LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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