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/*! @file dcomplex.c
* \brief Common arithmetic for complex type
*
* <pre>
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
* This file defines common arithmetic operations for complex type.
* </pre>
*/
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include "slu_dcomplex.h"
/*! \brief Complex Division c = a/b */
void z_div(doublecomplex *c, doublecomplex *a, doublecomplex *b)
{
double ratio, den;
double abr, abi, cr, ci;
if( (abr = b->r) < 0.)
abr = - abr;
if( (abi = b->i) < 0.)
abi = - abi;
if( abr <= abi ) {
if (abi == 0) {
fprintf(stderr, "z_div.c: division by zero\n");
exit(-1);
}
ratio = b->r / b->i ;
den = b->i * (1 + ratio*ratio);
cr = (a->r*ratio + a->i) / den;
ci = (a->i*ratio - a->r) / den;
} else {
ratio = b->i / b->r ;
den = b->r * (1 + ratio*ratio);
cr = (a->r + a->i*ratio) / den;
ci = (a->i - a->r*ratio) / den;
}
c->r = cr;
c->i = ci;
}
/*! \brief Returns sqrt(z.r^2 + z.i^2) */
double z_abs(doublecomplex *z)
{
double temp;
double real = z->r;
double imag = z->i;
if (real < 0) real = -real;
if (imag < 0) imag = -imag;
if (imag > real) {
temp = real;
real = imag;
imag = temp;
}
if ((real+imag) == real) return(real);
temp = imag/real;
temp = real*sqrt(1.0 + temp*temp); /*overflow!!*/
return (temp);
}
/*! \brief Approximates the abs. Returns abs(z.r) + abs(z.i) */
double z_abs1(doublecomplex *z)
{
double real = z->r;
double imag = z->i;
if (real < 0) real = -real;
if (imag < 0) imag = -imag;
return (real + imag);
}
/*! \brief Return the exponentiation */
void z_exp(doublecomplex *r, doublecomplex *z)
{
double expx;
expx = exp(z->r);
r->r = expx * cos(z->i);
r->i = expx * sin(z->i);
}
/*! \brief Return the complex conjugate */
void d_cnjg(doublecomplex *r, doublecomplex *z)
{
r->r = z->r;
r->i = -z->i;
}
/*! \brief Return the imaginary part */
double d_imag(doublecomplex *z)
{
return (z->i);
}
/*! \brief SIGN functions for complex number. Returns z/abs(z) */
doublecomplex z_sgn(doublecomplex *z)
{
register double t = z_abs(z);
register doublecomplex retval;
if (t == 0.0) {
retval.r = 1.0, retval.i = 0.0;
} else {
retval.r = z->r / t, retval.i = z->i / t;
}
return retval;
}
/*! \brief Square-root of a complex number. */
doublecomplex z_sqrt(doublecomplex *z)
{
doublecomplex retval;
register double cr, ci, real, imag;
real = z->r;
imag = z->i;
if ( imag == 0.0 ) {
retval.r = sqrt(real);
retval.i = 0.0;
} else {
ci = (sqrt(real*real + imag*imag) - real) / 2.0;
ci = sqrt(ci);
cr = imag / (2.0 * ci);
retval.r = cr;
retval.i = ci;
}
return retval;
}
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