LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ slqt03()

subroutine slqt03 ( 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 
)

SLQT03

Purpose:
 SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 SLQT03 compares the results of a call to SORMLQ with the results of
 forming Q explicitly by a call to SORGLQ 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 LQ factorization of an m-by-n matrix, as
          returned by SGELQF. See SGELQF 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 LQ 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 slqt03.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 ONE
154 parameter( 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, 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, sorglq, sormlq
170* ..
171* .. Local Arrays ..
172 INTEGER ISEED( 4 )
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC max, 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*
190* Copy the first k rows of the factorization to the array Q
191*
192 CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
193 CALL slacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
194*
195* Generate the n-by-n matrix Q
196*
197 srnamt = 'SORGLQ'
198 CALL sorglq( n, n, 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 = n
204 nc = m
205 ELSE
206 side = 'R'
207 mc = m
208 nc = n
209 END IF
210*
211* Generate MC by NC matrix C
212*
213 DO 10 j = 1, nc
214 CALL slarnv( 2, iseed, mc, c( 1, j ) )
215 10 CONTINUE
216 cnorm = slange( '1', mc, nc, c, lda, rwork )
217 IF( cnorm.EQ.0.0 )
218 $ cnorm = one
219*
220 DO 20 itrans = 1, 2
221 IF( itrans.EQ.1 ) THEN
222 trans = 'N'
223 ELSE
224 trans = 'T'
225 END IF
226*
227* Copy C
228*
229 CALL slacpy( 'Full', mc, nc, c, lda, cc, lda )
230*
231* Apply Q or Q' to C
232*
233 srnamt = 'SORMLQ'
234 CALL sormlq( 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 sgemm( trans, 'No transpose', mc, nc, mc, -one, q,
241 $ lda, c, lda, one, cc, lda )
242 ELSE
243 CALL sgemm( 'No transpose', trans, mc, nc, nc, -one, c,
244 $ lda, q, lda, one, cc, lda )
245 END IF
246*
247* Compute error in the difference
248*
249 resid = slange( '1', mc, nc, cc, lda, rwork )
250 result( ( iside-1 )*2+itrans ) = resid /
251 $ ( real( max( 1, n ) )*cnorm*eps )
252*
253 20 CONTINUE
254 30 CONTINUE
255*
256 RETURN
257*
258* End of SLQT03
259*
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
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
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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:127
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:168
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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