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
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA - Arnaud TORSET
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
*/
#include <stdlib.h>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include "logm.h"
/* FIXME : Untested*/
static void dlogmaTest(void){
int i=0;
double in4[4] = {0.0683740368112921714783,0.5608486062847077846527,
0.6623569373041391372681,0.7263506767340004444122 };
double in9[9] = {0.1985143842175602912903,0.5442573162727057933807,0.2320747897028923034668,
0.2312237196601927280426,0.2164632631465792655945,0.8833887814544141292572,
0.6525134947150945663452,0.3076090742833912372589,0.9329616213217377662659};
double in16[16] = {2.1460078610107302665710,3.126419968903064727783,3.6163610080257058143616,2.922266637906432151794,
5.664248815737664699554,4.8264719732105731964111,3.3217189135029911994934,5.9350947011262178421021,
5.0153415976092219352722,4.3685875833034515380859,2.6931248093023896217346,6.3257448654621839523315,
4.051954015158116817474,9.1847078315913677215576,0.4373343335464596748352,4.818508932366967201233};
double inHer[16] = {2,3,4,5,3,1,7,9,4,7,2,4,5,9,4,7};
double result4R[4]={- 0.8770746698483730119378,0.5288031941140065583795,
0.6245116064569415925689,- 0.2566930821175439358939};
double result9R[9]={- 0.8537183024765053751537,1.9622873186332121520081,- 0.8931518563294031931577,
- 0.6983367178614473536,- 1.1199049557115796638129,1.539392415892589571769,
1.0815849580686147657,- 0.4078285487954845245362,0.1789837218054647349774,};
double result16R[16]={1.4069394184534917968676,- 1.7915236034592834091228,2.3099248310776610004780,0.5320777350783232328979,
0.6986579270151970222358,0.9874373592109859654187,0.8902400742596190408307,0.6067035092100719895214,
0.0466142343271527676007,0.3821963653954382200695,1.129789301050062144682,1.2310339071369393870725,
0.424502387440284123521,3.4580528009566289249221,- 2.1337657344549150195689,1.0826836628584670663145};
double resultHerR[16]={- 0.0707459665791660696765,0.9744491331561414559914,0.0316695005563280007621,0.9186825501429138896015,
0.9744491331561416780360,1.9318283614573175110962,- 0.0664515082056250649956,0.3546926741474874522631,
0.0316695005563280562733,- 0.0664515082056250649956,0.3206743709780528472919,1.82590946141052867802,
0.9186825501429141116461,0.3546926741474875632854,1.82590946141052867802,0.9537374500729456361370};
double out4[4],out9[9],out16[16],outHer[16];
dlogma(in4,2,out4);
dlogma(in9,3,out9);
dlogma(in16,4,out16);
dlogma(inHer,4,outHer);
for(i=0;i<4;i++) {
assert( (fabs(out4[i]-result4R[i]) / fabs(out4[i])) <3e-15);
}
for(i=0;i<9;i++) {
assert( (fabs(out9[i]-result9R[i]) / fabs(out9[i])) <3e-14);
}
for(i=0;i<16;i++) {
assert( (fabs(out16[i]-result16R[i]) / fabs(out16[i])) <3e-14);
}
for(i=0;i<16;i++) {
assert( (fabs(outHer[i]-resultHerR[i]) / fabs(outHer[i])) <3e-13);
}
}
static void zlogmaTest(void){
int i;
double in4D[4] = {0.0683740368112921714783,0.5608486062847077846527,
0.6623569373041391372681,0.7263506767340004444122 };
double in9D[9] = {0.1985143842175602912903,0.5442573162727057933807,0.2320747897028923034668,
0.2312237196601927280426,0.2164632631465792655945,0.8833887814544141292572,
0.6525134947150945663452,0.3076090742833912372589,0.9329616213217377662659};
double in16D[16] = {2.1460078610107302665710,3.126419968903064727783,3.6163610080257058143616,2.922266637906432151794,
5.664248815737664699554,4.8264719732105731964111,3.3217189135029911994934,5.9350947011262178421021,
5.0153415976092219352722,4.3685875833034515380859,2.6931248093023896217346,6.3257448654621839523315,
4.051954015158116817474,9.1847078315913677215576,0.4373343335464596748352,4.818508932366967201233};
double inHerD[16] = {2,3,4,5,3,1,7,9,4,7,2,4,5,9,4,7};
double result4R[4]={- 0.8770746698483730119378,0.5288031941140065583795,
0.6245116064569415925689,- 0.2566930821175439358939};
double result4I[4]={2.3169161534469857599561,- 1.2719608554746495432397,
- 1.5021738258100643115256,0.8246765001428078001311};
double result9R[9]={- 0.8537183024765053751537,1.9622873186332121520081,- 0.8931518563294031931577,
- 0.6983367178614473536,- 1.1199049557115796638129,1.539392415892589571769,
1.0815849580686147657,- 0.4078285487954845245362,0.1789837218054647349774,};
double result9I[9]={+ 0.0000000000000006661338,-0.0000000000000005551115,+0.0000000000000001110223,
-0.0000000000000002844947,+0.0000000000000004163336,+ 0.0000000000000008743006,
-0.0000000000000001665335,+ 0.0000000000000004996004,-0.0000000000000003330669};
double result16R[16]={1.4069394184534917968676,- 1.7915236034592834091228,2.3099248310776610004780,0.5320777350783232328979,
0.6986579270151970222358,0.9874373592109859654187,0.8902400742596190408307,0.6067035092100719895214,
0.0466142343271527676007,0.3821963653954382200695,1.129789301050062144682,1.2310339071369393870725,
0.424502387440284123521,3.4580528009566289249221,- 2.1337657344549150195689,1.0826836628584670663145};
double result16I[16]={-1.4875734535892033427729,+ 1.8146634352088595321106,-0.0551064758054355952055,-0.8617364610492967980093,
+ 1.0892397305420760122985,-1.3287434690517783142383,+ 0.0403503858667347281575,+ 0.6309857092212021179023,
+ 1.3838992102024216813,-1.6881931367553519862668,+ 0.0512659110447117594145,+ 0.8016790061501579689463,
-0.6500053973791579675634,+ 0.7929296025459252605927,-0.0240791515993044047406,-0.3765416419935233571792};
doubleComplex out4[4],out9[9],out16[16],outHer[16];
doubleComplex in4[4],in9[9],in16[16],inHer[16];
for(i=0;i<4;i++) in4[i]=DoubleComplex(in4D[i],0);
for(i=0;i<9;i++) in9[i]=DoubleComplex(in9D[i],0);
for(i=0;i<16;i++) in16[i]=DoubleComplex(in16D[i],0);
for(i=0;i<16;i++) inHer[i]=DoubleComplex(inHerD[i],0);
zlogma(in4,2,out4);
zlogma(in9,3,out9);
zlogma(in16,4,out16);
zlogma(inHer,4,outHer);
for(i=0;i<4;i++) {
assert( fabs(zreals(out4[i])-result4R[i]) / fabs(zreals(out4[i])) <3e-15);
assert( fabs(zimags(out4[i])-result4I[i]) / fabs(zimags(out4[i])) <3e-15);
}
for(i=0;i<9;i++) {
assert( fabs(zreals(out9[i])-result9R[i]) / fabs(zreals(out9[i])) <3e-14);
if (zimags(out9[i])>3e-16) assert( fabs(zimags(out9[i])-result9I[i]) / fabs(zimags(out9[i])) <1e-16);
else assert(1);
}
/* FIXME : sign pb with the imaginary part below : it's due to the reals eigenvalues which are
stored like that : eigenvalues + (-0)*i instead of eigenvalues + 0 *i
When we do operations with eigenvalues the sign isn't good
*/
for(i=0;i<16;i++) {
printf("out[%d] = %f + %f *i ---result = %f + %f *i --- assert : %f + %f*i\n",
i,
zreals(out16[i]),
zimags(out16[i]),
result16R[i],
result16I[i],
fabs(zreals(out16[i])-result16R[i]) / fabs(zreals(out16[i])),
fabs(zimags(out16[i])-result16I[i]) / fabs(zimags(out16[i])));
assert( fabs(zreals(out16[i])-result16R[i]) / fabs(zreals(out16[i])) <3e-13);
assert( fabs(zimags(out16[i])-result16I[i]) / fabs(zimags(out16[i])) <3e-13);
}
}
static int logmTest(void){
dlogmaTest();
zlogmaTest();
return 0;
}
int main (void){
assert(logmTest()==0);
return 0;
}
|
