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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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