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
|
SUBROUTINE ZGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER ITYPE, LDA, LDB, LDU, LDV, N
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), U( LDU, * ),
$ V( LDV, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZGET51 generally checks a decomposition of the form
*
* A = U B V*
*
* where * means conjugate transpose and U and V are unitary.
*
* Specifically, if ITYPE=1
*
* RESULT = | A - U B V* | / ( |A| n ulp )
*
* If ITYPE=2, then:
*
* RESULT = | A - B | / ( |A| n ulp )
*
* If ITYPE=3, then:
*
* RESULT = | I - UU* | / ( n ulp )
*
* Arguments
* =========
*
* ITYPE (input) INTEGER
* Specifies the type of tests to be performed.
* =1: RESULT = | A - U B V* | / ( |A| n ulp )
* =2: RESULT = | A - B | / ( |A| n ulp )
* =3: RESULT = | I - UU* | / ( n ulp )
*
* N (input) INTEGER
* The size of the matrix. If it is zero, ZGET51 does nothing.
* It must be at least zero.
*
* A (input) COMPLEX*16 array, dimension (LDA, N)
* The original (unfactored) matrix.
*
* LDA (input) INTEGER
* The leading dimension of A. It must be at least 1
* and at least N.
*
* B (input) COMPLEX*16 array, dimension (LDB, N)
* The factored matrix.
*
* LDB (input) INTEGER
* The leading dimension of B. It must be at least 1
* and at least N.
*
* U (input) COMPLEX*16 array, dimension (LDU, N)
* The unitary matrix on the left-hand side in the
* decomposition.
* Not referenced if ITYPE=2
*
* LDU (input) INTEGER
* The leading dimension of U. LDU must be at least N and
* at least 1.
*
* V (input) COMPLEX*16 array, dimension (LDV, N)
* The unitary matrix on the left-hand side in the
* decomposition.
* Not referenced if ITYPE=2
*
* LDV (input) INTEGER
* The leading dimension of V. LDV must be at least N and
* at least 1.
*
* WORK (workspace) COMPLEX*16 array, dimension (2*N**2)
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESULT (output) DOUBLE PRECISION
* The values computed by the test specified by ITYPE. The
* value is currently limited to 1/ulp, to avoid overflow.
* Errors are flagged by RESULT=10/ulp.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 10.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER JCOL, JDIAG, JROW
DOUBLE PRECISION ANORM, ULP, UNFL, WNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL ZGEMM, ZLACPY
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
RESULT = ZERO
IF( N.LE.0 )
$ RETURN
*
* Constants
*
UNFL = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
*
* Some Error Checks
*
IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
RESULT = TEN / ULP
RETURN
END IF
*
IF( ITYPE.LE.2 ) THEN
*
* Tests scaled by the norm(A)
*
ANORM = MAX( ZLANGE( '1', N, N, A, LDA, RWORK ), UNFL )
*
IF( ITYPE.EQ.1 ) THEN
*
* ITYPE=1: Compute W = A - UBV'
*
CALL ZLACPY( ' ', N, N, A, LDA, WORK, N )
CALL ZGEMM( 'N', 'N', N, N, N, CONE, U, LDU, B, LDB, CZERO,
$ WORK( N**2+1 ), N )
*
CALL ZGEMM( 'N', 'C', N, N, N, -CONE, WORK( N**2+1 ), N, V,
$ LDV, CONE, WORK, N )
*
ELSE
*
* ITYPE=2: Compute W = A - B
*
CALL ZLACPY( ' ', N, N, B, LDB, WORK, N )
*
DO 20 JCOL = 1, N
DO 10 JROW = 1, N
WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
$ - A( JROW, JCOL )
10 CONTINUE
20 CONTINUE
END IF
*
* Compute norm(W)/ ( ulp*norm(A) )
*
WNORM = ZLANGE( '1', N, N, WORK, N, RWORK )
*
IF( ANORM.GT.WNORM ) THEN
RESULT = ( WNORM / ANORM ) / ( N*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
ELSE
RESULT = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
END IF
END IF
*
ELSE
*
* Tests not scaled by norm(A)
*
* ITYPE=3: Compute UU' - I
*
CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
$ WORK, N )
*
DO 30 JDIAG = 1, N
WORK( ( N+1 )*( JDIAG-1 )+1 ) = WORK( ( N+1 )*( JDIAG-1 )+
$ 1 ) - CONE
30 CONTINUE
*
RESULT = MIN( ZLANGE( '1', N, N, WORK, N, RWORK ),
$ DBLE( N ) ) / ( N*ULP )
END IF
*
RETURN
*
* End of ZGET51
*
END
|
