LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
slqt02.f
Go to the documentation of this file.
1 *> \brief \b SLQT02
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 SLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
12 * RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER K, LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL 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 *> SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with
30 *> orthonornmal rows that is defined as the product of k elementary
31 *> reflectors.
32 *>
33 *> Given the LQ factorization of an m-by-n matrix A, SLQT02 generates
34 *> the orthogonal matrix Q defined by the factorization of the first k
35 *> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
36 *> checks that the rows of Q are orthonormal.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] M
43 *> \verbatim
44 *> M is INTEGER
45 *> The number of rows of the matrix Q to be generated. M >= 0.
46 *> \endverbatim
47 *>
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGER
51 *> The number of columns of the matrix Q to be generated.
52 *> N >= M >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] K
56 *> \verbatim
57 *> K is INTEGER
58 *> The number of elementary reflectors whose product defines the
59 *> matrix Q. M >= K >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is REAL array, dimension (LDA,N)
65 *> The m-by-n matrix A which was factorized by SLQT01.
66 *> \endverbatim
67 *>
68 *> \param[in] AF
69 *> \verbatim
70 *> AF is REAL array, dimension (LDA,N)
71 *> Details of the LQ factorization of A, as returned by SGELQF.
72 *> See SGELQF for further details.
73 *> \endverbatim
74 *>
75 *> \param[out] Q
76 *> \verbatim
77 *> Q is REAL array, dimension (LDA,N)
78 *> \endverbatim
79 *>
80 *> \param[out] L
81 *> \verbatim
82 *> L is REAL array, dimension (LDA,M)
83 *> \endverbatim
84 *>
85 *> \param[in] LDA
86 *> \verbatim
87 *> LDA is INTEGER
88 *> The leading dimension of the arrays A, AF, Q and L. LDA >= N.
89 *> \endverbatim
90 *>
91 *> \param[in] TAU
92 *> \verbatim
93 *> TAU is REAL array, dimension (M)
94 *> The scalar factors of the elementary reflectors corresponding
95 *> to the LQ factorization in AF.
96 *> \endverbatim
97 *>
98 *> \param[out] WORK
99 *> \verbatim
100 *> WORK is REAL array, dimension (LWORK)
101 *> \endverbatim
102 *>
103 *> \param[in] LWORK
104 *> \verbatim
105 *> LWORK is INTEGER
106 *> The dimension of the array WORK.
107 *> \endverbatim
108 *>
109 *> \param[out] RWORK
110 *> \verbatim
111 *> RWORK is REAL array, dimension (M)
112 *> \endverbatim
113 *>
114 *> \param[out] RESULT
115 *> \verbatim
116 *> RESULT is REAL array, dimension (2)
117 *> The test ratios:
118 *> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
119 *> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
120 *> \endverbatim
121 *
122 * Authors:
123 * ========
124 *
125 *> \author Univ. of Tennessee
126 *> \author Univ. of California Berkeley
127 *> \author Univ. of Colorado Denver
128 *> \author NAG Ltd.
129 *
130 *> \ingroup single_lin
131 *
132 * =====================================================================
133  SUBROUTINE slqt02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
134  $ RWORK, RESULT )
135 *
136 * -- LAPACK test routine --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  INTEGER K, LDA, LWORK, M, N
142 * ..
143 * .. Array Arguments ..
144  REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
145  $ q( lda, * ), result( * ), rwork( * ), tau( * ),
146  $ work( lwork )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  REAL ZERO, ONE
153  parameter( zero = 0.0e+0, one = 1.0e+0 )
154  REAL ROGUE
155  parameter( rogue = -1.0e+10 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER INFO
159  REAL ANORM, EPS, RESID
160 * ..
161 * .. External Functions ..
162  REAL SLAMCH, SLANGE, SLANSY
163  EXTERNAL slamch, slange, slansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL sgemm, slacpy, slaset, sorglq, ssyrk
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC max, real
170 * ..
171 * .. Scalars in Common ..
172  CHARACTER*32 SRNAMT
173 * ..
174 * .. Common blocks ..
175  COMMON / srnamc / srnamt
176 * ..
177 * .. Executable Statements ..
178 *
179  eps = slamch( 'Epsilon' )
180 *
181 * Copy the first k rows of the factorization to the array Q
182 *
183  CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
184  CALL slacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
185 *
186 * Generate the first n columns of the matrix Q
187 *
188  srnamt = 'SORGLQ'
189  CALL sorglq( m, n, k, q, lda, tau, work, lwork, info )
190 *
191 * Copy L(1:k,1:m)
192 *
193  CALL slaset( 'Full', k, m, zero, zero, l, lda )
194  CALL slacpy( 'Lower', k, m, af, lda, l, lda )
195 *
196 * Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
197 *
198  CALL sgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
199  $ lda, one, l, lda )
200 *
201 * Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
202 *
203  anorm = slange( '1', k, n, a, lda, rwork )
204  resid = slange( '1', k, m, l, lda, rwork )
205  IF( anorm.GT.zero ) THEN
206  result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
207  ELSE
208  result( 1 ) = zero
209  END IF
210 *
211 * Compute I - Q*Q'
212 *
213  CALL slaset( 'Full', m, m, zero, one, l, lda )
214  CALL ssyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
215  $ lda )
216 *
217 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
218 *
219  resid = slansy( '1', 'Upper', m, l, lda, rwork )
220 *
221  result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
222 *
223  RETURN
224 *
225 * End of SLQT02
226 *
227  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:127
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine slqt02(M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
SLQT02
Definition: slqt02.f:135