 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zrqt03()

 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 )```

Definition at line 134 of file zrqt03.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, MINMN, 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, zungrq, zunmrq
170 * ..
171 * .. Local Arrays ..
172  INTEGER ISEED( 4 )
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC dble, dcmplx, max, min
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  minmn = min( m, n )
190 *
191 * Quick return if possible
192 *
193  IF( minmn.EQ.0 ) THEN
194  result( 1 ) = zero
195  result( 2 ) = zero
196  result( 3 ) = zero
197  result( 4 ) = zero
198  RETURN
199  END IF
200 *
201 * Copy the last k rows of the factorization to the array Q
202 *
203  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
204  IF( k.GT.0 .AND. n.GT.k )
205  \$ CALL zlacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
206  \$ q( n-k+1, 1 ), lda )
207  IF( k.GT.1 )
208  \$ CALL zlacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
209  \$ q( n-k+2, n-k+1 ), lda )
210 *
211 * Generate the n-by-n matrix Q
212 *
213  srnamt = 'ZUNGRQ'
214  CALL zungrq( n, n, k, q, lda, tau( minmn-k+1 ), work, lwork,
215  \$ info )
216 *
217  DO 30 iside = 1, 2
218  IF( iside.EQ.1 ) THEN
219  side = 'L'
220  mc = n
221  nc = m
222  ELSE
223  side = 'R'
224  mc = m
225  nc = n
226  END IF
227 *
228 * Generate MC by NC matrix C
229 *
230  DO 10 j = 1, nc
231  CALL zlarnv( 2, iseed, mc, c( 1, j ) )
232  10 CONTINUE
233  cnorm = zlange( '1', mc, nc, c, lda, rwork )
234  IF( cnorm.EQ.zero )
235  \$ cnorm = one
236 *
237  DO 20 itrans = 1, 2
238  IF( itrans.EQ.1 ) THEN
239  trans = 'N'
240  ELSE
241  trans = 'C'
242  END IF
243 *
244 * Copy C
245 *
246  CALL zlacpy( 'Full', mc, nc, c, lda, cc, lda )
247 *
248 * Apply Q or Q' to C
249 *
250  srnamt = 'ZUNMRQ'
251  IF( k.GT.0 )
252  \$ CALL zunmrq( side, trans, mc, nc, k, af( m-k+1, 1 ), lda,
253  \$ tau( minmn-k+1 ), cc, lda, work, lwork,
254  \$ info )
255 *
256 * Form explicit product and subtract
257 *
258  IF( lsame( side, 'L' ) ) THEN
259  CALL zgemm( trans, 'No transpose', mc, nc, mc,
260  \$ dcmplx( -one ), q, lda, c, lda,
261  \$ dcmplx( one ), cc, lda )
262  ELSE
263  CALL zgemm( 'No transpose', trans, mc, nc, nc,
264  \$ dcmplx( -one ), c, lda, q, lda,
265  \$ dcmplx( one ), cc, lda )
266  END IF
267 *
268 * Compute error in the difference
269 *
270  resid = zlange( '1', mc, nc, cc, lda, rwork )
271  result( ( iside-1 )*2+itrans ) = resid /
272  \$ ( dble( max( 1, n ) )*cnorm*eps )
273 *
274  20 CONTINUE
275  30 CONTINUE
276 *
277  RETURN
278 *
279 * End of ZRQT03
280 *
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 zungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGRQ
Definition: zungrq.f:128
subroutine zunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRQ
Definition: zunmrq.f:167
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