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
|
/*
* Copyright (c) 2009 Samit Basu
*
* 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#include "LAPACK.hpp"
#include "Array.hpp"
#include "MemPtr.hpp"
#include "Algorithms.hpp"
template <class T>
static bool isFiniteNonzero(T a) {
return ((a != 0) && IsFinite(a));
}
static float complexRecipCond(int m, int n, float *a) {
if ((m == 1) && (n == 1) && (isFiniteNonzero(a[0]) ||
isFiniteNonzero(a[1]))) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
float Anorm = 0;
float rcond = 0;
{
char NORM = '1';
Anorm = clange_(&NORM,&m,&n,a,&m,NULL,1);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
cgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<float> work(4*n);
MemBlock<float> rwork(2*n);
cgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&rwork,&info,1);
}
return rcond;
}
static float floatRecipCond(int m, int n, float *a) {
if ((m == 1) && (n == 1) && isFiniteNonzero(a[0])) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
float Anorm = 0;
float rcond = 0;
{
char NORM = '1';
Anorm = slange_(&NORM,&m,&n,a,&m,NULL,1);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
sgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<float> work(4*n);
MemBlock<int> iwork(n);
sgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&iwork,&info,1);
}
return rcond;
}
static double dcomplexRecipCond(int m, int n, double *a) {
if ((m == 1) && (n == 1) && (isFiniteNonzero(a[0]) || isFiniteNonzero(a[1])))
return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
double Anorm = 0;
double rcond = 0;
{
char NORM = '1';
Anorm = zlange_(&NORM,&m,&n,a,&m,NULL,1);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
zgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<double> work(4*n);
MemBlock<double> rwork(2*n);
zgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&rwork,&info,1);
}
return rcond;
}
static double doubleRecipCond(int m, int n, double *a) {
if ((m == 1) && (n == 1) && isFiniteNonzero(a[0])) return 1;
// Getting the estimated reciprocal condition number involves
// three steps:
// 1. Compute the 1-norm of a
double Anorm = 0;
double rcond = 0;
{
char NORM = '1';
Anorm = dlange_(&NORM,&m,&n,a,&m,NULL,1);
}
// 2. Compute the LU-decomposition of a
{
MemBlock<int> ipiv(std::min(m,n));
int info;
dgetrf_(&m,&n,a,&m,&ipiv,&info);
}
// 3. Call sgecon to compute rcond
{
char NORM = '1';
int info;
MemBlock<double> work(4*n);
MemBlock<int> iwork(n);
dgecon_(&NORM,&n,a,&m,&Anorm,&rcond,&work,&iwork,&info,1);
}
return rcond;
}
//@@Signature
//function rcond RcondFunction jitsafe
//inputs A
//outputs x
//DOCBLOCK array_rcond
ArrayVector RcondFunction(int nargout, const ArrayVector& arg) {
if (arg.size() < 1)
throw Exception("rcond function requires at least one argument - the matrix to compute the condition number for.");
Array A(arg[0].asDenseArray());
if (!A.is2D()) throw Exception("Cannot apply matrix operations to N-dimensional arrays.");
if (!A.isSquare()) throw Exception("rcond only applies to square matrices");
if (A.isEmpty())
return ArrayVector(Array(Inf()));
if (AnyNaN(A))
return ArrayVector(Array(NaN()));
switch (A.dataClass()) {
default: throw Exception("Unsupported type for rcond operation");
case Float:
if (A.allReal())
return ArrayVector(Array(floatRecipCond(int(A.rows()),
int(A.cols()),
A.real<float>().data())));
else
return ArrayVector(Array(complexRecipCond(int(A.rows()),
int(A.cols()),
A.fortran<float>().data())));
case Double:
if (A.allReal())
return ArrayVector(Array(doubleRecipCond(int(A.rows()),
int(A.cols()),
A.real<double>().data())));
else
return ArrayVector(Array(dcomplexRecipCond(int(A.rows()),
int(A.cols()),
A.fortran<double>().data())));
}
}
|
