LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine zrqt03 ( 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 
)

ZRQT03

Purpose: 
 ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 ZRQT03 compares the results of a call to ZUNMRQ with the results of
 forming Q explicitly by a call to ZUNGRQ and then performing matrix
 multiplication by a call to ZGEMM.
Parameters
[in]M
          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.
[in]N
          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.
[in]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          Details of the RQ factorization of an m-by-n matrix, as
          returned by ZGERQF. See CGERQF 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,N)
[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 RQ 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 n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 138 of file zrqt03.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, zungrq, zunmrq
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 rows of the factorization to the array Q
205 *
206  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. n.GT.k )
208  $ CALL zlacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
209  $ q( n-k+1, 1 ), lda )
210  IF( k.GT.1 )
211  $ CALL zlacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
212  $ q( n-k+2, n-k+1 ), lda )
213 *
214 * Generate the n-by-n matrix Q
215 *
216  srnamt = 'ZUNGRQ'
217  CALL zungrq( n, n, 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 = n
224  nc = m
225  ELSE
226  side = 'R'
227  mc = m
228  nc = n
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 = 'ZUNMRQ'
254  IF( k.GT.0 )
255  $ CALL zunmrq( side, trans, mc, nc, k, af( m-k+1, 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, n ) )*cnorm*eps )
276 *
277  20 CONTINUE
278  30 CONTINUE
279 *
280  RETURN
281 *
282 * End of ZRQT03
283 *
zlacpy
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
zlarnv
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
zgemm
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
zlaset
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
zlange
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
zungrq
subroutine zungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ
Definition: zungrq.f:130
zunmrq
subroutine zunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRQ
Definition: zunmrq.f:169
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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