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
|
SUBROUTINE CQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
$ 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 K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL RESULT( * ), RWORK( * )
COMPLEX AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
$ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* Purpose
* =======
*
* CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*
* CQRT03 compares the results of a call to CUNMQR with the results of
* forming Q explicitly by a call to CUNGQR and then performing matrix
* multiplication by a call to CGEMM.
*
* Arguments
* =========
*
* M (input) INTEGER
* The order of the orthogonal matrix Q. M >= 0.
*
* N (input) INTEGER
* The number of rows or columns of the matrix C; C is m-by-n if
* Q is applied from the left, or n-by-m if Q is applied from
* the right. N >= 0.
*
* K (input) INTEGER
* The number of elementary reflectors whose product defines the
* orthogonal matrix Q. M >= K >= 0.
*
* AF (input) COMPLEX array, dimension (LDA,N)
* Details of the QR factorization of an m-by-n matrix, as
* returnedby CGEQRF. See CGEQRF for further details.
*
* C (workspace) COMPLEX array, dimension (LDA,N)
*
* CC (workspace) COMPLEX array, dimension (LDA,N)
*
* Q (workspace) COMPLEX array, dimension (LDA,M)
*
* LDA (input) INTEGER
* The leading dimension of the arrays AF, C, CC, and Q.
*
* TAU (input) COMPLEX array, dimension (min(M,N))
* The scalar factors of the elementary reflectors corresponding
* to the QR factorization in AF.
*
* WORK (workspace) COMPLEX array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The length of WORK. LWORK must be at least M, and should be
* M*NB, where NB is the blocksize for this environment.
*
* RWORK (workspace) REAL array, dimension (M)
*
* RESULT (output) REAL array, dimension (4)
* The test ratios compare two techniques for multiplying a
* random matrix C by an m-by-m orthogonal matrix Q.
* RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
* RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
* RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
* RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX ROGUE
PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+10 ) )
* ..
* .. Local Scalars ..
CHARACTER SIDE, TRANS
INTEGER INFO, ISIDE, ITRANS, J, MC, NC
REAL CNORM, EPS, RESID
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANGE, SLAMCH
EXTERNAL LSAME, CLANGE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CLACPY, CLARNV, CLASET, CUNGQR, CUNMQR
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 )
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, REAL
* ..
* .. Scalars in Common ..
CHARACTER*6 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEED / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'Epsilon' )
*
* Copy the first k columns of the factorization to the array Q
*
CALL CLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
CALL CLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
*
* Generate the m-by-m matrix Q
*
SRNAMT = 'CUNGQR'
CALL CUNGQR( M, M, K, Q, LDA, TAU, WORK, LWORK, INFO )
*
DO 30 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
SIDE = 'L'
MC = M
NC = N
ELSE
SIDE = 'R'
MC = N
NC = M
END IF
*
* Generate MC by NC matrix C
*
DO 10 J = 1, NC
CALL CLARNV( 2, ISEED, MC, C( 1, J ) )
10 CONTINUE
CNORM = CLANGE( '1', MC, NC, C, LDA, RWORK )
IF( CNORM.EQ.ZERO )
$ CNORM = ONE
*
DO 20 ITRANS = 1, 2
IF( ITRANS.EQ.1 ) THEN
TRANS = 'N'
ELSE
TRANS = 'C'
END IF
*
* Copy C
*
CALL CLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
*
* Apply Q or Q' to C
*
SRNAMT = 'CUNMQR'
CALL CUNMQR( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA,
$ WORK, LWORK, INFO )
*
* Form explicit product and subtract
*
IF( LSAME( SIDE, 'L' ) ) THEN
CALL CGEMM( TRANS, 'No transpose', MC, NC, MC,
$ CMPLX( -ONE ), Q, LDA, C, LDA, CMPLX( ONE ),
$ CC, LDA )
ELSE
CALL CGEMM( 'No transpose', TRANS, MC, NC, NC,
$ CMPLX( -ONE ), C, LDA, Q, LDA, CMPLX( ONE ),
$ CC, LDA )
END IF
*
* Compute error in the difference
*
RESID = CLANGE( '1', MC, NC, CC, LDA, RWORK )
RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
$ ( REAL( MAX( 1, M ) )*CNORM*EPS )
*
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of CQRT03
*
END
|
