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