right = f_return(0).matrix_value();

            // left size
            parameter(j) = p - delta;
            f_args(minarg - 1) = parameter;
            f_return = feval(f, f_args);
            obj_left = f_return(0).matrix_value();

            parameter(j) = p;  // restore original parameter
            columnj = (obj_right - obj_left) / (2*delta);
            for (i=0; i<n; i++) derivative(i, j) = columnj(i);

      return octave_value(derivative);

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