LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dqlt03 ( integer M, integer N, integer K, double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

DQLT03

Purpose:
``` DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

DQLT03 compares the results of a call to DORMQL with the results of
forming Q explicitly by a call to DORGQL and then performing matrix
multiplication by a call to DGEMM.```
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 DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of an m-by-n matrix, as returned by DGEQLF. See SGEQLF for further details.``` [out] C ` C is DOUBLE PRECISION array, dimension (LDA,N)` [out] CC ` CC is DOUBLE PRECISION array, dimension (LDA,N)` [out] Q ` Q is DOUBLE PRECISION array, dimension (LDA,M)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.``` [out] WORK ` WORK is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M)` [out] RESULT ``` RESULT is DOUBLE PRECISION 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 )```
Date
November 2011

Definition at line 138 of file dqlt03.f.

138 *
139 * -- LAPACK test routine (version 3.4.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * November 2011
143 *
144 * .. Scalar Arguments ..
145  INTEGER k, lda, lwork, m, n
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION af( lda, * ), c( lda, * ), cc( lda, * ),
149  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
150  \$ work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION zero, one
157  parameter ( zero = 0.0d0, one = 1.0d0 )
158  DOUBLE PRECISION rogue
159  parameter ( rogue = -1.0d+10 )
160 * ..
161 * .. Local Scalars ..
162  CHARACTER side, trans
163  INTEGER info, iside, itrans, j, mc, minmn, nc
164  DOUBLE PRECISION cnorm, eps, resid
165 * ..
166 * .. External Functions ..
167  LOGICAL lsame
168  DOUBLE PRECISION dlamch, dlange
169  EXTERNAL lsame, dlamch, dlange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL dgemm, dlacpy, dlarnv, dlaset, dorgql, dormql
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC dble, max, min
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 = dlamch( '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 dlaset( 'Full', m, m, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. m.GT.k )
208  \$ CALL dlacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
209  \$ q( 1, m-k+1 ), lda )
210  IF( k.GT.1 )
211  \$ CALL dlacpy( '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 = 'DORGQL'
217  CALL dorgql( 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 dlarnv( 2, iseed, mc, c( 1, j ) )
235  10 CONTINUE
236  cnorm = dlange( '1', mc, nc, c, lda, rwork )
237  IF( cnorm.EQ.0.0d0 )
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 dlacpy( 'Full', mc, nc, c, lda, cc, lda )
250 *
251 * Apply Q or Q' to C
252 *
253  srnamt = 'DORMQL'
254  IF( k.GT.0 )
255  \$ CALL dormql( 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 dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
263  \$ lda, c, lda, one, cc, lda )
264  ELSE
265  CALL dgemm( '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 = dlange( '1', mc, nc, cc, lda, rwork )
272  result( ( iside-1 )*2+itrans ) = resid /
273  \$ ( dble( max( 1, m ) )*cnorm*eps )
274 *
275  20 CONTINUE
276  30 CONTINUE
277 *
278  RETURN
279 *
280 * End of DQLT03
281 *
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:112
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQL
Definition: dormql.f:169
subroutine dorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQL
Definition: dorgql.f:130
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:99
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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