1 SUBROUTINE ZGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
2 $ BWK, LDB, TAUB, WORK, LWORK, 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, LDB, LWORK, M, N, P
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION RESULT( 4 ), RWORK( * )
13 COMPLEX*16 A( LDA, * ), AF( LDA, * ), B( LDB, * ),
14 $ BF( LDB, * ), BWK( LDB, * ), Q( LDA, * ),
15 $ R( LDA, * ), T( LDB, * ), TAUA( * ), TAUB( * ),
16 $ WORK( LWORK ), Z( LDB, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZGRQTS tests ZGGRQF, which computes the GRQ factorization of an
23 * M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
24 *
25 * Arguments
26 * =========
27 *
28 * M (input) INTEGER
29 * The number of rows of the matrix A. M >= 0.
30 *
31 * P (input) INTEGER
32 * The number of rows of the matrix B. P >= 0.
33 *
34 * N (input) INTEGER
35 * The number of columns of the matrices A and B. N >= 0.
36 *
37 * A (input) COMPLEX*16 array, dimension (LDA,N)
38 * The M-by-N matrix A.
39 *
40 * AF (output) COMPLEX*16 array, dimension (LDA,N)
41 * Details of the GRQ factorization of A and B, as returned
42 * by ZGGRQF, see CGGRQF for further details.
43 *
44 * Q (output) COMPLEX*16 array, dimension (LDA,N)
45 * The N-by-N unitary matrix Q.
46 *
47 * R (workspace) COMPLEX*16 array, dimension (LDA,MAX(M,N))
48 *
49 * LDA (input) INTEGER
50 * The leading dimension of the arrays A, AF, R and Q.
51 * LDA >= max(M,N).
52 *
53 * TAUA (output) COMPLEX*16 array, dimension (min(M,N))
54 * The scalar factors of the elementary reflectors, as returned
55 * by DGGQRC.
56 *
57 * B (input) COMPLEX*16 array, dimension (LDB,N)
58 * On entry, the P-by-N matrix A.
59 *
60 * BF (output) COMPLEX*16 array, dimension (LDB,N)
61 * Details of the GQR factorization of A and B, as returned
62 * by ZGGRQF, see CGGRQF for further details.
63 *
64 * Z (output) DOUBLE PRECISION array, dimension (LDB,P)
65 * The P-by-P unitary matrix Z.
66 *
67 * T (workspace) COMPLEX*16 array, dimension (LDB,max(P,N))
68 *
69 * BWK (workspace) COMPLEX*16 array, dimension (LDB,N)
70 *
71 * LDB (input) INTEGER
72 * The leading dimension of the arrays B, BF, Z and T.
73 * LDB >= max(P,N).
74 *
75 * TAUB (output) COMPLEX*16 array, dimension (min(P,N))
76 * The scalar factors of the elementary reflectors, as returned
77 * by DGGRQF.
78 *
79 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
80 *
81 * LWORK (input) INTEGER
82 * The dimension of the array WORK, LWORK >= max(M,P,N)**2.
83 *
84 * RWORK (workspace) DOUBLE PRECISION array, dimension (M)
85 *
86 * RESULT (output) DOUBLE PRECISION array, dimension (4)
87 * The test ratios:
88 * RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
89 * RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
90 * RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
91 * RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
92 *
93 * =====================================================================
94 *
95 * .. Parameters ..
96 DOUBLE PRECISION ZERO, ONE
97 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
98 COMPLEX*16 CZERO, CONE
99 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
100 $ CONE = ( 1.0D+0, 0.0D+0 ) )
101 COMPLEX*16 CROGUE
102 PARAMETER ( CROGUE = ( -1.0D+10, 0.0D+0 ) )
103 * ..
104 * .. Local Scalars ..
105 INTEGER INFO
106 DOUBLE PRECISION ANORM, BNORM, RESID, ULP, UNFL
107 * ..
108 * .. External Functions ..
109 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
110 EXTERNAL DLAMCH, ZLANGE, ZLANHE
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL ZGEMM, ZGGRQF, ZHERK, ZLACPY, ZLASET, ZUNGQR,
114 $ ZUNGRQ
115 * ..
116 * .. Intrinsic Functions ..
117 INTRINSIC DBLE, MAX, MIN
118 * ..
119 * .. Executable Statements ..
120 *
121 ULP = DLAMCH( 'Precision' )
122 UNFL = DLAMCH( 'Safe minimum' )
123 *
124 * Copy the matrix A to the array AF.
125 *
126 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA )
127 CALL ZLACPY( 'Full', P, N, B, LDB, BF, LDB )
128 *
129 ANORM = MAX( ZLANGE( '1', M, N, A, LDA, RWORK ), UNFL )
130 BNORM = MAX( ZLANGE( '1', P, N, B, LDB, RWORK ), UNFL )
131 *
132 * Factorize the matrices A and B in the arrays AF and BF.
133 *
134 CALL ZGGRQF( M, P, N, AF, LDA, TAUA, BF, LDB, TAUB, WORK, LWORK,
135 $ INFO )
136 *
137 * Generate the N-by-N matrix Q
138 *
139 CALL ZLASET( 'Full', N, N, CROGUE, CROGUE, Q, LDA )
140 IF( M.LE.N ) THEN
141 IF( M.GT.0 .AND. M.LT.N )
142 $ CALL ZLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA )
143 IF( M.GT.1 )
144 $ CALL ZLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA,
145 $ Q( N-M+2, N-M+1 ), LDA )
146 ELSE
147 IF( N.GT.1 )
148 $ CALL ZLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA,
149 $ Q( 2, 1 ), LDA )
150 END IF
151 CALL ZUNGRQ( N, N, MIN( M, N ), Q, LDA, TAUA, WORK, LWORK, INFO )
152 *
153 * Generate the P-by-P matrix Z
154 *
155 CALL ZLASET( 'Full', P, P, CROGUE, CROGUE, Z, LDB )
156 IF( P.GT.1 )
157 $ CALL ZLACPY( 'Lower', P-1, N, BF( 2, 1 ), LDB, Z( 2, 1 ), LDB )
158 CALL ZUNGQR( P, P, MIN( P, N ), Z, LDB, TAUB, WORK, LWORK, INFO )
159 *
160 * Copy R
161 *
162 CALL ZLASET( 'Full', M, N, CZERO, CZERO, R, LDA )
163 IF( M.LE.N ) THEN
164 CALL ZLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, R( 1, N-M+1 ),
165 $ LDA )
166 ELSE
167 CALL ZLACPY( 'Full', M-N, N, AF, LDA, R, LDA )
168 CALL ZLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, R( M-N+1, 1 ),
169 $ LDA )
170 END IF
171 *
172 * Copy T
173 *
174 CALL ZLASET( 'Full', P, N, CZERO, CZERO, T, LDB )
175 CALL ZLACPY( 'Upper', P, N, BF, LDB, T, LDB )
176 *
177 * Compute R - A*Q'
178 *
179 CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N, -CONE,
180 $ A, LDA, Q, LDA, CONE, R, LDA )
181 *
182 * Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) .
183 *
184 RESID = ZLANGE( '1', M, N, R, LDA, RWORK )
185 IF( ANORM.GT.ZERO ) THEN
186 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) /
187 $ ULP
188 ELSE
189 RESULT( 1 ) = ZERO
190 END IF
191 *
192 * Compute T*Q - Z'*B
193 *
194 CALL ZGEMM( 'Conjugate transpose', 'No transpose', P, N, P, CONE,
195 $ Z, LDB, B, LDB, CZERO, BWK, LDB )
196 CALL ZGEMM( 'No transpose', 'No transpose', P, N, N, CONE, T, LDB,
197 $ Q, LDA, -CONE, BWK, LDB )
198 *
199 * Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
200 *
201 RESID = ZLANGE( '1', P, N, BWK, LDB, RWORK )
202 IF( BNORM.GT.ZERO ) THEN
203 RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, M ) ) ) / BNORM ) /
204 $ ULP
205 ELSE
206 RESULT( 2 ) = ZERO
207 END IF
208 *
209 * Compute I - Q*Q'
210 *
211 CALL ZLASET( 'Full', N, N, CZERO, CONE, R, LDA )
212 CALL ZHERK( 'Upper', 'No Transpose', N, N, -ONE, Q, LDA, ONE, R,
213 $ LDA )
214 *
215 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
216 *
217 RESID = ZLANHE( '1', 'Upper', N, R, LDA, RWORK )
218 RESULT( 3 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP
219 *
220 * Compute I - Z'*Z
221 *
222 CALL ZLASET( 'Full', P, P, CZERO, CONE, T, LDB )
223 CALL ZHERK( 'Upper', 'Conjugate transpose', P, P, -ONE, Z, LDB,
224 $ ONE, T, LDB )
225 *
226 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
227 *
228 RESID = ZLANHE( '1', 'Upper', P, T, LDB, RWORK )
229 RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP
230 *
231 RETURN
232 *
233 * End of ZGRQTS
234 *
235 END
2 $ BWK, LDB, TAUB, WORK, LWORK, 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, LDB, LWORK, M, N, P
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION RESULT( 4 ), RWORK( * )
13 COMPLEX*16 A( LDA, * ), AF( LDA, * ), B( LDB, * ),
14 $ BF( LDB, * ), BWK( LDB, * ), Q( LDA, * ),
15 $ R( LDA, * ), T( LDB, * ), TAUA( * ), TAUB( * ),
16 $ WORK( LWORK ), Z( LDB, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZGRQTS tests ZGGRQF, which computes the GRQ factorization of an
23 * M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
24 *
25 * Arguments
26 * =========
27 *
28 * M (input) INTEGER
29 * The number of rows of the matrix A. M >= 0.
30 *
31 * P (input) INTEGER
32 * The number of rows of the matrix B. P >= 0.
33 *
34 * N (input) INTEGER
35 * The number of columns of the matrices A and B. N >= 0.
36 *
37 * A (input) COMPLEX*16 array, dimension (LDA,N)
38 * The M-by-N matrix A.
39 *
40 * AF (output) COMPLEX*16 array, dimension (LDA,N)
41 * Details of the GRQ factorization of A and B, as returned
42 * by ZGGRQF, see CGGRQF for further details.
43 *
44 * Q (output) COMPLEX*16 array, dimension (LDA,N)
45 * The N-by-N unitary matrix Q.
46 *
47 * R (workspace) COMPLEX*16 array, dimension (LDA,MAX(M,N))
48 *
49 * LDA (input) INTEGER
50 * The leading dimension of the arrays A, AF, R and Q.
51 * LDA >= max(M,N).
52 *
53 * TAUA (output) COMPLEX*16 array, dimension (min(M,N))
54 * The scalar factors of the elementary reflectors, as returned
55 * by DGGQRC.
56 *
57 * B (input) COMPLEX*16 array, dimension (LDB,N)
58 * On entry, the P-by-N matrix A.
59 *
60 * BF (output) COMPLEX*16 array, dimension (LDB,N)
61 * Details of the GQR factorization of A and B, as returned
62 * by ZGGRQF, see CGGRQF for further details.
63 *
64 * Z (output) DOUBLE PRECISION array, dimension (LDB,P)
65 * The P-by-P unitary matrix Z.
66 *
67 * T (workspace) COMPLEX*16 array, dimension (LDB,max(P,N))
68 *
69 * BWK (workspace) COMPLEX*16 array, dimension (LDB,N)
70 *
71 * LDB (input) INTEGER
72 * The leading dimension of the arrays B, BF, Z and T.
73 * LDB >= max(P,N).
74 *
75 * TAUB (output) COMPLEX*16 array, dimension (min(P,N))
76 * The scalar factors of the elementary reflectors, as returned
77 * by DGGRQF.
78 *
79 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
80 *
81 * LWORK (input) INTEGER
82 * The dimension of the array WORK, LWORK >= max(M,P,N)**2.
83 *
84 * RWORK (workspace) DOUBLE PRECISION array, dimension (M)
85 *
86 * RESULT (output) DOUBLE PRECISION array, dimension (4)
87 * The test ratios:
88 * RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
89 * RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
90 * RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
91 * RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
92 *
93 * =====================================================================
94 *
95 * .. Parameters ..
96 DOUBLE PRECISION ZERO, ONE
97 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
98 COMPLEX*16 CZERO, CONE
99 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
100 $ CONE = ( 1.0D+0, 0.0D+0 ) )
101 COMPLEX*16 CROGUE
102 PARAMETER ( CROGUE = ( -1.0D+10, 0.0D+0 ) )
103 * ..
104 * .. Local Scalars ..
105 INTEGER INFO
106 DOUBLE PRECISION ANORM, BNORM, RESID, ULP, UNFL
107 * ..
108 * .. External Functions ..
109 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
110 EXTERNAL DLAMCH, ZLANGE, ZLANHE
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL ZGEMM, ZGGRQF, ZHERK, ZLACPY, ZLASET, ZUNGQR,
114 $ ZUNGRQ
115 * ..
116 * .. Intrinsic Functions ..
117 INTRINSIC DBLE, MAX, MIN
118 * ..
119 * .. Executable Statements ..
120 *
121 ULP = DLAMCH( 'Precision' )
122 UNFL = DLAMCH( 'Safe minimum' )
123 *
124 * Copy the matrix A to the array AF.
125 *
126 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA )
127 CALL ZLACPY( 'Full', P, N, B, LDB, BF, LDB )
128 *
129 ANORM = MAX( ZLANGE( '1', M, N, A, LDA, RWORK ), UNFL )
130 BNORM = MAX( ZLANGE( '1', P, N, B, LDB, RWORK ), UNFL )
131 *
132 * Factorize the matrices A and B in the arrays AF and BF.
133 *
134 CALL ZGGRQF( M, P, N, AF, LDA, TAUA, BF, LDB, TAUB, WORK, LWORK,
135 $ INFO )
136 *
137 * Generate the N-by-N matrix Q
138 *
139 CALL ZLASET( 'Full', N, N, CROGUE, CROGUE, Q, LDA )
140 IF( M.LE.N ) THEN
141 IF( M.GT.0 .AND. M.LT.N )
142 $ CALL ZLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA )
143 IF( M.GT.1 )
144 $ CALL ZLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA,
145 $ Q( N-M+2, N-M+1 ), LDA )
146 ELSE
147 IF( N.GT.1 )
148 $ CALL ZLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA,
149 $ Q( 2, 1 ), LDA )
150 END IF
151 CALL ZUNGRQ( N, N, MIN( M, N ), Q, LDA, TAUA, WORK, LWORK, INFO )
152 *
153 * Generate the P-by-P matrix Z
154 *
155 CALL ZLASET( 'Full', P, P, CROGUE, CROGUE, Z, LDB )
156 IF( P.GT.1 )
157 $ CALL ZLACPY( 'Lower', P-1, N, BF( 2, 1 ), LDB, Z( 2, 1 ), LDB )
158 CALL ZUNGQR( P, P, MIN( P, N ), Z, LDB, TAUB, WORK, LWORK, INFO )
159 *
160 * Copy R
161 *
162 CALL ZLASET( 'Full', M, N, CZERO, CZERO, R, LDA )
163 IF( M.LE.N ) THEN
164 CALL ZLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, R( 1, N-M+1 ),
165 $ LDA )
166 ELSE
167 CALL ZLACPY( 'Full', M-N, N, AF, LDA, R, LDA )
168 CALL ZLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, R( M-N+1, 1 ),
169 $ LDA )
170 END IF
171 *
172 * Copy T
173 *
174 CALL ZLASET( 'Full', P, N, CZERO, CZERO, T, LDB )
175 CALL ZLACPY( 'Upper', P, N, BF, LDB, T, LDB )
176 *
177 * Compute R - A*Q'
178 *
179 CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N, -CONE,
180 $ A, LDA, Q, LDA, CONE, R, LDA )
181 *
182 * Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) .
183 *
184 RESID = ZLANGE( '1', M, N, R, LDA, RWORK )
185 IF( ANORM.GT.ZERO ) THEN
186 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) /
187 $ ULP
188 ELSE
189 RESULT( 1 ) = ZERO
190 END IF
191 *
192 * Compute T*Q - Z'*B
193 *
194 CALL ZGEMM( 'Conjugate transpose', 'No transpose', P, N, P, CONE,
195 $ Z, LDB, B, LDB, CZERO, BWK, LDB )
196 CALL ZGEMM( 'No transpose', 'No transpose', P, N, N, CONE, T, LDB,
197 $ Q, LDA, -CONE, BWK, LDB )
198 *
199 * Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
200 *
201 RESID = ZLANGE( '1', P, N, BWK, LDB, RWORK )
202 IF( BNORM.GT.ZERO ) THEN
203 RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, M ) ) ) / BNORM ) /
204 $ ULP
205 ELSE
206 RESULT( 2 ) = ZERO
207 END IF
208 *
209 * Compute I - Q*Q'
210 *
211 CALL ZLASET( 'Full', N, N, CZERO, CONE, R, LDA )
212 CALL ZHERK( 'Upper', 'No Transpose', N, N, -ONE, Q, LDA, ONE, R,
213 $ LDA )
214 *
215 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
216 *
217 RESID = ZLANHE( '1', 'Upper', N, R, LDA, RWORK )
218 RESULT( 3 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP
219 *
220 * Compute I - Z'*Z
221 *
222 CALL ZLASET( 'Full', P, P, CZERO, CONE, T, LDB )
223 CALL ZHERK( 'Upper', 'Conjugate transpose', P, P, -ONE, Z, LDB,
224 $ ONE, T, LDB )
225 *
226 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
227 *
228 RESID = ZLANHE( '1', 'Upper', P, T, LDB, RWORK )
229 RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP
230 *
231 RETURN
232 *
233 * End of ZGRQTS
234 *
235 END