/* roots/test_funcs.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough

 * 

 * 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 3 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

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 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, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

#include <config.h>

#include <math.h>

#include <stdlib.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_roots.h>

#include "test.h"

gsl_function create_function (double (*f)(double, void *)) 

{

  gsl_function F ;

  F.function = f;

  F.params = 0;

  return F ;

}

gsl_function_fdf create_fdf (double (*f)(double, void *),

                             double (*df)(double, void *),

                             void (*fdf)(double, void *, double *, double *))

{

  gsl_function_fdf FDF ;

  FDF.f = f ;

  FDF.df = df ;

  FDF.fdf = fdf ;

  FDF.params = 0 ;

  return FDF ;

}

/* f(x) = x^{20} - 1 */

/* f'(x) = 20x^{19} */

/* zero at x = 1 or -1 */

double

func1 (double x, void *p)

{

  return pow (x, 20.0) - 1;

}

double

func1_df (double x, void * p)

{

  return 20.0 * pow (x, 19.0);

}

void

func1_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func1 (x, p);

  *yprime = 20.0 * pow (x, 19.0);

}

/* f(x) = sqrt(abs(x))*sgn(x) */

/* f'(x) = 1 / sqrt(abs(x) */

/* zero at x = 0 */

double

func2 (double x, void * p)

{

  double delta;

  if (x > 0)

    delta = 1.0;

  else if (x < 0)

    delta = -1.0;

  else

    delta = 0.0;

  return sqrt (fabs (x)) * delta;

}

double

func2_df (double x, void * p)

{

  return 1 / sqrt (fabs (x));

}

void

func2_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func2 (x, p);

  *yprime = 1 / sqrt (fabs (x));

}

/* f(x) = x^2 - 1e-8 */

/* f'(x) = 2x */

/* zero at x = sqrt(1e-8) or -sqrt(1e-8) */

double

func3 (double x, void * p)

{

  return pow (x, 2.0) - 1e-8;

}

double

func3_df (double x, void * p)

{

  return 2 * x;

}

void

func3_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func3 (x, p);

  *yprime = 2 * x;

}

/* f(x) = x exp(-x) */

/* f'(x) = exp(-x) - x exp(-x) */

/* zero at x = 0 */

double

func4 (double x, void * p)

{

  return x * exp (-x);

}

double

func4_df (double x, void * p)

{

  return exp (-x) - x * exp (-x);

}

void

func4_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func4 (x, p);

  *yprime = exp (-x) - x * exp (-x);

}

/* f(x) = 1/(1+exp(x)) */

/* f'(x) = -exp(x) / (1 + exp(x))^2 */

/* no roots! */

double

func5 (double x, void * p)

{

  return 1 / (1 + exp (x));

}

double

func5_df (double x, void * p)

{

  return -exp (x) / pow (1 + exp (x), 2.0);

}

void

func5_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func5 (x, p);

  *yprime = -exp (x) / pow (1 + exp (x), 2.0);

}

/* f(x) = (x - 1)^7 */

/* f'(x) = 7 * (x - 1)^6 */

/* zero at x = 1 */

double

func6 (double x, void * p)

{

  return pow (x - 1, 7.0);

}

double

func6_df (double x, void * p)

{

  return 7.0 * pow (x - 1, 6.0);

}

void

func6_fdf (double x, void * p, double *y, double *yprime)

{

  *y = func6 (x, p);

  *yprime = 7.0 * pow (x - 1, 6.0);

}

/* sin(x) packaged up nicely. */

double

sin_f (double x, void * p)

{

  return sin (x);

}

double

sin_df (double x, void * p)

{

  return cos (x);

}

void

sin_fdf (double x, void * p, double *y, double *yprime)

{

  *y = sin (x);

  *yprime = cos (x);

}

/* cos(x) packaged up nicely. */

double

cos_f (double x, void * p)

{

  return cos (x);

}

double

cos_df (double x, void * p)

{

  return -sin (x);

}

void

cos_fdf (double x, void * p, double *y, double *yprime)

{

  *y = cos (x);

  *yprime = -sin (x);

}

/* linear function to test that solvers exit correctly 

   when entered with an exact root */

double func7(double x, void * p)

{

	return -M_PI * x + M_E;

}

double func7_df(double x, void * p)

{

	return -M_PI;

}

void func7_fdf(double x, void * p, double *f, double *df)

{

	*f = func7(x, p);

	*df = func7_df(x, p);

}