LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ slqt03()

subroutine slqt03 ( integer  M,
integer  N,
integer  K,
real, dimension( lda, * )  AF,
real, dimension( lda, * )  C,
real, dimension( lda, * )  CC,
real, dimension( lda, * )  Q,
integer  LDA,
real, dimension( * )  TAU,
real, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( * )  RESULT 
)

SLQT03

Purpose:
 SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 SLQT03 compares the results of a call to SORMLQ with the results of
 forming Q explicitly by a call to SORGLQ and then performing matrix
 multiplication by a call to SGEMM.
Parameters
[in]M
          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.
[in]N
          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.
[in]AF
          AF is REAL array, dimension (LDA,N)
          Details of the LQ factorization of an m-by-n matrix, as
          returned by SGELQF. See SGELQF for further details.
[out]C
          C is REAL array, dimension (LDA,N)
[out]CC
          CC is REAL array, dimension (LDA,N)
[out]Q
          Q is REAL array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the LQ factorization in AF.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.
[out]RWORK
          RWORK is REAL array, dimension (M)
[out]RESULT
          RESULT is REAL array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 138 of file slqt03.f.

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 *
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
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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
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