1 SUBROUTINE ZLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
2 $ RWORK, RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION RESULT( * ), RWORK( * )
13 COMPLEX*16 A( LDA, * ), AF( LDA, * ), L( LDA, * ),
14 $ Q( LDA, * ), TAU( * ), WORK( LWORK )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n
21 * matrix A, and partially tests ZUNGLQ which forms the n-by-n
22 * orthogonal matrix Q.
23 *
24 * ZLQT01 compares L with A*Q', and checks that Q is orthogonal.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix A. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix A. N >= 0.
34 *
35 * A (input) COMPLEX*16 array, dimension (LDA,N)
36 * The m-by-n matrix A.
37 *
38 * AF (output) COMPLEX*16 array, dimension (LDA,N)
39 * Details of the LQ factorization of A, as returned by ZGELQF.
40 * See ZGELQF for further details.
41 *
42 * Q (output) COMPLEX*16 array, dimension (LDA,N)
43 * The n-by-n orthogonal matrix Q.
44 *
45 * L (workspace) COMPLEX*16 array, dimension (LDA,max(M,N))
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the arrays A, AF, Q and L.
49 * LDA >= max(M,N).
50 *
51 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
52 * The scalar factors of the elementary reflectors, as returned
53 * by ZGELQF.
54 *
55 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
56 *
57 * LWORK (input) INTEGER
58 * The dimension of the array WORK.
59 *
60 * RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))
61 *
62 * RESULT (output) DOUBLE PRECISION array, dimension (2)
63 * The test ratios:
64 * RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
65 * RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
66 *
67 * =====================================================================
68 *
69 * .. Parameters ..
70 DOUBLE PRECISION ZERO, ONE
71 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
72 COMPLEX*16 ROGUE
73 PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) )
74 * ..
75 * .. Local Scalars ..
76 INTEGER INFO, MINMN
77 DOUBLE PRECISION ANORM, EPS, RESID
78 * ..
79 * .. External Functions ..
80 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
81 EXTERNAL DLAMCH, ZLANGE, ZLANSY
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL ZGELQF, ZGEMM, ZHERK, ZLACPY, ZLASET, ZUNGLQ
85 * ..
86 * .. Intrinsic Functions ..
87 INTRINSIC DBLE, DCMPLX, MAX, MIN
88 * ..
89 * .. Scalars in Common ..
90 CHARACTER*32 SRNAMT
91 * ..
92 * .. Common blocks ..
93 COMMON / SRNAMC / SRNAMT
94 * ..
95 * .. Executable Statements ..
96 *
97 MINMN = MIN( M, N )
98 EPS = DLAMCH( 'Epsilon' )
99 *
100 * Copy the matrix A to the array AF.
101 *
102 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA )
103 *
104 * Factorize the matrix A in the array AF.
105 *
106 SRNAMT = 'ZGELQF'
107 CALL ZGELQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO )
108 *
109 * Copy details of Q
110 *
111 CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
112 IF( N.GT.1 )
113 $ CALL ZLACPY( 'Upper', M, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA )
114 *
115 * Generate the n-by-n matrix Q
116 *
117 SRNAMT = 'ZUNGLQ'
118 CALL ZUNGLQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO )
119 *
120 * Copy L
121 *
122 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), L,
123 $ LDA )
124 CALL ZLACPY( 'Lower', M, N, AF, LDA, L, LDA )
125 *
126 * Compute L - A*Q'
127 *
128 CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N,
129 $ DCMPLX( -ONE ), A, LDA, Q, LDA, DCMPLX( ONE ), L,
130 $ LDA )
131 *
132 * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
133 *
134 ANORM = ZLANGE( '1', M, N, A, LDA, RWORK )
135 RESID = ZLANGE( '1', M, N, L, LDA, RWORK )
136 IF( ANORM.GT.ZERO ) THEN
137 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, N ) ) ) / ANORM ) / EPS
138 ELSE
139 RESULT( 1 ) = ZERO
140 END IF
141 *
142 * Compute I - Q*Q'
143 *
144 CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), L, LDA )
145 CALL ZHERK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, L,
146 $ LDA )
147 *
148 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
149 *
150 RESID = ZLANSY( '1', 'Upper', N, L, LDA, RWORK )
151 *
152 RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS
153 *
154 RETURN
155 *
156 * End of ZLQT01
157 *
158 END
2 $ RWORK, RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION RESULT( * ), RWORK( * )
13 COMPLEX*16 A( LDA, * ), AF( LDA, * ), L( LDA, * ),
14 $ Q( LDA, * ), TAU( * ), WORK( LWORK )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n
21 * matrix A, and partially tests ZUNGLQ which forms the n-by-n
22 * orthogonal matrix Q.
23 *
24 * ZLQT01 compares L with A*Q', and checks that Q is orthogonal.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix A. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix A. N >= 0.
34 *
35 * A (input) COMPLEX*16 array, dimension (LDA,N)
36 * The m-by-n matrix A.
37 *
38 * AF (output) COMPLEX*16 array, dimension (LDA,N)
39 * Details of the LQ factorization of A, as returned by ZGELQF.
40 * See ZGELQF for further details.
41 *
42 * Q (output) COMPLEX*16 array, dimension (LDA,N)
43 * The n-by-n orthogonal matrix Q.
44 *
45 * L (workspace) COMPLEX*16 array, dimension (LDA,max(M,N))
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the arrays A, AF, Q and L.
49 * LDA >= max(M,N).
50 *
51 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
52 * The scalar factors of the elementary reflectors, as returned
53 * by ZGELQF.
54 *
55 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
56 *
57 * LWORK (input) INTEGER
58 * The dimension of the array WORK.
59 *
60 * RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))
61 *
62 * RESULT (output) DOUBLE PRECISION array, dimension (2)
63 * The test ratios:
64 * RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
65 * RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
66 *
67 * =====================================================================
68 *
69 * .. Parameters ..
70 DOUBLE PRECISION ZERO, ONE
71 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
72 COMPLEX*16 ROGUE
73 PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) )
74 * ..
75 * .. Local Scalars ..
76 INTEGER INFO, MINMN
77 DOUBLE PRECISION ANORM, EPS, RESID
78 * ..
79 * .. External Functions ..
80 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
81 EXTERNAL DLAMCH, ZLANGE, ZLANSY
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL ZGELQF, ZGEMM, ZHERK, ZLACPY, ZLASET, ZUNGLQ
85 * ..
86 * .. Intrinsic Functions ..
87 INTRINSIC DBLE, DCMPLX, MAX, MIN
88 * ..
89 * .. Scalars in Common ..
90 CHARACTER*32 SRNAMT
91 * ..
92 * .. Common blocks ..
93 COMMON / SRNAMC / SRNAMT
94 * ..
95 * .. Executable Statements ..
96 *
97 MINMN = MIN( M, N )
98 EPS = DLAMCH( 'Epsilon' )
99 *
100 * Copy the matrix A to the array AF.
101 *
102 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA )
103 *
104 * Factorize the matrix A in the array AF.
105 *
106 SRNAMT = 'ZGELQF'
107 CALL ZGELQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO )
108 *
109 * Copy details of Q
110 *
111 CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
112 IF( N.GT.1 )
113 $ CALL ZLACPY( 'Upper', M, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA )
114 *
115 * Generate the n-by-n matrix Q
116 *
117 SRNAMT = 'ZUNGLQ'
118 CALL ZUNGLQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO )
119 *
120 * Copy L
121 *
122 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), L,
123 $ LDA )
124 CALL ZLACPY( 'Lower', M, N, AF, LDA, L, LDA )
125 *
126 * Compute L - A*Q'
127 *
128 CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N,
129 $ DCMPLX( -ONE ), A, LDA, Q, LDA, DCMPLX( ONE ), L,
130 $ LDA )
131 *
132 * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
133 *
134 ANORM = ZLANGE( '1', M, N, A, LDA, RWORK )
135 RESID = ZLANGE( '1', M, N, L, LDA, RWORK )
136 IF( ANORM.GT.ZERO ) THEN
137 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, N ) ) ) / ANORM ) / EPS
138 ELSE
139 RESULT( 1 ) = ZERO
140 END IF
141 *
142 * Compute I - Q*Q'
143 *
144 CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), L, LDA )
145 CALL ZHERK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, L,
146 $ LDA )
147 *
148 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
149 *
150 RESID = ZLANSY( '1', 'Upper', N, L, LDA, RWORK )
151 *
152 RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS
153 *
154 RETURN
155 *
156 * End of ZLQT01
157 *
158 END