LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zqlt03 ( integer M, integer N, integer K, complex*16, dimension( lda, * ) AF, complex*16, dimension( lda, * ) C, complex*16, dimension( lda, * ) CC, complex*16, dimension( lda, * ) Q, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

ZQLT03

Purpose:
``` ZQLT03 tests ZUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

ZQLT03 compares the results of a call to ZUNMQL with the results of
forming Q explicitly by a call to ZUNGQL and then performing matrix
multiplication by a call to ZGEMM.```
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 COMPLEX*16 array, dimension (LDA,N) Details of the QL factorization of an m-by-n matrix, as returned by ZGEQLF. See CGEQLF for further details.``` [out] C ` C is COMPLEX*16 array, dimension (LDA,N)` [out] CC ` CC is COMPLEX*16 array, dimension (LDA,N)` [out] Q ` Q is COMPLEX*16 array, dimension (LDA,M)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.``` [in] TAU ``` TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.``` [out] WORK ` WORK is COMPLEX*16 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 zqlt03.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 result( * ), rwork( * )
149  COMPLEX*16 af( lda, * ), c( lda, * ), cc( lda, * ),
150  \$ q( lda, * ), tau( * ), work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION zero, one
157  parameter ( zero = 0.0d+0, one = 1.0d+0 )
158  COMPLEX*16 rogue
159  parameter ( rogue = ( -1.0d+10, -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, zlange
169  EXTERNAL lsame, dlamch, zlange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL zgemm, zlacpy, zlarnv, zlaset, zungql, zunmql
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC dble, dcmplx, 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 zlaset( 'Full', m, m, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. m.GT.k )
208  \$ CALL zlacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
209  \$ q( 1, m-k+1 ), lda )
210  IF( k.GT.1 )
211  \$ CALL zlacpy( '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 = 'ZUNGQL'
217  CALL zungql( 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 zlarnv( 2, iseed, mc, c( 1, j ) )
235  10 CONTINUE
236  cnorm = zlange( '1', mc, nc, c, lda, rwork )
237  IF( cnorm.EQ.zero )
238  \$ cnorm = one
239 *
240  DO 20 itrans = 1, 2
241  IF( itrans.EQ.1 ) THEN
242  trans = 'N'
243  ELSE
244  trans = 'C'
245  END IF
246 *
247 * Copy C
248 *
249  CALL zlacpy( 'Full', mc, nc, c, lda, cc, lda )
250 *
251 * Apply Q or Q' to C
252 *
253  srnamt = 'ZUNMQL'
254  IF( k.GT.0 )
255  \$ CALL zunmql( 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 zgemm( trans, 'No transpose', mc, nc, mc,
263  \$ dcmplx( -one ), q, lda, c, lda,
264  \$ dcmplx( one ), cc, lda )
265  ELSE
266  CALL zgemm( 'No transpose', trans, mc, nc, nc,
267  \$ dcmplx( -one ), c, lda, q, lda,
268  \$ dcmplx( one ), cc, lda )
269  END IF
270 *
271 * Compute error in the difference
272 *
273  resid = zlange( '1', mc, nc, cc, lda, rwork )
274  result( ( iside-1 )*2+itrans ) = resid /
275  \$ ( dble( max( 1, m ) )*cnorm*eps )
276 *
277  20 CONTINUE
278  30 CONTINUE
279 *
280  RETURN
281 *
282 * End of ZQLT03
283 *
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zungql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQL
Definition: zungql.f:130
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:117
subroutine zunmql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQL
Definition: zunmql.f:169
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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