// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_OPTIMIZATION_TEST_FUNCTiONS_H_h_
#define DLIB_OPTIMIZATION_TEST_FUNCTiONS_H_h_
#include <dlib/matrix.h>
#include <sstream>
#include <cmath>
/*
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
*/
// GCC 4.8 gives false alarms about some variables being uninitialized. Disable these
// false warnings.
#if ( defined(__GNUC__) && __GNUC__ == 4 && __GNUC_MINOR__ == 8)
#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
#endif
namespace dlib
{
namespace test_functions
{
// ----------------------------------------------------------------------------------------
matrix<double,0,1> chebyquad_residuals(const matrix<double,0,1>& x);
double chebyquad_residual(int i, const matrix<double,0,1>& x);
int& chebyquad_calls();
double chebyquad(const matrix<double,0,1>& x );
matrix<double,0,1> chebyquad_derivative (const matrix<double,0,1>& x);
matrix<double,0,1> chebyquad_start (int n);
matrix<double,0,1> chebyquad_solution (int n);
matrix<double> chebyquad_hessian(const matrix<double,0,1>& x);
// ----------------------------------------------------------------------------------------
class chebyquad_function_model
{
public:
// Define the type used to represent column vectors
typedef matrix<double,0,1> column_vector;
// Define the type used to represent the hessian matrix
typedef matrix<double> general_matrix;
double operator() (
const column_vector& x
) const
{
return chebyquad(x);
}
void get_derivative_and_hessian (
const column_vector& x,
column_vector& d,
general_matrix& h
) const
{
d = chebyquad_derivative(x);
h = chebyquad_hessian(x);
}
};
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
double brown_residual (int i, const matrix<double,4,1>& x);
/*!
requires
- 1 <= i <= 20
ensures
- returns the ith brown residual
!*/
double brown ( const matrix<double,4,1>& x);
matrix<double,4,1> brown_derivative ( const matrix<double,4,1>& x);
matrix<double,4,4> brown_hessian ( const matrix<double,4,1>& x);
matrix<double,4,1> brown_start ();
matrix<double,4,1> brown_solution ();
class brown_function_model
{
public:
// Define the type used to represent column vectors
typedef matrix<double,4,1> column_vector;
// Define the type used to represent the hessian matrix
typedef matrix<double> general_matrix;
double operator() (
const column_vector& x
) const
{
return brown(x);
}
void get_derivative_and_hessian (
const column_vector& x,
column_vector& d,
general_matrix& h
) const
{
d = brown_derivative(x);
h = brown_hessian(x);
}
};
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
template <typename T>
matrix<T,2,1> rosen_big_start()
{
matrix<T,2,1> x;
x = -1.2, -1;
return x;
}
// This is a variation on the Rosenbrock test function but with large residuals. The
// minimum is at 1, 1 and the objective value is 1.
template <typename T>
T rosen_big_residual (int i, const matrix<T,2,1>& m)
{
using std::pow;
const T x = m(0);
const T y = m(1);
if (i == 1)
{
return 100*pow(y - x*x,2)+1.0;
}
else
{
return pow(1 - x,2) + 1.0;
}
}
template <typename T>
T rosen_big ( const matrix<T,2,1>& m)
{
using std::pow;
return 0.5*(pow(rosen_big_residual(1,m),2) + pow(rosen_big_residual(2,m),2));
}
template <typename T>
matrix<T,2,1> rosen_big_solution ()
{
matrix<T,2,1> x;
// solution from original documentation.
x = 1,1;
return x;
}
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
template <typename T>
matrix<T,2,1> rosen_start()
{
matrix<T,2,1> x;
x = -1.2, -1;
return x;
}
template <typename T>
T rosen ( const matrix<T,2,1>& m)
{
const T x = m(0);
const T y = m(1);
using std::pow;
// compute Rosenbrock's function and return the result
return 100.0*pow(y - x*x,2) + pow(1 - x,2);
}
template <typename T>
T rosen_residual (int i, const matrix<T,2,1>& m)
{
const T x = m(0);
const T y = m(1);
if (i == 1)
{
return 10*(y - x*x);
}
else
{
return 1 - x;
}
}
template <typename T>
matrix<T,2,1> rosen_residual_derivative (int i, const matrix<T,2,1>& m)
{
const T x = m(0);
matrix<T,2,1> d;
if (i == 1)
{
d = -20*x, 10;
}
else
{
d = -1, 0;
}
return d;
}
template <typename T>
const matrix<T,2,1> rosen_derivative ( const matrix<T,2,1>& m)
{
const T x = m(0);
const T y = m(1);
// make us a column vector of length 2
matrix<T,2,1> res(2);
// now compute the gradient vector
res(0) = -400*x*(y-x*x) - 2*(1-x); // derivative of rosen() with respect to x
res(1) = 200*(y-x*x); // derivative of rosen() with respect to y
return res;
}
template <typename T>
const matrix<T,2,2> rosen_hessian ( const matrix<T,2,1>& m)
{
const T x = m(0);
const T y = m(1);
// make us a column vector of length 2
matrix<T,2,2> res;
// now compute the gradient vector
res(0,0) = -400*y + 3*400*x*x + 2;
res(1,1) = 200;
res(0,1) = -400*x;
res(1,0) = -400*x;
return res;
}
template <typename T>
matrix<T,2,1> rosen_solution ()
{
matrix<T,2,1> x;
// solution from original documentation.
x = 1,1;
return x;
}
// ------------------------------------------------------------------------------------
template <typename T>
struct rosen_function_model
{
typedef matrix<T,2,1> column_vector;
typedef matrix<T,2,2> general_matrix;
T operator() ( column_vector x) const
{
return static_cast<T>(rosen(x));
}
void get_derivative_and_hessian (
const column_vector& x,
column_vector& d,
general_matrix& h
) const
{
d = rosen_derivative(x);
h = rosen_hessian(x);
}
};
// ----------------------------------------------------------------------------------------
}
}
#endif // DLIB_OPTIMIZATION_TEST_FUNCTiONS_H_h_