1 SUBROUTINE SGQRTS( 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 A( LDA, * ), AF( LDA, * ), R( LDA, * ),
13 $ Q( LDA, * ), B( LDB, * ), BF( LDB, * ),
14 $ T( LDB, * ), Z( LDB, * ), BWK( LDB, * ),
15 $ TAUA( * ), TAUB( * ), RESULT( 4 ),
16 $ RWORK( * ), WORK( LWORK )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * SGQRTS tests SGGQRF, 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) REAL array, dimension (LDA,M)
38 * The N-by-M matrix A.
39 *
40 * AF (output) REAL array, dimension (LDA,N)
41 * Details of the GQR factorization of A and B, as returned
42 * by SGGQRF, see SGGQRF for further details.
43 *
44 * Q (output) REAL array, dimension (LDA,N)
45 * The M-by-M orthogonal matrix Q.
46 *
47 * R (workspace) REAL 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) REAL array, dimension (min(M,N))
54 * The scalar factors of the elementary reflectors, as returned
55 * by SGGQRF.
56 *
57 * B (input) REAL array, dimension (LDB,P)
58 * On entry, the N-by-P matrix A.
59 *
60 * BF (output) REAL array, dimension (LDB,N)
61 * Details of the GQR factorization of A and B, as returned
62 * by SGGQRF, see SGGQRF for further details.
63 *
64 * Z (output) REAL array, dimension (LDB,P)
65 * The P-by-P orthogonal matrix Z.
66 *
67 * T (workspace) REAL array, dimension (LDB,max(P,N))
68 *
69 * BWK (workspace) REAL 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) REAL array, dimension (min(P,N))
76 * The scalar factors of the elementary reflectors, as returned
77 * by SGGRQF.
78 *
79 * WORK (workspace) REAL 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 REAL ROGUE
99 PARAMETER ( ROGUE = -1.0E+10 )
100 * ..
101 * .. Local Scalars ..
102 INTEGER INFO
103 REAL ANORM, BNORM, ULP, UNFL, RESID
104 * ..
105 * .. External Functions ..
106 REAL SLAMCH, SLANGE, SLANSY
107 EXTERNAL SLAMCH, SLANGE, SLANSY
108 * ..
109 * .. External Subroutines ..
110 EXTERNAL SGEMM, SLACPY, SLASET, SORGQR,
111 $ SORGRQ, SSYRK
112 * ..
113 * .. Intrinsic Functions ..
114 INTRINSIC MAX, MIN, REAL
115 * ..
116 * .. Executable Statements ..
117 *
118 ULP = SLAMCH( 'Precision' )
119 UNFL = SLAMCH( 'Safe minimum' )
120 *
121 * Copy the matrix A to the array AF.
122 *
123 CALL SLACPY( 'Full', N, M, A, LDA, AF, LDA )
124 CALL SLACPY( 'Full', N, P, B, LDB, BF, LDB )
125 *
126 ANORM = MAX( SLANGE( '1', N, M, A, LDA, RWORK ), UNFL )
127 BNORM = MAX( SLANGE( '1', N, P, B, LDB, RWORK ), UNFL )
128 *
129 * Factorize the matrices A and B in the arrays AF and BF.
130 *
131 CALL SGGQRF( N, M, P, AF, LDA, TAUA, BF, LDB, TAUB, WORK,
132 $ LWORK, INFO )
133 *
134 * Generate the N-by-N matrix Q
135 *
136 CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
137 CALL SLACPY( 'Lower', N-1, M, AF( 2,1 ), LDA, Q( 2,1 ), LDA )
138 CALL SORGQR( N, N, MIN( N, M ), Q, LDA, TAUA, WORK, LWORK, INFO )
139 *
140 * Generate the P-by-P matrix Z
141 *
142 CALL SLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB )
143 IF( N.LE.P ) THEN
144 IF( N.GT.0 .AND. N.LT.P )
145 $ CALL SLACPY( 'Full', N, P-N, BF, LDB, Z( P-N+1, 1 ), LDB )
146 IF( N.GT.1 )
147 $ CALL SLACPY( 'Lower', N-1, N-1, BF( 2, P-N+1 ), LDB,
148 $ Z( P-N+2, P-N+1 ), LDB )
149 ELSE
150 IF( P.GT.1)
151 $ CALL SLACPY( 'Lower', P-1, P-1, BF( N-P+2, 1 ), LDB,
152 $ Z( 2, 1 ), LDB )
153 END IF
154 CALL SORGRQ( P, P, MIN( N, P ), Z, LDB, TAUB, WORK, LWORK, INFO )
155 *
156 * Copy R
157 *
158 CALL SLASET( 'Full', N, M, ZERO, ZERO, R, LDA )
159 CALL SLACPY( 'Upper', N, M, AF, LDA, R, LDA )
160 *
161 * Copy T
162 *
163 CALL SLASET( 'Full', N, P, ZERO, ZERO, T, LDB )
164 IF( N.LE.P ) THEN
165 CALL SLACPY( 'Upper', N, N, BF( 1, P-N+1 ), LDB, T( 1, P-N+1 ),
166 $ LDB )
167 ELSE
168 CALL SLACPY( 'Full', N-P, P, BF, LDB, T, LDB )
169 CALL SLACPY( 'Upper', P, P, BF( N-P+1, 1 ), LDB, T( N-P+1, 1 ),
170 $ LDB )
171 END IF
172 *
173 * Compute R - Q'*A
174 *
175 CALL SGEMM( 'Transpose', 'No transpose', N, M, N, -ONE, Q, LDA, A,
176 $ LDA, ONE, R, LDA )
177 *
178 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
179 *
180 RESID = SLANGE( '1', N, M, R, LDA, RWORK )
181 IF( ANORM.GT.ZERO ) THEN
182 RESULT( 1 ) = ( ( RESID / REAL( MAX(1,M,N) ) ) / ANORM ) / ULP
183 ELSE
184 RESULT( 1 ) = ZERO
185 END IF
186 *
187 * Compute T*Z - Q'*B
188 *
189 CALL SGEMM( 'No Transpose', 'No transpose', N, P, P, ONE, T, LDB,
190 $ Z, LDB, ZERO, BWK, LDB )
191 CALL SGEMM( 'Transpose', 'No transpose', N, P, N, -ONE, Q, LDA,
192 $ B, LDB, ONE, BWK, LDB )
193 *
194 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
195 *
196 RESID = SLANGE( '1', N, P, BWK, LDB, RWORK )
197 IF( BNORM.GT.ZERO ) THEN
198 RESULT( 2 ) = ( ( RESID / REAL( MAX(1,P,N ) ) )/BNORM ) / ULP
199 ELSE
200 RESULT( 2 ) = ZERO
201 END IF
202 *
203 * Compute I - Q'*Q
204 *
205 CALL SLASET( 'Full', N, N, ZERO, ONE, R, LDA )
206 CALL SSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDA, ONE, R,
207 $ LDA )
208 *
209 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
210 *
211 RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK )
212 RESULT( 3 ) = ( RESID / REAL( MAX( 1, N ) ) ) / ULP
213 *
214 * Compute I - Z'*Z
215 *
216 CALL SLASET( 'Full', P, P, ZERO, ONE, T, LDB )
217 CALL SSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T,
218 $ LDB )
219 *
220 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
221 *
222 RESID = SLANSY( '1', 'Upper', P, T, LDB, RWORK )
223 RESULT( 4 ) = ( RESID / REAL( MAX( 1, P ) ) ) / ULP
224 *
225 RETURN
226 *
227 * End of SGQRTS
228 *
229 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 A( LDA, * ), AF( LDA, * ), R( LDA, * ),
13 $ Q( LDA, * ), B( LDB, * ), BF( LDB, * ),
14 $ T( LDB, * ), Z( LDB, * ), BWK( LDB, * ),
15 $ TAUA( * ), TAUB( * ), RESULT( 4 ),
16 $ RWORK( * ), WORK( LWORK )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * SGQRTS tests SGGQRF, 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) REAL array, dimension (LDA,M)
38 * The N-by-M matrix A.
39 *
40 * AF (output) REAL array, dimension (LDA,N)
41 * Details of the GQR factorization of A and B, as returned
42 * by SGGQRF, see SGGQRF for further details.
43 *
44 * Q (output) REAL array, dimension (LDA,N)
45 * The M-by-M orthogonal matrix Q.
46 *
47 * R (workspace) REAL 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) REAL array, dimension (min(M,N))
54 * The scalar factors of the elementary reflectors, as returned
55 * by SGGQRF.
56 *
57 * B (input) REAL array, dimension (LDB,P)
58 * On entry, the N-by-P matrix A.
59 *
60 * BF (output) REAL array, dimension (LDB,N)
61 * Details of the GQR factorization of A and B, as returned
62 * by SGGQRF, see SGGQRF for further details.
63 *
64 * Z (output) REAL array, dimension (LDB,P)
65 * The P-by-P orthogonal matrix Z.
66 *
67 * T (workspace) REAL array, dimension (LDB,max(P,N))
68 *
69 * BWK (workspace) REAL 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) REAL array, dimension (min(P,N))
76 * The scalar factors of the elementary reflectors, as returned
77 * by SGGRQF.
78 *
79 * WORK (workspace) REAL 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 REAL ROGUE
99 PARAMETER ( ROGUE = -1.0E+10 )
100 * ..
101 * .. Local Scalars ..
102 INTEGER INFO
103 REAL ANORM, BNORM, ULP, UNFL, RESID
104 * ..
105 * .. External Functions ..
106 REAL SLAMCH, SLANGE, SLANSY
107 EXTERNAL SLAMCH, SLANGE, SLANSY
108 * ..
109 * .. External Subroutines ..
110 EXTERNAL SGEMM, SLACPY, SLASET, SORGQR,
111 $ SORGRQ, SSYRK
112 * ..
113 * .. Intrinsic Functions ..
114 INTRINSIC MAX, MIN, REAL
115 * ..
116 * .. Executable Statements ..
117 *
118 ULP = SLAMCH( 'Precision' )
119 UNFL = SLAMCH( 'Safe minimum' )
120 *
121 * Copy the matrix A to the array AF.
122 *
123 CALL SLACPY( 'Full', N, M, A, LDA, AF, LDA )
124 CALL SLACPY( 'Full', N, P, B, LDB, BF, LDB )
125 *
126 ANORM = MAX( SLANGE( '1', N, M, A, LDA, RWORK ), UNFL )
127 BNORM = MAX( SLANGE( '1', N, P, B, LDB, RWORK ), UNFL )
128 *
129 * Factorize the matrices A and B in the arrays AF and BF.
130 *
131 CALL SGGQRF( N, M, P, AF, LDA, TAUA, BF, LDB, TAUB, WORK,
132 $ LWORK, INFO )
133 *
134 * Generate the N-by-N matrix Q
135 *
136 CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
137 CALL SLACPY( 'Lower', N-1, M, AF( 2,1 ), LDA, Q( 2,1 ), LDA )
138 CALL SORGQR( N, N, MIN( N, M ), Q, LDA, TAUA, WORK, LWORK, INFO )
139 *
140 * Generate the P-by-P matrix Z
141 *
142 CALL SLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB )
143 IF( N.LE.P ) THEN
144 IF( N.GT.0 .AND. N.LT.P )
145 $ CALL SLACPY( 'Full', N, P-N, BF, LDB, Z( P-N+1, 1 ), LDB )
146 IF( N.GT.1 )
147 $ CALL SLACPY( 'Lower', N-1, N-1, BF( 2, P-N+1 ), LDB,
148 $ Z( P-N+2, P-N+1 ), LDB )
149 ELSE
150 IF( P.GT.1)
151 $ CALL SLACPY( 'Lower', P-1, P-1, BF( N-P+2, 1 ), LDB,
152 $ Z( 2, 1 ), LDB )
153 END IF
154 CALL SORGRQ( P, P, MIN( N, P ), Z, LDB, TAUB, WORK, LWORK, INFO )
155 *
156 * Copy R
157 *
158 CALL SLASET( 'Full', N, M, ZERO, ZERO, R, LDA )
159 CALL SLACPY( 'Upper', N, M, AF, LDA, R, LDA )
160 *
161 * Copy T
162 *
163 CALL SLASET( 'Full', N, P, ZERO, ZERO, T, LDB )
164 IF( N.LE.P ) THEN
165 CALL SLACPY( 'Upper', N, N, BF( 1, P-N+1 ), LDB, T( 1, P-N+1 ),
166 $ LDB )
167 ELSE
168 CALL SLACPY( 'Full', N-P, P, BF, LDB, T, LDB )
169 CALL SLACPY( 'Upper', P, P, BF( N-P+1, 1 ), LDB, T( N-P+1, 1 ),
170 $ LDB )
171 END IF
172 *
173 * Compute R - Q'*A
174 *
175 CALL SGEMM( 'Transpose', 'No transpose', N, M, N, -ONE, Q, LDA, A,
176 $ LDA, ONE, R, LDA )
177 *
178 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
179 *
180 RESID = SLANGE( '1', N, M, R, LDA, RWORK )
181 IF( ANORM.GT.ZERO ) THEN
182 RESULT( 1 ) = ( ( RESID / REAL( MAX(1,M,N) ) ) / ANORM ) / ULP
183 ELSE
184 RESULT( 1 ) = ZERO
185 END IF
186 *
187 * Compute T*Z - Q'*B
188 *
189 CALL SGEMM( 'No Transpose', 'No transpose', N, P, P, ONE, T, LDB,
190 $ Z, LDB, ZERO, BWK, LDB )
191 CALL SGEMM( 'Transpose', 'No transpose', N, P, N, -ONE, Q, LDA,
192 $ B, LDB, ONE, BWK, LDB )
193 *
194 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
195 *
196 RESID = SLANGE( '1', N, P, BWK, LDB, RWORK )
197 IF( BNORM.GT.ZERO ) THEN
198 RESULT( 2 ) = ( ( RESID / REAL( MAX(1,P,N ) ) )/BNORM ) / ULP
199 ELSE
200 RESULT( 2 ) = ZERO
201 END IF
202 *
203 * Compute I - Q'*Q
204 *
205 CALL SLASET( 'Full', N, N, ZERO, ONE, R, LDA )
206 CALL SSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDA, ONE, R,
207 $ LDA )
208 *
209 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
210 *
211 RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK )
212 RESULT( 3 ) = ( RESID / REAL( MAX( 1, N ) ) ) / ULP
213 *
214 * Compute I - Z'*Z
215 *
216 CALL SLASET( 'Full', P, P, ZERO, ONE, T, LDB )
217 CALL SSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T,
218 $ LDB )
219 *
220 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
221 *
222 RESID = SLANSY( '1', 'Upper', P, T, LDB, RWORK )
223 RESULT( 4 ) = ( RESID / REAL( MAX( 1, P ) ) ) / ULP
224 *
225 RETURN
226 *
227 * End of SGQRTS
228 *
229 END