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/* poly/gsl_poly.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2007 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.
*/
#ifndef __GSL_POLY_H__
#define __GSL_POLY_H__
#include <stdlib.h>
#include <gsl/gsl_inline.h>
#include <gsl/gsl_complex.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
/* Evaluate polynomial
*
* c[0] + c[1] x + c[2] x^2 + ... + c[len-1] x^(len-1)
*
* exceptions: none
*/
/* real polynomial, real x */
INLINE_DECL double gsl_poly_eval(const double c[], const int len, const double x);
/* real polynomial, complex x */
INLINE_DECL gsl_complex gsl_poly_complex_eval (const double c [], const int len, const gsl_complex z);
/* complex polynomial, complex x */
INLINE_DECL gsl_complex gsl_complex_poly_complex_eval (const gsl_complex c [], const int len, const gsl_complex z);
int gsl_poly_eval_derivs(const double c[], const size_t lenc, const double x, double res[], const size_t lenres);
#ifdef HAVE_INLINE
INLINE_FUN
double
gsl_poly_eval(const double c[], const int len, const double x)
{
int i;
double ans = c[len-1];
for(i=len-1; i>0; i--) ans = c[i-1] + x * ans;
return ans;
}
INLINE_FUN
gsl_complex
gsl_poly_complex_eval(const double c[], const int len, const gsl_complex z)
{
int i;
gsl_complex ans;
GSL_SET_COMPLEX (&ans, c[len-1], 0.0);
for(i=len-1; i>0; i--) {
/* The following three lines are equivalent to
ans = gsl_complex_add_real (gsl_complex_mul (z, ans), c[i-1]);
but faster */
double tmp = c[i-1] + GSL_REAL (z) * GSL_REAL (ans) - GSL_IMAG (z) * GSL_IMAG (ans);
GSL_SET_IMAG (&ans, GSL_IMAG (z) * GSL_REAL (ans) + GSL_REAL (z) * GSL_IMAG (ans));
GSL_SET_REAL (&ans, tmp);
}
return ans;
}
INLINE_FUN
gsl_complex
gsl_complex_poly_complex_eval(const gsl_complex c[], const int len, const gsl_complex z)
{
int i;
gsl_complex ans = c[len-1];
for(i=len-1; i>0; i--) {
/* The following three lines are equivalent to
ans = gsl_complex_add (c[i-1], gsl_complex_mul (x, ans));
but faster */
double tmp = GSL_REAL (c[i-1]) + GSL_REAL (z) * GSL_REAL (ans) - GSL_IMAG (z) * GSL_IMAG (ans);
GSL_SET_IMAG (&ans, GSL_IMAG (c[i-1]) + GSL_IMAG (z) * GSL_REAL (ans) + GSL_REAL (z) * GSL_IMAG (ans));
GSL_SET_REAL (&ans, tmp);
}
return ans;
}
#endif /* HAVE_INLINE */
/* Work with divided-difference polynomials, Abramowitz & Stegun 25.2.26 */
int
gsl_poly_dd_init (double dd[], const double x[], const double y[],
size_t size);
INLINE_DECL double
gsl_poly_dd_eval (const double dd[], const double xa[], const size_t size, const double x);
#ifdef HAVE_INLINE
INLINE_FUN
double
gsl_poly_dd_eval(const double dd[], const double xa[], const size_t size, const double x)
{
size_t i;
double y = dd[size - 1];
for (i = size - 1; i--;) y = dd[i] + (x - xa[i]) * y;
return y;
}
#endif /* HAVE_INLINE */
int
gsl_poly_dd_taylor (double c[], double xp,
const double dd[], const double x[], size_t size,
double w[]);
int
gsl_poly_dd_hermite_init (double dd[], double z[], const double xa[], const double ya[],
const double dya[], const size_t size);
/* Solve for real or complex roots of the standard quadratic equation,
* returning the number of real roots.
*
* Roots are returned ordered.
*/
int gsl_poly_solve_quadratic (double a, double b, double c,
double * x0, double * x1);
int
gsl_poly_complex_solve_quadratic (double a, double b, double c,
gsl_complex * z0, gsl_complex * z1);
/* Solve for real roots of the cubic equation
* x^3 + a x^2 + b x + c = 0, returning the
* number of real roots.
*
* Roots are returned ordered.
*/
int gsl_poly_solve_cubic (double a, double b, double c,
double * x0, double * x1, double * x2);
int
gsl_poly_complex_solve_cubic (double a, double b, double c,
gsl_complex * z0, gsl_complex * z1,
gsl_complex * z2);
/* Solve for the complex roots of a general real polynomial */
typedef struct
{
size_t nc ;
double * matrix ;
}
gsl_poly_complex_workspace ;
gsl_poly_complex_workspace * gsl_poly_complex_workspace_alloc (size_t n);
void gsl_poly_complex_workspace_free (gsl_poly_complex_workspace * w);
int
gsl_poly_complex_solve (const double * a, size_t n,
gsl_poly_complex_workspace * w,
gsl_complex_packed_ptr z);
__END_DECLS
#endif /* __GSL_POLY_H__ */
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