diff options
Diffstat (limited to 'gsl-1.9/poly/zsolve_cubic.c')
| -rw-r--r-- | gsl-1.9/poly/zsolve_cubic.c | 153 |
1 files changed, 153 insertions, 0 deletions
diff --git a/gsl-1.9/poly/zsolve_cubic.c b/gsl-1.9/poly/zsolve_cubic.c new file mode 100644 index 0000000..548423e --- /dev/null +++ b/gsl-1.9/poly/zsolve_cubic.c @@ -0,0 +1,153 @@ +/* poly/zsolve_cubic.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 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. + */ + +/* zsolve_cubic.c - finds the complex roots of x^3 + a x^2 + b x + c = 0 */ + +#include <config.h> +#include <math.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_complex.h> +#include <gsl/gsl_poly.h> + +#define SWAP(a,b) do { double tmp = b ; b = a ; a = tmp ; } while(0) + +int +gsl_poly_complex_solve_cubic (double a, double b, double c, + gsl_complex *z0, gsl_complex *z1, + gsl_complex *z2) +{ + double q = (a * a - 3 * b); + double r = (2 * a * a * a - 9 * a * b + 27 * c); + + double Q = q / 9; + double R = r / 54; + + double Q3 = Q * Q * Q; + double R2 = R * R; + + double CR2 = 729 * r * r; + double CQ3 = 2916 * q * q * q; + + if (R == 0 && Q == 0) + { + GSL_REAL (*z0) = -a / 3; + GSL_IMAG (*z0) = 0; + GSL_REAL (*z1) = -a / 3; + GSL_IMAG (*z1) = 0; + GSL_REAL (*z2) = -a / 3; + GSL_IMAG (*z2) = 0; + return 3; + } + else if (CR2 == CQ3) + { + /* this test is actually R2 == Q3, written in a form suitable + for exact computation with integers */ + + /* Due to finite precision some double roots may be missed, and + will be considered to be a pair of complex roots z = x +/- + epsilon i close to the real axis. */ + + double sqrtQ = sqrt (Q); + + if (R > 0) + { + GSL_REAL (*z0) = -2 * sqrtQ - a / 3; + GSL_IMAG (*z0) = 0; + GSL_REAL (*z1) = sqrtQ - a / 3; + GSL_IMAG (*z1) = 0; + GSL_REAL (*z2) = sqrtQ - a / 3; + GSL_IMAG (*z2) = 0; + } + else + { + GSL_REAL (*z0) = -sqrtQ - a / 3; + GSL_IMAG (*z0) = 0; + GSL_REAL (*z1) = -sqrtQ - a / 3; + GSL_IMAG (*z1) = 0; + GSL_REAL (*z2) = 2 * sqrtQ - a / 3; + GSL_IMAG (*z2) = 0; + } + return 3; + } + else if (CR2 < CQ3) /* equivalent to R2 < Q3 */ + { + double sqrtQ = sqrt (Q); + double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ; + double theta = acos (R / sqrtQ3); + double norm = -2 * sqrtQ; + double r0 = norm * cos (theta / 3) - a / 3; + double r1 = norm * cos ((theta + 2.0 * M_PI) / 3) - a / 3; + double r2 = norm * cos ((theta - 2.0 * M_PI) / 3) - a / 3; + + /* Sort r0, r1, r2 into increasing order */ + + if (r0 > r1) + SWAP (r0, r1); + + if (r1 > r2) + { + SWAP (r1, r2); + + if (r0 > r1) + SWAP (r0, r1); + } + + GSL_REAL (*z0) = r0; + GSL_IMAG (*z0) = 0; + + GSL_REAL (*z1) = r1; + GSL_IMAG (*z1) = 0; + + GSL_REAL (*z2) = r2; + GSL_IMAG (*z2) = 0; + + return 3; + } + else + { + double sgnR = (R >= 0 ? 1 : -1); + double A = -sgnR * pow (fabs (R) + sqrt (R2 - Q3), 1.0 / 3.0); + double B = Q / A; + + if (A + B < 0) + { + GSL_REAL (*z0) = A + B - a / 3; + GSL_IMAG (*z0) = 0; + + GSL_REAL (*z1) = -0.5 * (A + B) - a / 3; + GSL_IMAG (*z1) = -(sqrt (3.0) / 2.0) * fabs(A - B); + + GSL_REAL (*z2) = -0.5 * (A + B) - a / 3; + GSL_IMAG (*z2) = (sqrt (3.0) / 2.0) * fabs(A - B); + } + else + { + GSL_REAL (*z0) = -0.5 * (A + B) - a / 3; + GSL_IMAG (*z0) = -(sqrt (3.0) / 2.0) * fabs(A - B); + + GSL_REAL (*z1) = -0.5 * (A + B) - a / 3; + GSL_IMAG (*z1) = (sqrt (3.0) / 2.0) * fabs(A - B); + + GSL_REAL (*z2) = A + B - a / 3; + GSL_IMAG (*z2) = 0; + } + + return 3; + } +} |