```// Copyright (C) 2010  Davis E. King (davis@dlib.net)
#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> 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)
{
}

// ----------------------------------------------------------------------------------------

{
static int count = 0;
return count;
}

{
}

// ----------------------------------------------------------------------------------------

{
const int n = x.size();
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;
}

// ----------------------------------------------------------------------------------------

{
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> 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;
}

// ----------------------------------------------------------------------------------------

{
const int lda = x.size();
const int n = x.size();
double d1;
double d2;
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;
}

// ----------------------------------------------------------------------------------------

}
}

```