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Diffstat (limited to 'thirdparty/includes/GSL/gsl/gsl_poly.h')
| -rw-r--r-- | thirdparty/includes/GSL/gsl/gsl_poly.h | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/thirdparty/includes/GSL/gsl/gsl_poly.h b/thirdparty/includes/GSL/gsl/gsl_poly.h new file mode 100644 index 0000000..2352857 --- /dev/null +++ b/thirdparty/includes/GSL/gsl/gsl_poly.h @@ -0,0 +1,183 @@ +/* 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__ */ |