| /* poly/gsl_poly.h |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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 2 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_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 |
| */ |
| double gsl_poly_eval(const double c[], const int len, const double x); |
| |
| |
| #ifdef HAVE_INLINE |
| extern inline |
| 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; |
| } |
| #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); |
| |
| double |
| gsl_poly_dd_eval (const double dd[], const double xa[], const size_t size, const double x); |
| |
| #ifdef HAVE_INLINE |
| extern inline |
| 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[]); |
| |
| /* 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__ */ |