LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgrqts()

subroutine sgrqts ( integer  M,
integer  P,
integer  N,
real, dimension( lda, * )  A,
real, dimension( lda, * )  AF,
real, dimension( lda, * )  Q,
real, dimension( lda, * )  R,
integer  LDA,
real, dimension( * )  TAUA,
real, dimension( ldb, * )  B,
real, dimension( ldb, * )  BF,
real, dimension( ldb, * )  Z,
real, dimension( ldb, * )  T,
real, dimension( ldb, * )  BWK,
integer  LDB,
real, dimension( * )  TAUB,
real, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( 4 )  RESULT 
)

SGRQTS

Purpose:
 SGRQTS tests SGGRQF, which computes the GRQ factorization of an
 M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]P
          P is INTEGER
          The number of rows of the matrix B.  P >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The M-by-N matrix A.
[out]AF
          AF is REAL array, dimension (LDA,N)
          Details of the GRQ factorization of A and B, as returned
          by SGGRQF, see SGGRQF for further details.
[out]Q
          Q is REAL array, dimension (LDA,N)
          The N-by-N orthogonal matrix Q.
[out]R
          R is REAL array, dimension (LDA,MAX(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, R and Q.
          LDA >= max(M,N).
[out]TAUA
          TAUA is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGQRC.
[in]B
          B is REAL array, dimension (LDB,N)
          On entry, the P-by-N matrix A.
[out]BF
          BF is REAL array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by SGGRQF, see SGGRQF for further details.
[out]Z
          Z is REAL array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z.
[out]T
          T is REAL array, dimension (LDB,max(P,N))
[out]BWK
          BWK is REAL array, dimension (LDB,N)
[in]LDB
          LDB is INTEGER
          The leading dimension of the arrays B, BF, Z and T.
          LDB >= max(P,N).
[out]TAUB
          TAUB is REAL array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGRQF.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2.
[out]RWORK
          RWORK is REAL array, dimension (M)
[out]RESULT
          RESULT is REAL array, dimension (4)
          The test ratios:
            RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
            RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
            RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 175 of file sgrqts.f.

177 *
178 * -- LAPACK test routine --
179 * -- LAPACK is a software package provided by Univ. of Tennessee, --
180 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181 *
182 * .. Scalar Arguments ..
183  INTEGER LDA, LDB, LWORK, M, P, N
184 * ..
185 * .. Array Arguments ..
186  REAL A( LDA, * ), AF( LDA, * ), R( LDA, * ),
187  $ Q( LDA, * ),
188  $ B( LDB, * ), BF( LDB, * ), T( LDB, * ),
189  $ Z( LDB, * ), BWK( LDB, * ),
190  $ TAUA( * ), TAUB( * ),
191  $ RESULT( 4 ), RWORK( * ), WORK( LWORK )
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. Parameters ..
197  REAL ZERO, ONE
198  parameter( zero = 0.0e+0, one = 1.0e+0 )
199  REAL ROGUE
200  parameter( rogue = -1.0e+10 )
201 * ..
202 * .. Local Scalars ..
203  INTEGER INFO
204  REAL ANORM, BNORM, ULP, UNFL, RESID
205 * ..
206 * .. External Functions ..
207  REAL SLAMCH, SLANGE, SLANSY
208  EXTERNAL slamch, slange, slansy
209 * ..
210 * .. External Subroutines ..
211  EXTERNAL sgemm, sggrqf, slacpy, slaset, sorgqr,
212  $ sorgrq, ssyrk
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC max, min, real
216 * ..
217 * .. Executable Statements ..
218 *
219  ulp = slamch( 'Precision' )
220  unfl = slamch( 'Safe minimum' )
221 *
222 * Copy the matrix A to the array AF.
223 *
224  CALL slacpy( 'Full', m, n, a, lda, af, lda )
225  CALL slacpy( 'Full', p, n, b, ldb, bf, ldb )
226 *
227  anorm = max( slange( '1', m, n, a, lda, rwork ), unfl )
228  bnorm = max( slange( '1', p, n, b, ldb, rwork ), unfl )
229 *
230 * Factorize the matrices A and B in the arrays AF and BF.
231 *
232  CALL sggrqf( m, p, n, af, lda, taua, bf, ldb, taub, work,
233  $ lwork, info )
234 *
235 * Generate the N-by-N matrix Q
236 *
237  CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
238  IF( m.LE.n ) THEN
239  IF( m.GT.0 .AND. m.LT.n )
240  $ CALL slacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
241  IF( m.GT.1 )
242  $ CALL slacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
243  $ q( n-m+2, n-m+1 ), lda )
244  ELSE
245  IF( n.GT.1 )
246  $ CALL slacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
247  $ q( 2, 1 ), lda )
248  END IF
249  CALL sorgrq( n, n, min( m, n ), q, lda, taua, work, lwork, info )
250 *
251 * Generate the P-by-P matrix Z
252 *
253  CALL slaset( 'Full', p, p, rogue, rogue, z, ldb )
254  IF( p.GT.1 )
255  $ CALL slacpy( 'Lower', p-1, n, bf( 2,1 ), ldb, z( 2,1 ), ldb )
256  CALL sorgqr( p, p, min( p,n ), z, ldb, taub, work, lwork, info )
257 *
258 * Copy R
259 *
260  CALL slaset( 'Full', m, n, zero, zero, r, lda )
261  IF( m.LE.n )THEN
262  CALL slacpy( 'Upper', m, m, af( 1, n-m+1 ), lda, r( 1, n-m+1 ),
263  $ lda )
264  ELSE
265  CALL slacpy( 'Full', m-n, n, af, lda, r, lda )
266  CALL slacpy( 'Upper', n, n, af( m-n+1, 1 ), lda, r( m-n+1, 1 ),
267  $ lda )
268  END IF
269 *
270 * Copy T
271 *
272  CALL slaset( 'Full', p, n, zero, zero, t, ldb )
273  CALL slacpy( 'Upper', p, n, bf, ldb, t, ldb )
274 *
275 * Compute R - A*Q'
276 *
277  CALL sgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
278  $ lda, one, r, lda )
279 *
280 * Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) .
281 *
282  resid = slange( '1', m, n, r, lda, rwork )
283  IF( anorm.GT.zero ) THEN
284  result( 1 ) = ( ( resid / real(max(1,m,n) ) ) / anorm ) / ulp
285  ELSE
286  result( 1 ) = zero
287  END IF
288 *
289 * Compute T*Q - Z'*B
290 *
291  CALL sgemm( 'Transpose', 'No transpose', p, n, p, one, z, ldb, b,
292  $ ldb, zero, bwk, ldb )
293  CALL sgemm( 'No transpose', 'No transpose', p, n, n, one, t, ldb,
294  $ q, lda, -one, bwk, ldb )
295 *
296 * Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
297 *
298  resid = slange( '1', p, n, bwk, ldb, rwork )
299  IF( bnorm.GT.zero ) THEN
300  result( 2 ) = ( ( resid / real( max( 1,p,m ) ) )/bnorm ) / ulp
301  ELSE
302  result( 2 ) = zero
303  END IF
304 *
305 * Compute I - Q*Q'
306 *
307  CALL slaset( 'Full', n, n, zero, one, r, lda )
308  CALL ssyrk( 'Upper', 'No Transpose', n, n, -one, q, lda, one, r,
309  $ lda )
310 *
311 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
312 *
313  resid = slansy( '1', 'Upper', n, r, lda, rwork )
314  result( 3 ) = ( resid / real( max( 1,n ) ) ) / ulp
315 *
316 * Compute I - Z'*Z
317 *
318  CALL slaset( 'Full', p, p, zero, one, t, ldb )
319  CALL ssyrk( 'Upper', 'Transpose', p, p, -one, z, ldb, one, t,
320  $ ldb )
321 *
322 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
323 *
324  resid = slansy( '1', 'Upper', p, t, ldb, rwork )
325  result( 4 ) = ( resid / real( max( 1,p ) ) ) / ulp
326 *
327  RETURN
328 *
329 * End of SGRQTS
330 *
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
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 sorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGRQ
Definition: sorgrq.f:128
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:128
subroutine sggrqf(M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO)
SGGRQF
Definition: sggrqf.f:214
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
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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