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/* roots/test_funcs.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <stdlib.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_roots.h>
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#include "test.h"
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gsl_function create_function (double (*f)(double, void *))
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{
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gsl_function F ;
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F.function = f;
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F.params = 0;
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return F ;
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}
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gsl_function_fdf create_fdf (double (*f)(double, void *),
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double (*df)(double, void *),
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void (*fdf)(double, void *, double *, double *))
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{
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gsl_function_fdf FDF ;
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FDF.f = f ;
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FDF.df = df ;
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FDF.fdf = fdf ;
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FDF.params = 0 ;
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return FDF ;
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}
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/* f(x) = x^{20} - 1 */
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/* f'(x) = 20x^{19} */
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/* zero at x = 1 or -1 */
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double
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func1 (double x, void *p)
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{
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return pow (x, 20.0) - 1;
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}
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double
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func1_df (double x, void * p)
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{
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return 20.0 * pow (x, 19.0);
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}
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void
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func1_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func1 (x, p);
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*yprime = 20.0 * pow (x, 19.0);
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}
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/* f(x) = sqrt(abs(x))*sgn(x) */
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/* f'(x) = 1 / sqrt(abs(x) */
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/* zero at x = 0 */
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double
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func2 (double x, void * p)
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{
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double delta;
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if (x > 0)
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delta = 1.0;
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else if (x < 0)
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delta = -1.0;
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else
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delta = 0.0;
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return sqrt (fabs (x)) * delta;
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}
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double
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func2_df (double x, void * p)
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{
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return 1 / sqrt (fabs (x));
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}
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void
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func2_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func2 (x, p);
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*yprime = 1 / sqrt (fabs (x));
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}
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/* f(x) = x^2 - 1e-8 */
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/* f'(x) = 2x */
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/* zero at x = sqrt(1e-8) or -sqrt(1e-8) */
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double
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func3 (double x, void * p)
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{
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return pow (x, 2.0) - 1e-8;
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}
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double
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func3_df (double x, void * p)
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{
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return 2 * x;
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}
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void
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func3_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func3 (x, p);
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*yprime = 2 * x;
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}
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/* f(x) = x exp(-x) */
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/* f'(x) = exp(-x) - x exp(-x) */
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/* zero at x = 0 */
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double
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func4 (double x, void * p)
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{
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return x * exp (-x);
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}
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double
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func4_df (double x, void * p)
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{
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return exp (-x) - x * exp (-x);
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}
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void
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func4_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func4 (x, p);
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*yprime = exp (-x) - x * exp (-x);
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}
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/* f(x) = 1/(1+exp(x)) */
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/* f'(x) = -exp(x) / (1 + exp(x))^2 */
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/* no roots! */
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double
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func5 (double x, void * p)
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{
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return 1 / (1 + exp (x));
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}
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double
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func5_df (double x, void * p)
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{
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return -exp (x) / pow (1 + exp (x), 2.0);
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}
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void
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func5_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func5 (x, p);
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*yprime = -exp (x) / pow (1 + exp (x), 2.0);
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}
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/* f(x) = (x - 1)^7 */
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/* f'(x) = 7 * (x - 1)^6 */
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/* zero at x = 1 */
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double
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func6 (double x, void * p)
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{
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return pow (x - 1, 7.0);
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}
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double
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func6_df (double x, void * p)
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{
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return 7.0 * pow (x - 1, 6.0);
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}
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void
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func6_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = func6 (x, p);
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*yprime = 7.0 * pow (x - 1, 6.0);
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}
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/* sin(x) packaged up nicely. */
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double
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sin_f (double x, void * p)
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{
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return sin (x);
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}
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double
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sin_df (double x, void * p)
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{
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return cos (x);
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}
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void
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sin_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = sin (x);
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*yprime = cos (x);
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}
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/* cos(x) packaged up nicely. */
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double
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cos_f (double x, void * p)
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{
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return cos (x);
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}
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double
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cos_df (double x, void * p)
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{
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return -sin (x);
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}
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void
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cos_fdf (double x, void * p, double *y, double *yprime)
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{
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*y = cos (x);
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*yprime = -sin (x);
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}
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/* linear function to test that solvers exit correctly
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when entered with an exact root */
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double func7(double x, void * p)
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{
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return -M_PI * x + M_E;
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}
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double func7_df(double x, void * p)
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{
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return -M_PI;
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}
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void func7_fdf(double x, void * p, double *f, double *df)
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{
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*f = func7(x, p);
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*df = func7_df(x, p);
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}
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