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diff --git a/ml/dlib/dlib/test/optimization_test_functions.cpp b/ml/dlib/dlib/test/optimization_test_functions.cpp
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+// Copyright (C) 2010 Davis E. King (davis@dlib.net)
+// License: Boost Software License See LICENSE.txt for the full license.
+#include "optimization_test_functions.h"
+
+/*
+
+ Most of the code in this file is converted from the set of Fortran 90 routines
+ created by John Burkardt.
+
+ The original Fortran can be found here: http://orion.math.iastate.edu/burkardt/f_src/testopt/testopt.html
+
+*/
+
+
+namespace dlib
+{
+ namespace test_functions
+ {
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,0,1> chebyquad_residuals(const matrix<double,0,1>& x)
+ {
+ matrix<double,0,1> fvec(x.size());
+ const int n = x.size();
+ int i;
+ int j;
+ double t;
+ double t1;
+ double t2;
+ double th;
+ fvec = 0;
+
+ for (j = 1; j <= n; ++j)
+ {
+ t1 = 1.0E+00;
+ t2 = 2.0E+00 * x(j-1) - 1.0E+00;
+ t = 2.0E+00 * t2;
+ for (i = 1; i <= n; ++i)
+ {
+ fvec(i-1) = fvec(i-1) + t2;
+ th = t * t2 - t1;
+ t1 = t2;
+ t2 = th;
+ }
+ }
+
+ for (i = 1; i <= n; ++i)
+ {
+ fvec(i-1) = fvec(i-1) / (double) ( n );
+ if ( ( i%2 ) == 0 )
+ fvec(i-1) = fvec(i-1) + 1.0E+00 / ( (double)i*i - 1.0E+00 );
+ }
+
+ return fvec;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ double chebyquad_residual(int i, const matrix<double,0,1>& x)
+ {
+ return chebyquad_residuals(x)(i);
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ int& chebyquad_calls()
+ {
+ static int count = 0;
+ return count;
+ }
+
+ double chebyquad(const matrix<double,0,1>& x )
+ {
+ chebyquad_calls()++;
+ return sum(squared(chebyquad_residuals(x)));
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,0,1> chebyquad_derivative (const matrix<double,0,1>& x)
+ {
+ const int n = x.size();
+ matrix<double,0,1> fvec = chebyquad_residuals(x);
+ matrix<double,0,1> g(n);
+ int i;
+ int j;
+ double s1;
+ double s2;
+ double t;
+ double t1;
+ double t2;
+ double th;
+
+ for (j = 1; j <= n; ++j)
+ {
+ g(j-1) = 0.0E+00;
+ t1 = 1.0E+00;
+ t2 = 2.0E+00 * x(j-1) - 1.0E+00;
+ t = 2.0E+00 * t2;
+ s1 = 0.0E+00;
+ s2 = 2.0E+00;
+ for (i = 1; i <= n; ++i)
+ {
+ g(j-1) = g(j-1) + fvec(i-1) * s2;
+ th = 4.0E+00 * t2 + t * s2 - s1;
+ s1 = s2;
+ s2 = th;
+ th = t * t2 - t1;
+ t1 = t2;
+ t2 = th;
+ }
+ }
+
+ g = 2.0E+00 * g / (double) ( n );
+
+ return g;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,0,1> chebyquad_start (int n)
+ {
+ int i;
+ matrix<double,0,1> x(n);
+
+ for (i = 1; i <= n; ++i)
+ x(i-1) = double ( i ) / double ( n + 1 );
+
+ return x;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,0,1> chebyquad_solution (int n)
+ {
+ matrix<double,0,1> x(n);
+
+ x = 0;
+ switch (n)
+ {
+ case 2:
+ x = 0.2113249E+00, 0.7886751E+00;
+ break;
+ case 4:
+ x = 0.1026728E+00, 0.4062037E+00, 0.5937963E+00, 0.8973272E+00;
+ break;
+ case 6:
+ x = 0.066877E+00, 0.288741E+00, 0.366682E+00, 0.633318E+00, 0.711259E+00, 0.933123E+00;
+ break;
+ case 8:
+ x = 0.043153E+00, 0.193091E+00, 0.266329E+00, 0.500000E+00, 0.500000E+00, 0.733671E+00, 0.806910E+00, 0.956847E+00;
+ break;
+ default:
+ std::ostringstream sout;
+ sout << "don't know chebyquad solution for n = " << n;
+ throw dlib::error(sout.str());
+ break;
+ }
+
+ return x;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double> chebyquad_hessian(const matrix<double,0,1>& x)
+ {
+ const int lda = x.size();
+ const int n = x.size();
+ double d1;
+ double d2;
+ matrix<double,0,1> fvec = chebyquad_residuals(x);
+ matrix<double,0,1> gvec(n);
+ matrix<double> h(lda,n);
+ int i;
+ int j;
+ int k;
+ double p1;
+ double p2;
+ double s1;
+ double s2;
+ double ss1;
+ double ss2;
+ double t;
+ double t1;
+ double t2;
+ double th;
+ double tt;
+ double tth;
+ double tt1;
+ double tt2;
+ h = 0;
+
+ d1 = 1.0E+00 / double ( n );
+ d2 = 2.0E+00 * d1;
+
+ for (j = 1; j <= n; ++j)
+ {
+
+ h(j-1,j-1) = 4.0E+00 * d1;
+ t1 = 1.0E+00;
+ t2 = 2.0E+00 * x(j-1) - 1.0E+00;
+ t = 2.0E+00 * t2;
+ s1 = 0.0E+00;
+ s2 = 2.0E+00;
+ p1 = 0.0E+00;
+ p2 = 0.0E+00;
+ gvec(0) = s2;
+
+ for (i = 2; i <= n; ++i)
+ {
+ th = 4.0E+00 * t2 + t * s2 - s1;
+ s1 = s2;
+ s2 = th;
+ th = t * t2 - t1;
+ t1 = t2;
+ t2 = th;
+ th = 8.0E+00 * s1 + t * p2 - p1;
+ p1 = p2;
+ p2 = th;
+ gvec(i-1) = s2;
+ h(j-1,j-1) = h(j-1,j-1) + fvec(i-1) * th + d1 * s2*s2;
+ }
+
+ h(j-1,j-1) = d2 * h(j-1,j-1);
+
+ for (k = 1; k <= j-1; ++k)
+ {
+
+ h(j-1,k-1) = 0.0;
+ tt1 = 1.0E+00;
+ tt2 = 2.0E+00 * x(k-1) - 1.0E+00;
+ tt = 2.0E+00 * tt2;
+ ss1 = 0.0E+00;
+ ss2 = 2.0E+00;
+
+ for (i = 1; i <= n; ++i)
+ {
+ h(j-1,k-1) = h(j-1,k-1) + ss2 * gvec(i-1);
+ tth = 4.0E+00 * tt2 + tt * ss2 - ss1;
+ ss1 = ss2;
+ ss2 = tth;
+ tth = tt * tt2 - tt1;
+ tt1 = tt2;
+ tt2 = tth;
+ }
+
+ h(j-1,k-1) = d2 * d1 * h(j-1,k-1);
+
+ }
+
+ }
+
+ h = make_symmetric(h);
+ return h;
+ }
+
+ // ----------------------------------------------------------------------------------------
+ // ----------------------------------------------------------------------------------------
+ // ----------------------------------------------------------------------------------------
+ // ----------------------------------------------------------------------------------------
+
+ double brown_residual (int i, const matrix<double,4,1>& x)
+ /*!
+ requires
+ - 1 <= i <= 20
+ ensures
+ - returns the ith brown residual
+ !*/
+ {
+ double c;
+ double f;
+ double f1;
+ double f2;
+
+ f = 0.0E+00;
+
+
+ c = double ( i ) / 5.0E+00;
+ f1 = x(0) + c * x(1) - std::exp ( c );
+ f2 = x(2) + std::sin ( c ) * x(3) - std::cos ( c );
+
+ f = f1*f1 + f2*f2;
+
+ return f;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ double brown ( const matrix<double,4,1>& x)
+ {
+ double f;
+ int i;
+
+ f = 0;
+
+ for (i = 1; i <= 20; ++i)
+ {
+ f += std::pow(brown_residual(i, x), 2);
+ }
+
+ return f;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,4,1> brown_derivative ( const matrix<double,4,1>& x)
+ {
+ double c;
+ double df1dx1;
+ double df1dx2;
+ double df2dx3;
+ double df2dx4;
+ double f1;
+ double f2;
+ matrix<double,4,1> g;
+ int i;
+
+ g = 0;
+
+ for (i = 1; i <= 20; ++i)
+ {
+
+ c = double ( i ) / 5.0E+00;
+
+ f1 = x(0) + c * x(1) - std::exp ( c );
+ f2 = x(2) + std::sin ( c ) * x(3) - std::cos ( c );
+
+ df1dx1 = 1.0E+00;
+ df1dx2 = c;
+ df2dx3 = 1.0E+00;
+ df2dx4 = std::sin ( c );
+
+ using std::pow;
+ g(0) = g(0) + 4.0E+00 * ( pow(f1,3) * df1dx1 + f1 * pow(f2,2) * df1dx1 );
+ g(1) = g(1) + 4.0E+00 * ( pow(f1,3) * df1dx2 + f1 * pow(f2,2) * df1dx2 );
+ g(2) = g(2) + 4.0E+00 * ( pow(f1,2) * f2 * df2dx3 + pow(f2,3) * df2dx3 );
+ g(3) = g(3) + 4.0E+00 * ( pow(f1,2) * f2 * df2dx4 + pow(f2,3) * df2dx4 );
+
+ }
+
+ return g;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,4,4> brown_hessian ( const matrix<double,4,1>& x)
+ {
+ double c;
+ double df1dx1;
+ double df1dx2;
+ double df2dx3;
+ double df2dx4;
+ double f1;
+ double f2;
+ matrix<double,4,4> h;
+ int i;
+
+ h = 0;
+
+ for (i = 1; i <= 20; ++i)
+ {
+
+ c = double ( i ) / 5.0E+00;
+
+ f1 = x(0) + c * x(1) - std::exp ( c );
+ f2 = x(2) + std::sin ( c ) * x(3) - std::cos ( c );
+
+ df1dx1 = 1.0E+00;
+ df1dx2 = c;
+ df2dx3 = 1.0E+00;
+ df2dx4 = std::sin ( c );
+
+ using std::pow;
+ h(0,0) = h(0,0) + 12.0E+00 * pow(f1,2) * df1dx1 * df1dx1 + 4.0E+00 * pow(f2,2) * df1dx1 * df1dx1;
+ h(0,1) = h(0,1) + 12.0E+00 * pow(f1,2) * df1dx1 * df1dx2 + 4.0E+00 * pow(f2,2) * df1dx1 * df1dx2;
+ h(0,2) = h(0,2) + 8.0E+00 * f1 * f2 * df1dx1 * df2dx3;
+ h(0,3) = h(0,3) + 8.0E+00 * f1 * f2 * df1dx1 * df2dx4;
+
+ h(1,0) = h(1,0) + 12.0E+00 * pow(f1,2) * df1dx2 * df1dx1 + 4.0E+00 * pow(f2,2) * df1dx2 * df1dx1;
+ h(1,1) = h(1,1) + 12.0E+00 * pow(f1,2) * df1dx2 * df1dx2 + 4.0E+00 * pow(f2,2) * df1dx2 * df1dx2;
+ h(1,2) = h(1,2) + 8.0E+00 * f1 * f2 * df1dx2 * df2dx3;
+ h(1,3) = h(1,3) + 8.0E+00 * f1 * f2 * df1dx2 * df2dx4;
+
+ h(2,0) = h(2,0) + 8.0E+00 * f1 * f2 * df2dx3 * df1dx1;
+ h(2,1) = h(2,1) + 8.0E+00 * f1 * f2 * df2dx3 * df1dx2;
+ h(2,2) = h(2,2) + 4.0E+00 * pow(f1,2) * df2dx3 * df2dx3 + 12.0E+00 * pow(f2,2) * df2dx3 * df2dx3;
+ h(2,3) = h(2,3) + 4.0E+00 * pow(f1,2) * df2dx4 * df2dx3 + 12.0E+00 * pow(f2,2) * df2dx3 * df2dx4;
+
+ h(3,0) = h(3,0) + 8.0E+00 * f1 * f2 * df2dx4 * df1dx1;
+ h(3,1) = h(3,1) + 8.0E+00 * f1 * f2 * df2dx4 * df1dx2;
+ h(3,2) = h(3,2) + 4.0E+00 * pow(f1,2) * df2dx3 * df2dx4 + 12.0E+00 * pow(f2,2) * df2dx4 * df2dx3;
+ h(3,3) = h(3,3) + 4.0E+00 * pow(f1,2) * df2dx4 * df2dx4 + 12.0E+00 * pow(f2,2) * df2dx4 * df2dx4;
+
+ }
+
+ return make_symmetric(h);
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,4,1> brown_start ()
+ {
+ matrix<double,4,1> x;
+ x = 25.0E+00, 5.0E+00, -5.0E+00, -1.0E+00;
+ return x;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ matrix<double,4,1> brown_solution ()
+ {
+ matrix<double,4,1> x;
+ // solution from original documentation.
+ //x = -11.5844E+00, 13.1999E+00, -0.406200E+00, 0.240998E+00;
+ x = -11.594439905669450042, 13.203630051593080452, -0.40343948856573402795, 0.23677877338218666914;
+ return x;
+ }
+
+ // ----------------------------------------------------------------------------------------
+
+ }
+}
+
+
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