LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dqlt03()

 subroutine dqlt03 ( 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 )

DQLT03

Purpose:
``` DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

DQLT03 compares the results of a call to DORMQL with the results of
forming Q explicitly by a call to DORGQL 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 QL factorization of an m-by-n matrix, as returned by DGEQLF. See SGEQLF 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 QL 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 )```

Definition at line 134 of file dqlt03.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 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
146 \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147 \$ WORK( LWORK )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 DOUBLE PRECISION ZERO, ONE
154 parameter( zero = 0.0d0, one = 1.0d0 )
155 DOUBLE PRECISION ROGUE
156 parameter( rogue = -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, DLANGE
166 EXTERNAL lsame, dlamch, dlange
167* ..
168* .. External Subroutines ..
169 EXTERNAL dgemm, dlacpy, dlarnv, dlaset, dorgql, dormql
170* ..
171* .. Local Arrays ..
172 INTEGER ISEED( 4 )
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC dble, 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 columns of the factorization to the array Q
202*
203 CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
204 IF( k.GT.0 .AND. m.GT.k )
205 \$ CALL dlacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
206 \$ q( 1, m-k+1 ), lda )
207 IF( k.GT.1 )
208 \$ CALL dlacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
209 \$ q( m-k+1, m-k+2 ), lda )
210*
211* Generate the m-by-m matrix Q
212*
213 srnamt = 'DORGQL'
214 CALL dorgql( m, m, 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 = m
221 nc = n
222 ELSE
223 side = 'R'
224 mc = n
225 nc = m
226 END IF
227*
228* Generate MC by NC matrix C
229*
230 DO 10 j = 1, nc
231 CALL dlarnv( 2, iseed, mc, c( 1, j ) )
232 10 CONTINUE
233 cnorm = dlange( '1', mc, nc, c, lda, rwork )
234 IF( cnorm.EQ.0.0d0 )
235 \$ cnorm = one
236*
237 DO 20 itrans = 1, 2
238 IF( itrans.EQ.1 ) THEN
239 trans = 'N'
240 ELSE
241 trans = 'T'
242 END IF
243*
244* Copy C
245*
246 CALL dlacpy( 'Full', mc, nc, c, lda, cc, lda )
247*
248* Apply Q or Q' to C
249*
250 srnamt = 'DORMQL'
251 IF( k.GT.0 )
252 \$ CALL dormql( side, trans, mc, nc, k, af( 1, n-k+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 dgemm( trans, 'No transpose', mc, nc, mc, -one, q,
260 \$ lda, c, lda, one, cc, lda )
261 ELSE
262 CALL dgemm( 'No transpose', trans, mc, nc, nc, -one, c,
263 \$ lda, q, lda, one, cc, lda )
264 END IF
265*
266* Compute error in the difference
267*
268 resid = dlange( '1', mc, nc, cc, lda, rwork )
269 result( ( iside-1 )*2+itrans ) = resid /
270 \$ ( dble( max( 1, m ) )*cnorm*eps )
271*
272 20 CONTINUE
273 30 CONTINUE
274*
275 RETURN
276*
277* End of DQLT03
278*
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
subroutine dlacpy(uplo, m, n, a, lda, b, ldb)
DLACPY copies all or part of one two-dimensional array to another.
Definition dlacpy.f:103
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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:114
subroutine dlarnv(idist, iseed, n, x)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition dlarnv.f:97
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:110
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine dorgql(m, n, k, a, lda, tau, work, lwork, info)
DORGQL
Definition dorgql.f:128
subroutine dormql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
Definition dormql.f:167
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