LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
drqt01.f
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1 *> \brief \b DRQT01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
12 * RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
19 * $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20 * $ WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n
30 *> matrix A, and partially tests DORGRQ which forms the n-by-n
31 *> orthogonal matrix Q.
32 *>
33 *> DRQT01 compares R with A*Q', and checks that Q is orthogonal.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] M
40 *> \verbatim
41 *> M is INTEGER
42 *> The number of rows of the matrix A. M >= 0.
43 *> \endverbatim
44 *>
45 *> \param[in] N
46 *> \verbatim
47 *> N is INTEGER
48 *> The number of columns of the matrix A. N >= 0.
49 *> \endverbatim
50 *>
51 *> \param[in] A
52 *> \verbatim
53 *> A is DOUBLE PRECISION array, dimension (LDA,N)
54 *> The m-by-n matrix A.
55 *> \endverbatim
56 *>
57 *> \param[out] AF
58 *> \verbatim
59 *> AF is DOUBLE PRECISION array, dimension (LDA,N)
60 *> Details of the RQ factorization of A, as returned by DGERQF.
61 *> See DGERQF for further details.
62 *> \endverbatim
63 *>
64 *> \param[out] Q
65 *> \verbatim
66 *> Q is DOUBLE PRECISION array, dimension (LDA,N)
67 *> The n-by-n orthogonal matrix Q.
68 *> \endverbatim
69 *>
70 *> \param[out] R
71 *> \verbatim
72 *> R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of the arrays A, AF, Q and L.
79 *> LDA >= max(M,N).
80 *> \endverbatim
81 *>
82 *> \param[out] TAU
83 *> \verbatim
84 *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
85 *> The scalar factors of the elementary reflectors, as returned
86 *> by DGERQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
92 *> \endverbatim
93 *>
94 *> \param[in] LWORK
95 *> \verbatim
96 *> LWORK is INTEGER
97 *> The dimension of the array WORK.
98 *> \endverbatim
99 *>
100 *> \param[out] RWORK
101 *> \verbatim
102 *> RWORK is DOUBLE PRECISION array, dimension (max(M,N))
103 *> \endverbatim
104 *>
105 *> \param[out] RESULT
106 *> \verbatim
107 *> RESULT is DOUBLE PRECISION array, dimension (2)
108 *> The test ratios:
109 *> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
110 *> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
111 *> \endverbatim
112 *
113 * Authors:
114 * ========
115 *
116 *> \author Univ. of Tennessee
117 *> \author Univ. of California Berkeley
118 *> \author Univ. of Colorado Denver
119 *> \author NAG Ltd.
120 *
121 *> \ingroup double_lin
122 *
123 * =====================================================================
124  SUBROUTINE drqt01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
125  $ RWORK, RESULT )
126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  INTEGER LDA, LWORK, M, N
133 * ..
134 * .. Array Arguments ..
135  DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
136  $ r( lda, * ), result( * ), rwork( * ), tau( * ),
137  $ work( lwork )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145  DOUBLE PRECISION ROGUE
146  parameter( rogue = -1.0d+10 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER INFO, MINMN
150  DOUBLE PRECISION ANORM, EPS, RESID
151 * ..
152 * .. External Functions ..
153  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
154  EXTERNAL dlamch, dlange, dlansy
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL dgemm, dgerqf, dlacpy, dlaset, dorgrq, dsyrk
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC dble, max, min
161 * ..
162 * .. Scalars in Common ..
163  CHARACTER*32 SRNAMT
164 * ..
165 * .. Common blocks ..
166  COMMON / srnamc / srnamt
167 * ..
168 * .. Executable Statements ..
169 *
170  minmn = min( m, n )
171  eps = dlamch( 'Epsilon' )
172 *
173 * Copy the matrix A to the array AF.
174 *
175  CALL dlacpy( 'Full', m, n, a, lda, af, lda )
176 *
177 * Factorize the matrix A in the array AF.
178 *
179  srnamt = 'DGERQF'
180  CALL dgerqf( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL dlaset( 'Full', n, n, rogue, rogue, q, lda )
185  IF( m.LE.n ) THEN
186  IF( m.GT.0 .AND. m.LT.n )
187  $ CALL dlacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188  IF( m.GT.1 )
189  $ CALL dlacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
190  $ q( n-m+2, n-m+1 ), lda )
191  ELSE
192  IF( n.GT.1 )
193  $ CALL dlacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
194  $ q( 2, 1 ), lda )
195  END IF
196 *
197 * Generate the n-by-n matrix Q
198 *
199  srnamt = 'DORGRQ'
200  CALL dorgrq( n, n, minmn, q, lda, tau, work, lwork, info )
201 *
202 * Copy R
203 *
204  CALL dlaset( 'Full', m, n, zero, zero, r, lda )
205  IF( m.LE.n ) THEN
206  IF( m.GT.0 )
207  $ CALL dlacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
208  $ r( 1, n-m+1 ), lda )
209  ELSE
210  IF( m.GT.n .AND. n.GT.0 )
211  $ CALL dlacpy( 'Full', m-n, n, af, lda, r, lda )
212  IF( n.GT.0 )
213  $ CALL dlacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
214  $ r( m-n+1, 1 ), lda )
215  END IF
216 *
217 * Compute R - A*Q'
218 *
219  CALL dgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
220  $ lda, one, r, lda )
221 *
222 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
223 *
224  anorm = dlange( '1', m, n, a, lda, rwork )
225  resid = dlange( '1', m, n, r, lda, rwork )
226  IF( anorm.GT.zero ) THEN
227  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
228  ELSE
229  result( 1 ) = zero
230  END IF
231 *
232 * Compute I - Q*Q'
233 *
234  CALL dlaset( 'Full', n, n, zero, one, r, lda )
235  CALL dsyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
236  $ lda )
237 *
238 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
239 *
240  resid = dlansy( '1', 'Upper', n, r, lda, rwork )
241 *
242  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
243 *
244  RETURN
245 *
246 * End of DRQT01
247 *
248  END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine drqt01(M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DRQT01
Definition: drqt01.f:126
subroutine dgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGERQF
Definition: dgerqf.f:138
subroutine dorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGRQ
Definition: dorgrq.f:128