LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
slqt03.f
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1 *> \brief \b SLQT03
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 SLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
12 * RWORK, RESULT )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER K, LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
19 * $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
20 * $ WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
30 *>
31 *> SLQT03 compares the results of a call to SORMLQ with the results of
32 *> forming Q explicitly by a call to SORGLQ and then performing matrix
33 *> multiplication by a call to SGEMM.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] M
40 *> \verbatim
41 *> M is INTEGER
42 *> The number of rows or columns of the matrix C; C is n-by-m if
43 *> Q is applied from the left, or m-by-n if Q is applied from
44 *> the right. M >= 0.
45 *> \endverbatim
46 *>
47 *> \param[in] N
48 *> \verbatim
49 *> N is INTEGER
50 *> The order of the orthogonal matrix Q. N >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] K
54 *> \verbatim
55 *> K is INTEGER
56 *> The number of elementary reflectors whose product defines the
57 *> orthogonal matrix Q. N >= K >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] AF
61 *> \verbatim
62 *> AF is REAL array, dimension (LDA,N)
63 *> Details of the LQ factorization of an m-by-n matrix, as
64 *> returned by SGELQF. See SGELQF for further details.
65 *> \endverbatim
66 *>
67 *> \param[out] C
68 *> \verbatim
69 *> C is REAL array, dimension (LDA,N)
70 *> \endverbatim
71 *>
72 *> \param[out] CC
73 *> \verbatim
74 *> CC is REAL array, dimension (LDA,N)
75 *> \endverbatim
76 *>
77 *> \param[out] Q
78 *> \verbatim
79 *> Q is REAL array, dimension (LDA,N)
80 *> \endverbatim
81 *>
82 *> \param[in] LDA
83 *> \verbatim
84 *> LDA is INTEGER
85 *> The leading dimension of the arrays AF, C, CC, and Q.
86 *> \endverbatim
87 *>
88 *> \param[in] TAU
89 *> \verbatim
90 *> TAU is REAL array, dimension (min(M,N))
91 *> The scalar factors of the elementary reflectors corresponding
92 *> to the LQ factorization in AF.
93 *> \endverbatim
94 *>
95 *> \param[out] WORK
96 *> \verbatim
97 *> WORK is REAL array, dimension (LWORK)
98 *> \endverbatim
99 *>
100 *> \param[in] LWORK
101 *> \verbatim
102 *> LWORK is INTEGER
103 *> The length of WORK. LWORK must be at least M, and should be
104 *> M*NB, where NB is the blocksize for this environment.
105 *> \endverbatim
106 *>
107 *> \param[out] RWORK
108 *> \verbatim
109 *> RWORK is REAL array, dimension (M)
110 *> \endverbatim
111 *>
112 *> \param[out] RESULT
113 *> \verbatim
114 *> RESULT is REAL array, dimension (4)
115 *> The test ratios compare two techniques for multiplying a
116 *> random matrix C by an n-by-n orthogonal matrix Q.
117 *> RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
118 *> RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
119 *> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
120 *> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
121 *> \endverbatim
122 *
123 * Authors:
124 * ========
125 *
126 *> \author Univ. of Tennessee
127 *> \author Univ. of California Berkeley
128 *> \author Univ. of Colorado Denver
129 *> \author NAG Ltd.
130 *
131 *> \date December 2016
132 *
133 *> \ingroup single_lin
134 *
135 * =====================================================================
136  SUBROUTINE slqt03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
137  $ RWORK, RESULT )
138 *
139 * -- LAPACK test routine (version 3.7.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * December 2016
143 *
144 * .. Scalar Arguments ..
145  INTEGER K, LDA, LWORK, M, N
146 * ..
147 * .. Array Arguments ..
148  REAL AF( lda, * ), C( lda, * ), CC( lda, * ),
149  $ q( lda, * ), result( * ), rwork( * ), tau( * ),
150  $ work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  REAL ONE
157  parameter( one = 1.0e0 )
158  REAL ROGUE
159  parameter( rogue = -1.0e+10 )
160 * ..
161 * .. Local Scalars ..
162  CHARACTER SIDE, TRANS
163  INTEGER INFO, ISIDE, ITRANS, J, MC, NC
164  REAL CNORM, EPS, RESID
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  REAL SLAMCH, SLANGE
169  EXTERNAL lsame, slamch, slange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL sgemm, slacpy, slarnv, slaset, sorglq, sormlq
173 * ..
174 * .. Local Arrays ..
175  INTEGER ISEED( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC max, real
179 * ..
180 * .. Scalars in Common ..
181  CHARACTER*32 SRNAMT
182 * ..
183 * .. Common blocks ..
184  COMMON / srnamc / srnamt
185 * ..
186 * .. Data statements ..
187  DATA iseed / 1988, 1989, 1990, 1991 /
188 * ..
189 * .. Executable Statements ..
190 *
191  eps = slamch( 'Epsilon' )
192 *
193 * Copy the first k rows of the factorization to the array Q
194 *
195  CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
196  CALL slacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
197 *
198 * Generate the n-by-n matrix Q
199 *
200  srnamt = 'SORGLQ'
201  CALL sorglq( n, n, k, q, lda, tau, work, lwork, info )
202 *
203  DO 30 iside = 1, 2
204  IF( iside.EQ.1 ) THEN
205  side = 'L'
206  mc = n
207  nc = m
208  ELSE
209  side = 'R'
210  mc = m
211  nc = n
212  END IF
213 *
214 * Generate MC by NC matrix C
215 *
216  DO 10 j = 1, nc
217  CALL slarnv( 2, iseed, mc, c( 1, j ) )
218  10 CONTINUE
219  cnorm = slange( '1', mc, nc, c, lda, rwork )
220  IF( cnorm.EQ.0.0 )
221  $ cnorm = one
222 *
223  DO 20 itrans = 1, 2
224  IF( itrans.EQ.1 ) THEN
225  trans = 'N'
226  ELSE
227  trans = 'T'
228  END IF
229 *
230 * Copy C
231 *
232  CALL slacpy( 'Full', mc, nc, c, lda, cc, lda )
233 *
234 * Apply Q or Q' to C
235 *
236  srnamt = 'SORMLQ'
237  CALL sormlq( side, trans, mc, nc, k, af, lda, tau, cc, lda,
238  $ work, lwork, info )
239 *
240 * Form explicit product and subtract
241 *
242  IF( lsame( side, 'L' ) ) THEN
243  CALL sgemm( trans, 'No transpose', mc, nc, mc, -one, q,
244  $ lda, c, lda, one, cc, lda )
245  ELSE
246  CALL sgemm( 'No transpose', trans, mc, nc, nc, -one, c,
247  $ lda, q, lda, one, cc, lda )
248  END IF
249 *
250 * Compute error in the difference
251 *
252  resid = slange( '1', mc, nc, cc, lda, rwork )
253  result( ( iside-1 )*2+itrans ) = resid /
254  $ ( REAL( MAX( 1, N ) )*cnorm*eps )
255 *
256  20 CONTINUE
257  30 CONTINUE
258 *
259  RETURN
260 *
261 * End of SLQT03
262 *
263  END
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:170
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:129
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine slqt03(M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
SLQT03
Definition: slqt03.f:138
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:112
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:99
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105