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/* poly/zsolve_quadratic.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.
*/
/* complex_solve_quadratic.c - finds complex roots of a x^2 + b x + c = 0 */
#include <config.h>
#include <math.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_poly.h>
int
gsl_poly_complex_solve_quadratic (double a, double b, double c,
gsl_complex *z0, gsl_complex *z1)
{
double disc = b * b - 4 * a * c;
if (a == 0) /* Handle linear case */
{
if (b == 0)
{
return 0;
}
else
{
GSL_REAL(*z0) = -c / b;
GSL_IMAG(*z0) = 0;
return 1;
};
}
if (disc > 0)
{
if (b == 0)
{
double s = fabs (0.5 * sqrt (disc) / a);
GSL_REAL (*z0) = -s;
GSL_IMAG (*z0) = 0;
GSL_REAL (*z1) = s;
GSL_IMAG (*z1) = 0;
}
else
{
double sgnb = (b > 0 ? 1 : -1);
double temp = -0.5 * (b + sgnb * sqrt (disc));
double r1 = temp / a;
double r2 = c / temp;
if (r1 < r2)
{
GSL_REAL (*z0) = r1;
GSL_IMAG (*z0) = 0;
GSL_REAL (*z1) = r2;
GSL_IMAG (*z1) = 0;
}
else
{
GSL_REAL (*z0) = r2;
GSL_IMAG (*z0) = 0;
GSL_REAL (*z1) = r1;
GSL_IMAG (*z1) = 0;
}
}
return 2;
}
else if (disc == 0)
{
GSL_REAL (*z0) = -0.5 * b / a;
GSL_IMAG (*z0) = 0;
GSL_REAL (*z1) = -0.5 * b / a;
GSL_IMAG (*z1) = 0;
return 2;
}
else
{
double s = fabs (0.5 * sqrt (-disc) / a);
GSL_REAL (*z0) = -0.5 * b / a;
GSL_IMAG (*z0) = -s;
GSL_REAL (*z1) = -0.5 * b / a;
GSL_IMAG (*z1) = s;
return 2;
}
}
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