1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
|
/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @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;
}
|
