LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sqlt03()

subroutine sqlt03 ( 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 
)

SQLT03

Purpose:
 SQLT03 tests SORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

 SQLT03 compares the results of a call to SORMQL with the results of
 forming Q explicitly by a call to SORGQL and then performing matrix
 multiplication by a call to SGEMM.
Parameters
[in]M
          M is INTEGER
          The order of the orthogonal matrix Q.  M >= 0.
[in]N
          N is INTEGER
          The number of rows or columns of the matrix C; C is m-by-n if
          Q is applied from the left, or n-by-m if Q is applied from
          the right.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  M >= K >= 0.
[in]AF
          AF is REAL array, dimension (LDA,N)
          Details of the QL factorization of an m-by-n matrix, as
          returned by SGEQLF. See SGEQLF 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,M)
[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 QL 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 m-by-m orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * 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 sqlt03.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 zero, one
157  parameter( zero = 0.0e0, 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, minmn, 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, sorgql, sormql
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC max, min, 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  minmn = min( m, n )
193 *
194 * Quick return if possible
195 *
196  IF( minmn.EQ.0 ) THEN
197  result( 1 ) = zero
198  result( 2 ) = zero
199  result( 3 ) = zero
200  result( 4 ) = zero
201  RETURN
202  END IF
203 *
204 * Copy the last k columns of the factorization to the array Q
205 *
206  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. m.GT.k )
208  $ CALL slacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
209  $ q( 1, m-k+1 ), lda )
210  IF( k.GT.1 )
211  $ CALL slacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
212  $ q( m-k+1, m-k+2 ), lda )
213 *
214 * Generate the m-by-m matrix Q
215 *
216  srnamt = 'SORGQL'
217  CALL sorgql( m, m, k, q, lda, tau( minmn-k+1 ), work, lwork,
218  $ info )
219 *
220  DO 30 iside = 1, 2
221  IF( iside.EQ.1 ) THEN
222  side = 'L'
223  mc = m
224  nc = n
225  ELSE
226  side = 'R'
227  mc = n
228  nc = m
229  END IF
230 *
231 * Generate MC by NC matrix C
232 *
233  DO 10 j = 1, nc
234  CALL slarnv( 2, iseed, mc, c( 1, j ) )
235  10 CONTINUE
236  cnorm = slange( '1', mc, nc, c, lda, rwork )
237  IF( cnorm.EQ.0.0 )
238  $ cnorm = one
239 *
240  DO 20 itrans = 1, 2
241  IF( itrans.EQ.1 ) THEN
242  trans = 'N'
243  ELSE
244  trans = 'T'
245  END IF
246 *
247 * Copy C
248 *
249  CALL slacpy( 'Full', mc, nc, c, lda, cc, lda )
250 *
251 * Apply Q or Q' to C
252 *
253  srnamt = 'SORMQL'
254  IF( k.GT.0 )
255  $ CALL sormql( side, trans, mc, nc, k, af( 1, n-k+1 ), lda,
256  $ tau( minmn-k+1 ), cc, lda, work, lwork,
257  $ info )
258 *
259 * Form explicit product and subtract
260 *
261  IF( lsame( side, 'L' ) ) THEN
262  CALL sgemm( trans, 'No transpose', mc, nc, mc, -one, q,
263  $ lda, c, lda, one, cc, lda )
264  ELSE
265  CALL sgemm( 'No transpose', trans, mc, nc, nc, -one, c,
266  $ lda, q, lda, one, cc, lda )
267  END IF
268 *
269 * Compute error in the difference
270 *
271  resid = slange( '1', mc, nc, cc, lda, rwork )
272  result( ( iside-1 )*2+itrans ) = resid /
273  $ ( REAL( MAX( 1, M ) )*cnorm*eps )
274 *
275  20 CONTINUE
276  30 CONTINUE
277 *
278  RETURN
279 *
280 * End of SQLT03
281 *
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.f:130
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
subroutine sormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQL
Definition: sormql.f:170
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