LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dqrt03()

 subroutine dqrt03 ( integer M, integer N, integer K, double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

DQRT03

Purpose:
DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

DQRT03 compares the results of a call to DORMQR with the results of
forming Q explicitly by a call to DORGQR and then performing matrix
multiplication by a call to DGEMM.
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 DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returned by DGEQRF. See DGEQRF for further details. [out] C C is DOUBLE PRECISION array, dimension (LDA,N) [out] CC CC is DOUBLE PRECISION array, dimension (LDA,N) [out] Q Q is DOUBLE PRECISION array, dimension (LDA,M) [in] LDA LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q. [in] TAU TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF. [out] WORK WORK is DOUBLE PRECISION 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 )
Date
December 2016

Definition at line 138 of file dqrt03.f.

138 *
139 * -- LAPACK test routine (version 3.7.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * December 2016
143 *
144 * .. Scalar Arguments ..
145  INTEGER k, lda, lwork, m, n
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION af( lda, * ), c( lda, * ), cc( lda, * ),
149  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
150  \$ work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION one
157  parameter( one = 1.0d0 )
158  DOUBLE PRECISION rogue
159  parameter( rogue = -1.0d+10 )
160 * ..
161 * .. Local Scalars ..
162  CHARACTER side, trans
163  INTEGER info, iside, itrans, j, mc, nc
164  DOUBLE PRECISION cnorm, eps, resid
165 * ..
166 * .. External Functions ..
167  LOGICAL lsame
168  DOUBLE PRECISION dlamch, dlange
169  EXTERNAL lsame, dlamch, dlange
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL dgemm, dlacpy, dlarnv, dlaset, dorgqr, dormqr
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC dble, max
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 *
193 * Copy the first k columns of the factorization to the array Q
194 *
195  CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
196  CALL dlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
197 *
198 * Generate the m-by-m matrix Q
199 *
200  srnamt = 'DORGQR'
201  CALL dorgqr( m, m, k, q, lda, tau, work, lwork, info )
202 *
203  DO 30 iside = 1, 2
204  IF( iside.EQ.1 ) THEN
205  side = 'L'
206  mc = m
207  nc = n
208  ELSE
209  side = 'R'
210  mc = n
211  nc = m
212  END IF
213 *
214 * Generate MC by NC matrix C
215 *
216  DO 10 j = 1, nc
217  CALL dlarnv( 2, iseed, mc, c( 1, j ) )
218  10 CONTINUE
219  cnorm = dlange( '1', mc, nc, c, lda, rwork )
220  IF( cnorm.EQ.0.0d0 )
221  \$ cnorm = one
222 *
223  DO 20 itrans = 1, 2
224  IF( itrans.EQ.1 ) THEN
225  trans = 'N'
226  ELSE
227  trans = 'T'
228  END IF
229 *
230 * Copy C
231 *
232  CALL dlacpy( 'Full', mc, nc, c, lda, cc, lda )
233 *
234 * Apply Q or Q' to C
235 *
236  srnamt = 'DORMQR'
237  CALL dormqr( side, trans, mc, nc, k, af, lda, tau, cc, lda,
238  \$ work, lwork, info )
239 *
240 * Form explicit product and subtract
241 *
242  IF( lsame( side, 'L' ) ) THEN
243  CALL dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
244  \$ lda, c, lda, one, cc, lda )
245  ELSE
246  CALL dgemm( 'No transpose', trans, mc, nc, nc, -one, c,
247  \$ lda, q, lda, one, cc, lda )
248  END IF
249 *
250 * Compute error in the difference
251 *
252  resid = dlange( '1', mc, nc, cc, lda, rwork )
253  result( ( iside-1 )*2+itrans ) = resid /
254  \$ ( dble( max( 1, m ) )*cnorm*eps )
255 *
256  20 CONTINUE
257  30 CONTINUE
258 *
259  RETURN
260 *
261 * End of DQRT03
262 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine dorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQR
Definition: dorgqr.f:130
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:169
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:99
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
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