LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
dlqt01.f
Go to the documentation of this file.
1 *> \brief \b DLQT01
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 DLQT01( M, N, A, AF, Q, L, 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, * ), L( LDA, * ),
19 * \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20 * \$ WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DLQT01 tests DGELQF, which computes the LQ factorization of an m-by-n
30 *> matrix A, and partially tests DORGLQ which forms the n-by-n
31 *> orthogonal matrix Q.
32 *>
33 *> DLQT01 compares L 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 LQ factorization of A, as returned by DGELQF.
61 *> See DGELQF 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] L
71 *> \verbatim
72 *> L 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 DGELQF.
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( L - 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 dlqt01( M, N, A, AF, Q, L, 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, * ), L( LDA, * ),
136  \$ q( 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 dgelqf, dgemm, dlacpy, dlaset, dorglq, 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 = 'DGELQF'
180  CALL dgelqf( 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( n.GT.1 )
186  \$ CALL dlacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187 *
188 * Generate the n-by-n matrix Q
189 *
190  srnamt = 'DORGLQ'
191  CALL dorglq( n, n, minmn, q, lda, tau, work, lwork, info )
192 *
193 * Copy L
194 *
195  CALL dlaset( 'Full', m, n, zero, zero, l, lda )
196  CALL dlacpy( 'Lower', m, n, af, lda, l, lda )
197 *
198 * Compute L - A*Q'
199 *
200  CALL dgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
201  \$ lda, one, l, lda )
202 *
203 * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
204 *
205  anorm = dlange( '1', m, n, a, lda, rwork )
206  resid = dlange( '1', m, n, l, lda, rwork )
207  IF( anorm.GT.zero ) THEN
208  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
209  ELSE
210  result( 1 ) = zero
211  END IF
212 *
213 * Compute I - Q*Q'
214 *
215  CALL dlaset( 'Full', n, n, zero, one, l, lda )
216  CALL dsyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
217  \$ lda )
218 *
219 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
220 *
221  resid = dlansy( '1', 'Upper', n, l, lda, rwork )
222 *
223  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
224 *
225  RETURN
226 *
227 * End of DLQT01
228 *
229  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 dlqt01(M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DLQT01
Definition: dlqt01.f:126
subroutine dgelqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGELQF
Definition: dgelqf.f:143
subroutine dorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGLQ
Definition: dorglq.f:127