 LAPACK  3.10.0 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 )

Definition at line 134 of file zqrt03.f.

136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  INTEGER K, LDA, LWORK, M, N
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION RESULT( * ), RWORK( * )
146  COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
147  \$ Q( LDA, * ), TAU( * ), WORK( LWORK )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION ZERO, ONE
154  parameter( zero = 0.0d+0, one = 1.0d+0 )
155  COMPLEX*16 ROGUE
156  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
157 * ..
158 * .. Local Scalars ..
159  CHARACTER SIDE, TRANS
160  INTEGER INFO, ISIDE, ITRANS, J, MC, NC
161  DOUBLE PRECISION CNORM, EPS, RESID
162 * ..
163 * .. External Functions ..
164  LOGICAL LSAME
165  DOUBLE PRECISION DLAMCH, ZLANGE
166  EXTERNAL lsame, dlamch, zlange
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL zgemm, zlacpy, zlarnv, zlaset, zungqr, zunmqr
170 * ..
171 * .. Local Arrays ..
172  INTEGER ISEED( 4 )
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC dble, dcmplx, max
176 * ..
177 * .. Scalars in Common ..
178  CHARACTER*32 SRNAMT
179 * ..
180 * .. Common blocks ..
181  COMMON / srnamc / srnamt
182 * ..
183 * .. Data statements ..
184  DATA iseed / 1988, 1989, 1990, 1991 /
185 * ..
186 * .. Executable Statements ..
187 *
188  eps = dlamch( 'Epsilon' )
189 *
190 * Copy the first k columns of the factorization to the array Q
191 *
192  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
193  CALL zlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
194 *
195 * Generate the m-by-m matrix Q
196 *
197  srnamt = 'ZUNGQR'
198  CALL zungqr( m, m, k, q, lda, tau, work, lwork, info )
199 *
200  DO 30 iside = 1, 2
201  IF( iside.EQ.1 ) THEN
202  side = 'L'
203  mc = m
204  nc = n
205  ELSE
206  side = 'R'
207  mc = n
208  nc = m
209  END IF
210 *
211 * Generate MC by NC matrix C
212 *
213  DO 10 j = 1, nc
214  CALL zlarnv( 2, iseed, mc, c( 1, j ) )
215  10 CONTINUE
216  cnorm = zlange( '1', mc, nc, c, lda, rwork )
217  IF( cnorm.EQ.zero )
218  \$ cnorm = one
219 *
220  DO 20 itrans = 1, 2
221  IF( itrans.EQ.1 ) THEN
222  trans = 'N'
223  ELSE
224  trans = 'C'
225  END IF
226 *
227 * Copy C
228 *
229  CALL zlacpy( 'Full', mc, nc, c, lda, cc, lda )
230 *
231 * Apply Q or Q' to C
232 *
233  srnamt = 'ZUNMQR'
234  CALL zunmqr( side, trans, mc, nc, k, af, lda, tau, cc, lda,
235  \$ work, lwork, info )
236 *
237 * Form explicit product and subtract
238 *
239  IF( lsame( side, 'L' ) ) THEN
240  CALL zgemm( trans, 'No transpose', mc, nc, mc,
241  \$ dcmplx( -one ), q, lda, c, lda,
242  \$ dcmplx( one ), cc, lda )
243  ELSE
244  CALL zgemm( 'No transpose', trans, mc, nc, nc,
245  \$ dcmplx( -one ), c, lda, q, lda,
246  \$ dcmplx( one ), cc, lda )
247  END IF
248 *
249 * Compute error in the difference
250 *
251  resid = zlange( '1', mc, nc, cc, lda, rwork )
252  result( ( iside-1 )*2+itrans ) = resid /
253  \$ ( dble( max( 1, m ) )*cnorm*eps )
254 *
255  20 CONTINUE
256  30 CONTINUE
257 *
258  RETURN
259 *
260 * End of ZQRT03
261 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
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:115
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
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:106
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:128
subroutine zunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQR
Definition: zunmqr.f:167
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