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
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
|
*> \brief \b CGET54
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
* LDV, WORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
* REAL RESULT
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), S( LDS, * ),
* $ T( LDT, * ), U( LDU, * ), V( LDV, * ),
* $ WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGET54 checks a generalized decomposition of the form
*>
*> A = U*S*V' and B = U*T* V'
*>
*> where ' means conjugate transpose and U and V are unitary.
*>
*> Specifically,
*>
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, SGET54 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA, N)
*> The original (unfactored) matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB, N)
*> The original (unfactored) matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of B. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is COMPLEX array, dimension (LDS, N)
*> The factored matrix S.
*> \endverbatim
*>
*> \param[in] LDS
*> \verbatim
*> LDS is INTEGER
*> The leading dimension of S. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*> T is COMPLEX array, dimension (LDT, N)
*> The factored matrix T.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of T. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*> U is COMPLEX array, dimension (LDU, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U. LDU must be at least N and
*> at least 1.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is COMPLEX array, dimension (LDV, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of V. LDV must be at least N and
*> at least 1.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (3*N**2)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL
*> The value RESULT, It is currently limited to 1/ulp, to
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_eig
*
* =====================================================================
SUBROUTINE CGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
$ LDV, WORK, RESULT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
REAL RESULT
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), S( LDS, * ),
$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
$ WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
REAL ABNORM, ULP, UNFL, WNORM
* ..
* .. Local Arrays ..
REAL DUM( 1 )
* ..
* .. External Functions ..
REAL CLANGE, SLAMCH
EXTERNAL CLANGE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CLACPY
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
RESULT = ZERO
IF( N.LE.0 )
$ RETURN
*
* Constants
*
UNFL = SLAMCH( 'Safe minimum' )
ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
*
* compute the norm of (A,B)
*
CALL CLACPY( 'Full', N, N, A, LDA, WORK, N )
CALL CLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
ABNORM = MAX( CLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
*
* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
*
CALL CLACPY( ' ', N, N, A, LDA, WORK, N )
CALL CGEMM( 'N', 'N', N, N, N, CONE, U, LDU, S, LDS, CZERO,
$ WORK( N*N+1 ), N )
*
CALL CGEMM( 'N', 'C', N, N, N, -CONE, WORK( N*N+1 ), N, V, LDV,
$ CONE, WORK, N )
*
* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
*
CALL CLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
CALL CGEMM( 'N', 'N', N, N, N, CONE, U, LDU, T, LDT, CZERO,
$ WORK( 2*N*N+1 ), N )
*
CALL CGEMM( 'N', 'C', N, N, N, -CONE, WORK( 2*N*N+1 ), N, V, LDV,
$ CONE, WORK( N*N+1 ), N )
*
* Compute norm(W)/ ( ulp*norm((A,B)) )
*
WNORM = CLANGE( '1', N, 2*N, WORK, N, DUM )
*
IF( ABNORM.GT.WNORM ) THEN
RESULT = ( WNORM / ABNORM ) / ( 2*N*ULP )
ELSE
IF( ABNORM.LT.ONE ) THEN
RESULT = ( MIN( WNORM, 2*N*ABNORM ) / ABNORM ) / ( 2*N*ULP )
ELSE
RESULT = MIN( WNORM / ABNORM, REAL( 2*N ) ) / ( 2*N*ULP )
END IF
END IF
*
RETURN
*
* End of CGET54
*
END
|
