LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ crqt03()

subroutine crqt03 ( integer  M,
integer  N,
integer  K,
complex, dimension( lda, * )  AF,
complex, dimension( lda, * )  C,
complex, dimension( lda, * )  CC,
complex, dimension( lda, * )  Q,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( * )  RESULT 
)

CRQT03

Purpose:
 CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 CRQT03 compares the results of a call to CUNMRQ with the results of
 forming Q explicitly by a call to CUNGRQ and then performing matrix
 multiplication by a call to CGEMM.
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 COMPLEX array, dimension (LDA,N)
          Details of the RQ factorization of an m-by-n matrix, as
          returned by CGERQF. See CGERQF for further details.
[out]C
          C is COMPLEX array, dimension (LDA,N)
[out]CC
          CC is COMPLEX array, dimension (LDA,N)
[out]Q
          Q is COMPLEX array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.
[out]WORK
          WORK is COMPLEX 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.
Date
December 2016

Definition at line 138 of file crqt03.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  REAL result( * ), rwork( * )
149  COMPLEX af( lda, * ), c( lda, * ), cc( lda, * ),
150  $ q( lda, * ), tau( * ), work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  REAL zero, one
157  parameter( zero = 0.0e+0, one = 1.0e+0 )
158  COMPLEX rogue
159  parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
160 * ..
161 * .. Local Scalars ..
162  CHARACTER side, trans
163  INTEGER info, iside, itrans, j, mc, minmn, nc
164  REAL cnorm, eps, resid
165 * ..
166 * .. External Functions ..
167  LOGICAL lsame
168  REAL clange, slamch
169  EXTERNAL lsame, clange, slamch
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL cgemm, clacpy, clarnv, claset, cungrq, cunmrq
173 * ..
174 * .. Local Arrays ..
175  INTEGER iseed( 4 )
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC cmplx, max, min, real
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 = slamch( 'Epsilon' )
192  minmn = min( m, n )
193 *
194 * Quick return if possible
195 *
196  IF( minmn.EQ.0 ) THEN
197  result( 1 ) = zero
198  result( 2 ) = zero
199  result( 3 ) = zero
200  result( 4 ) = zero
201  RETURN
202  END IF
203 *
204 * Copy the last k rows of the factorization to the array Q
205 *
206  CALL claset( 'Full', n, n, rogue, rogue, q, lda )
207  IF( k.GT.0 .AND. n.GT.k )
208  $ CALL clacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
209  $ q( n-k+1, 1 ), lda )
210  IF( k.GT.1 )
211  $ CALL clacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
212  $ q( n-k+2, n-k+1 ), lda )
213 *
214 * Generate the n-by-n matrix Q
215 *
216  srnamt = 'CUNGRQ'
217  CALL cungrq( n, n, k, q, lda, tau( minmn-k+1 ), work, lwork,
218  $ info )
219 *
220  DO 30 iside = 1, 2
221  IF( iside.EQ.1 ) THEN
222  side = 'L'
223  mc = n
224  nc = m
225  ELSE
226  side = 'R'
227  mc = m
228  nc = n
229  END IF
230 *
231 * Generate MC by NC matrix C
232 *
233  DO 10 j = 1, nc
234  CALL clarnv( 2, iseed, mc, c( 1, j ) )
235  10 CONTINUE
236  cnorm = clange( '1', mc, nc, c, lda, rwork )
237  IF( cnorm.EQ.zero )
238  $ cnorm = one
239 *
240  DO 20 itrans = 1, 2
241  IF( itrans.EQ.1 ) THEN
242  trans = 'N'
243  ELSE
244  trans = 'C'
245  END IF
246 *
247 * Copy C
248 *
249  CALL clacpy( 'Full', mc, nc, c, lda, cc, lda )
250 *
251 * Apply Q or Q' to C
252 *
253  srnamt = 'CUNMRQ'
254  IF( k.GT.0 )
255  $ CALL cunmrq( side, trans, mc, nc, k, af( m-k+1, 1 ), lda,
256  $ tau( minmn-k+1 ), cc, lda, work, lwork,
257  $ info )
258 *
259 * Form explicit product and subtract
260 *
261  IF( lsame( side, 'L' ) ) THEN
262  CALL cgemm( trans, 'No transpose', mc, nc, mc,
263  $ cmplx( -one ), q, lda, c, lda, cmplx( one ),
264  $ cc, lda )
265  ELSE
266  CALL cgemm( 'No transpose', trans, mc, nc, nc,
267  $ cmplx( -one ), c, lda, q, lda, cmplx( one ),
268  $ cc, lda )
269  END IF
270 *
271 * Compute error in the difference
272 *
273  resid = clange( '1', mc, nc, cc, lda, rwork )
274  result( ( iside-1 )*2+itrans ) = resid /
275  $ ( REAL( MAX( 1, N ) )*cnorm*eps )
276 *
277  20 CONTINUE
278  30 CONTINUE
279 *
280  RETURN
281 *
282 * End of CRQT03
283 *
subroutine cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:130
subroutine cunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMRQ
Definition: cunmrq.f:170
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine clarnv(IDIST, ISEED, N, X)
CLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: clarnv.f:101
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
Here is the call graph for this function:
Here is the caller graph for this function: