LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ srqt03()

subroutine srqt03 ( integer  m,
integer  n,
integer  k,
real, dimension( lda, * )  af,
real, dimension( lda, * )  c,
real, dimension( lda, * )  cc,
real, dimension( lda, * )  q,
integer  lda,
real, dimension( * )  tau,
real, dimension( lwork )  work,
integer  lwork,
real, dimension( * )  rwork,
real, dimension( * )  result 
)

SRQT03

Purpose:
 SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 SRQT03 compares the results of a call to SORMRQ with the results of
 forming Q explicitly by a call to SORGRQ and then performing matrix
 multiplication by a call to SGEMM.
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 REAL array, dimension (LDA,N)
          Details of the RQ factorization of an m-by-n matrix, as
          returned by SGERQF. See SGERQF for further details.
[out]C
          C is REAL array, dimension (LDA,N)
[out]CC
          CC is REAL array, dimension (LDA,N)
[out]Q
          Q is REAL array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.
[out]WORK
          WORK is REAL 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 REAL array, dimension (M)
[out]RESULT
          RESULT is REAL 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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 134 of file srqt03.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 REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
146 $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147 $ WORK( LWORK )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 REAL ZERO, ONE
154 parameter( zero = 0.0e0, one = 1.0e0 )
155 REAL ROGUE
156 parameter( rogue = -1.0e+10 )
157* ..
158* .. Local Scalars ..
159 CHARACTER SIDE, TRANS
160 INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC
161 REAL CNORM, EPS, RESID
162* ..
163* .. External Functions ..
164 LOGICAL LSAME
165 REAL SLAMCH, SLANGE
166 EXTERNAL lsame, slamch, slange
167* ..
168* .. External Subroutines ..
169 EXTERNAL sgemm, slacpy, slarnv, slaset, sorgrq, sormrq
170* ..
171* .. Local Arrays ..
172 INTEGER ISEED( 4 )
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC max, min, real
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 = slamch( '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 slaset( 'Full', n, n, rogue, rogue, q, lda )
204 IF( k.GT.0 .AND. n.GT.k )
205 $ CALL slacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
206 $ q( n-k+1, 1 ), lda )
207 IF( k.GT.1 )
208 $ CALL slacpy( '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 = 'SORGRQ'
214 CALL sorgrq( 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 slarnv( 2, iseed, mc, c( 1, j ) )
232 10 CONTINUE
233 cnorm = slange( '1', mc, nc, c, lda, rwork )
234 IF( cnorm.EQ.0.0 )
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 slacpy( 'Full', mc, nc, c, lda, cc, lda )
247*
248* Apply Q or Q' to C
249*
250 srnamt = 'SORMRQ'
251 IF( k.GT.0 )
252 $ CALL sormrq( 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 sgemm( trans, 'No transpose', mc, nc, mc, -one, q,
260 $ lda, c, lda, one, cc, lda )
261 ELSE
262 CALL sgemm( '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 = slange( '1', mc, nc, cc, lda, rwork )
269 result( ( iside-1 )*2+itrans ) = resid /
270 $ ( real( max( 1, n ) )*cnorm*eps )
271*
272 20 CONTINUE
273 30 CONTINUE
274*
275 RETURN
276*
277* End of SRQT03
278*
sgemm
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
slacpy
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
slange
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
slarnv
subroutine slarnv(idist, iseed, n, x)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition slarnv.f:97
slaset
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
sorgrq
subroutine sorgrq(m, n, k, a, lda, tau, work, lwork, info)
SORGRQ
Definition sorgrq.f:128
sormrq
subroutine sormrq(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMRQ
Definition sormrq.f:168
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