LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 *
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 sormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRQ
Definition: sormrq.f:168
subroutine sorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGRQ
Definition: sorgrq.f:128
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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