LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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