/usr/include/gsl/gsl_poly.h is in libgsl-dev 2.1+dfsg-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 | /* 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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