LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zqrt03()

 subroutine zqrt03 ( 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 )

ZQRT03

Purpose:
``` ZQRT03 tests ZUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

ZQRT03 compares the results of a call to ZUNMQR with the results of
forming Q explicitly by a call to ZUNGQR 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 QR factorization of an m-by-n matrix, as returned by ZGEQRF. See ZGEQRF 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 QR 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
December 2016

Definition at line 138 of file zqrt03.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  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, 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, zungqr, zunmqr
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC dble, dcmplx, max
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 *
193 * Copy the first k columns of the factorization to the array Q
194 *
195  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
196  CALL zlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
197 *
198 * Generate the m-by-m matrix Q
199 *
200  srnamt = 'ZUNGQR'
201  CALL zungqr( m, m, 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 = m
207  nc = n
208  ELSE
209  side = 'R'
210  mc = n
211  nc = m
212  END IF
213 *
214 * Generate MC by NC matrix C
215 *
216  DO 10 j = 1, nc
217  CALL zlarnv( 2, iseed, mc, c( 1, j ) )
218  10 CONTINUE
219  cnorm = zlange( '1', mc, nc, c, lda, rwork )
220  IF( cnorm.EQ.zero )
221  \$ cnorm = one
222 *
223  DO 20 itrans = 1, 2
224  IF( itrans.EQ.1 ) THEN
225  trans = 'N'
226  ELSE
227  trans = 'C'
228  END IF
229 *
230 * Copy C
231 *
232  CALL zlacpy( 'Full', mc, nc, c, lda, cc, lda )
233 *
234 * Apply Q or Q' to C
235 *
236  srnamt = 'ZUNMQR'
237  CALL zunmqr( 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 zgemm( trans, 'No transpose', mc, nc, mc,
244  \$ dcmplx( -one ), q, lda, c, lda,
245  \$ dcmplx( one ), cc, lda )
246  ELSE
247  CALL zgemm( 'No transpose', trans, mc, nc, nc,
248  \$ dcmplx( -one ), c, lda, q, lda,
249  \$ dcmplx( one ), cc, lda )
250  END IF
251 *
252 * Compute error in the difference
253 *
254  resid = zlange( '1', mc, nc, cc, lda, rwork )
255  result( ( iside-1 )*2+itrans ) = resid /
256  \$ ( dble( max( 1, m ) )*cnorm*eps )
257 *
258  20 CONTINUE
259  30 CONTINUE
260 *
261  RETURN
262 *
263 * End of ZQRT03
264 *
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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:130
subroutine zunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQR
Definition: zunmqr.f:169
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