LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sqrt03()

subroutine sqrt03 ( 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 
)

SQRT03

Purpose:
 SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 SQRT03 compares the results of a call to SORMQR with the results of
 forming Q explicitly by a call to SORGQR and then performing matrix
 multiplication by a call to SGEMM.
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 REAL array, dimension (LDA,N)
          Details of the QR factorization of an m-by-n matrix, as
          returned by SGEQRF. See SGEQRF 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,M)
[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 QR 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 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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 134 of file sqrt03.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, sorgqr, sormqr
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 columns of the factorization to the array Q
191 *
192  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
193  CALL slacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
194 *
195 * Generate the m-by-m matrix Q
196 *
197  srnamt = 'SORGQR'
198  CALL sorgqr( m, m, 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 = m
204  nc = n
205  ELSE
206  side = 'R'
207  mc = n
208  nc = m
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 = 'SORMQR'
234  CALL sormqr( 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, m ) )*cnorm*eps )
252 *
253  20 CONTINUE
254  30 CONTINUE
255 *
256  RETURN
257 *
258 * End of SQRT03
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 sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:128
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
Definition: sormqr.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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