LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zgsvts3()

subroutine zgsvts3 ( integer m,
integer p,
integer n,
complex*16, dimension( lda, * ) a,
complex*16, dimension( lda, * ) af,
integer lda,
complex*16, dimension( ldb, * ) b,
complex*16, dimension( ldb, * ) bf,
integer ldb,
complex*16, dimension( ldu, * ) u,
integer ldu,
complex*16, dimension( ldv, * ) v,
integer ldv,
complex*16, dimension( ldq, * ) q,
integer ldq,
double precision, dimension( * ) alpha,
double precision, dimension( * ) beta,
complex*16, dimension( ldr, * ) r,
integer ldr,
integer, dimension( * ) iwork,
complex*16, dimension( lwork ) work,
integer lwork,
double precision, dimension( * ) rwork,
double precision, dimension( 6 ) result )

ZGSVTS3

Purpose:
!>
!> ZGSVTS3 tests ZGGSVD3, which computes the GSVD of an M-by-N matrix A
!> and a P-by-N matrix B:
!>              U'*A*Q = D1*R and V'*B*Q = D2*R.
!>
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 COMPLEX*16 array, dimension (LDA,M)
!>          The M-by-N matrix A.
!>
[out]AF
!>          AF is COMPLEX*16 array, dimension (LDA,N)
!>          Details of the GSVD of A and B, as returned by ZGGSVD3,
!>          see ZGGSVD3 for further details.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the arrays A and AF.
!>          LDA >= max( 1,M ).
!>
[in]B
!>          B is COMPLEX*16 array, dimension (LDB,P)
!>          On entry, the P-by-N matrix B.
!>
[out]BF
!>          BF is COMPLEX*16 array, dimension (LDB,N)
!>          Details of the GSVD of A and B, as returned by ZGGSVD3,
!>          see ZGGSVD3 for further details.
!>
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of the arrays B and BF.
!>          LDB >= max(1,P).
!>
[out]U
!>          U is COMPLEX*16 array, dimension(LDU,M)
!>          The M by M unitary matrix U.
!>
[in]LDU
!>          LDU is INTEGER
!>          The leading dimension of the array U. LDU >= max(1,M).
!>
[out]V
!>          V is COMPLEX*16 array, dimension(LDV,M)
!>          The P by P unitary matrix V.
!>
[in]LDV
!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= max(1,P).
!>
[out]Q
!>          Q is COMPLEX*16 array, dimension(LDQ,N)
!>          The N by N unitary matrix Q.
!>
[in]LDQ
!>          LDQ is INTEGER
!>          The leading dimension of the array Q. LDQ >= max(1,N).
!>
[out]ALPHA
!>          ALPHA is DOUBLE PRECISION array, dimension (N)
!>
[out]BETA
!>          BETA is DOUBLE PRECISION array, dimension (N)
!>
!>          The generalized singular value pairs of A and B, the
!>          ``diagonal'' matrices D1 and D2 are constructed from
!>          ALPHA and BETA, see subroutine ZGGSVD3 for details.
!>
[out]R
!>          R is COMPLEX*16 array, dimension(LDQ,N)
!>          The upper triangular matrix R.
!>
[in]LDR
!>          LDR is INTEGER
!>          The leading dimension of the array R. LDR >= max(1,N).
!>
[out]IWORK
!>          IWORK is INTEGER array, dimension (N)
!>
[out]WORK
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The dimension of the array WORK,
!>          LWORK >= max(M,P,N)*max(M,P,N).
!>
[out]RWORK
!>          RWORK is DOUBLE PRECISION array, dimension (max(M,P,N))
!>
[out]RESULT
!>          RESULT is DOUBLE PRECISION array, dimension (6)
!>          The test ratios:
!>          RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
!>          RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
!>          RESULT(3) = norm( I - U'*U ) / ( M*ULP )
!>          RESULT(4) = norm( I - V'*V ) / ( P*ULP )
!>          RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
!>          RESULT(6) = 0        if ALPHA is in decreasing order;
!>                    = ULPINV   otherwise.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 206 of file zgsvts3.f.

209*
210* -- LAPACK test routine --
211* -- LAPACK is a software package provided by Univ. of Tennessee, --
212* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
213*
214* .. Scalar Arguments ..
215 INTEGER LDA, LDB, LDQ, LDR, LDU, LDV, LWORK, M, N, P
216* ..
217* .. Array Arguments ..
218 INTEGER IWORK( * )
219 DOUBLE PRECISION ALPHA( * ), BETA( * ), RESULT( 6 ), RWORK( * )
220 COMPLEX*16 A( LDA, * ), AF( LDA, * ), B( LDB, * ),
221 $ BF( LDB, * ), Q( LDQ, * ), R( LDR, * ),
222 $ U( LDU, * ), V( LDV, * ), WORK( LWORK )
223* ..
224*
225* =====================================================================
226*
227* .. Parameters ..
228 DOUBLE PRECISION ZERO, ONE
229 parameter( zero = 0.0d+0, one = 1.0d+0 )
230 COMPLEX*16 CZERO, CONE
231 parameter( czero = ( 0.0d+0, 0.0d+0 ),
232 $ cone = ( 1.0d+0, 0.0d+0 ) )
233* ..
234* .. Local Scalars ..
235 INTEGER I, INFO, J, K, L
236 DOUBLE PRECISION ANORM, BNORM, RESID, TEMP, ULP, ULPINV, UNFL
237* ..
238* .. External Functions ..
239 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
240 EXTERNAL dlamch, zlange, zlanhe
241* ..
242* .. External Subroutines ..
243 EXTERNAL dcopy, zgemm, zggsvd3, zherk, zlacpy, zlaset
244* ..
245* .. Intrinsic Functions ..
246 INTRINSIC dble, max, min
247* ..
248* .. Executable Statements ..
249*
250 ulp = dlamch( 'Precision' )
251 ulpinv = one / ulp
252 unfl = dlamch( 'Safe minimum' )
253*
254* Copy the matrix A to the array AF.
255*
256 CALL zlacpy( 'Full', m, n, a, lda, af, lda )
257 CALL zlacpy( 'Full', p, n, b, ldb, bf, ldb )
258*
259 anorm = max( zlange( '1', m, n, a, lda, rwork ), unfl )
260 bnorm = max( zlange( '1', p, n, b, ldb, rwork ), unfl )
261*
262* Factorize the matrices A and B in the arrays AF and BF.
263*
264 CALL zggsvd3( 'U', 'V', 'Q', m, n, p, k, l, af, lda, bf, ldb,
265 $ alpha, beta, u, ldu, v, ldv, q, ldq, work, lwork,
266 $ rwork, iwork, info )
267*
268* Copy R
269*
270 DO 20 i = 1, min( k+l, m )
271 DO 10 j = i, k + l
272 r( i, j ) = af( i, n-k-l+j )
273 10 CONTINUE
274 20 CONTINUE
275*
276 IF( m-k-l.LT.0 ) THEN
277 DO 40 i = m + 1, k + l
278 DO 30 j = i, k + l
279 r( i, j ) = bf( i-k, n-k-l+j )
280 30 CONTINUE
281 40 CONTINUE
282 END IF
283*
284* Compute A:= U'*A*Q - D1*R
285*
286 CALL zgemm( 'No transpose', 'No transpose', m, n, n, cone, a, lda,
287 $ q, ldq, czero, work, lda )
288*
289 CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m, cone,
290 $ u, ldu, work, lda, czero, a, lda )
291*
292 DO 60 i = 1, k
293 DO 50 j = i, k + l
294 a( i, n-k-l+j ) = a( i, n-k-l+j ) - r( i, j )
295 50 CONTINUE
296 60 CONTINUE
297*
298 DO 80 i = k + 1, min( k+l, m )
299 DO 70 j = i, k + l
300 a( i, n-k-l+j ) = a( i, n-k-l+j ) - alpha( i )*r( i, j )
301 70 CONTINUE
302 80 CONTINUE
303*
304* Compute norm( U'*A*Q - D1*R ) / ( MAX(1,M,N)*norm(A)*ULP ) .
305*
306 resid = zlange( '1', m, n, a, lda, rwork )
307 IF( anorm.GT.zero ) THEN
308 result( 1 ) = ( ( resid / dble( max( 1, m, n ) ) ) / anorm ) /
309 $ ulp
310 ELSE
311 result( 1 ) = zero
312 END IF
313*
314* Compute B := V'*B*Q - D2*R
315*
316 CALL zgemm( 'No transpose', 'No transpose', p, n, n, cone, b, ldb,
317 $ q, ldq, czero, work, ldb )
318*
319 CALL zgemm( 'Conjugate transpose', 'No transpose', p, n, p, cone,
320 $ v, ldv, work, ldb, czero, b, ldb )
321*
322 DO 100 i = 1, l
323 DO 90 j = i, l
324 b( i, n-l+j ) = b( i, n-l+j ) - beta( k+i )*r( k+i, k+j )
325 90 CONTINUE
326 100 CONTINUE
327*
328* Compute norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP ) .
329*
330 resid = zlange( '1', p, n, b, ldb, rwork )
331 IF( bnorm.GT.zero ) THEN
332 result( 2 ) = ( ( resid / dble( max( 1, p, n ) ) ) / bnorm ) /
333 $ ulp
334 ELSE
335 result( 2 ) = zero
336 END IF
337*
338* Compute I - U'*U
339*
340 CALL zlaset( 'Full', m, m, czero, cone, work, ldq )
341 CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, u, ldu,
342 $ one, work, ldu )
343*
344* Compute norm( I - U'*U ) / ( M * ULP ) .
345*
346 resid = zlanhe( '1', 'Upper', m, work, ldu, rwork )
347 result( 3 ) = ( resid / dble( max( 1, m ) ) ) / ulp
348*
349* Compute I - V'*V
350*
351 CALL zlaset( 'Full', p, p, czero, cone, work, ldv )
352 CALL zherk( 'Upper', 'Conjugate transpose', p, p, -one, v, ldv,
353 $ one, work, ldv )
354*
355* Compute norm( I - V'*V ) / ( P * ULP ) .
356*
357 resid = zlanhe( '1', 'Upper', p, work, ldv, rwork )
358 result( 4 ) = ( resid / dble( max( 1, p ) ) ) / ulp
359*
360* Compute I - Q'*Q
361*
362 CALL zlaset( 'Full', n, n, czero, cone, work, ldq )
363 CALL zherk( 'Upper', 'Conjugate transpose', n, n, -one, q, ldq,
364 $ one, work, ldq )
365*
366* Compute norm( I - Q'*Q ) / ( N * ULP ) .
367*
368 resid = zlanhe( '1', 'Upper', n, work, ldq, rwork )
369 result( 5 ) = ( resid / dble( max( 1, n ) ) ) / ulp
370*
371* Check sorting
372*
373 CALL dcopy( n, alpha, 1, rwork, 1 )
374 DO 110 i = k + 1, min( k+l, m )
375 j = iwork( i )
376 IF( i.NE.j ) THEN
377 temp = rwork( i )
378 rwork( i ) = rwork( j )
379 rwork( j ) = temp
380 END IF
381 110 CONTINUE
382*
383 result( 6 ) = zero
384 DO 120 i = k + 1, min( k+l, m ) - 1
385 IF( rwork( i ).LT.rwork( i+1 ) )
386 $ result( 6 ) = ulpinv
387 120 CONTINUE
388*
389 RETURN
390*
391* End of ZGSVTS3
392*
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
zggsvd3
subroutine zggsvd3(jobu, jobv, jobq, m, n, p, k, l, a, lda, b, ldb, alpha, beta, u, ldu, v, ldv, q, ldq, work, lwork, rwork, iwork, info)
ZGGSVD3 computes the singular value decomposition (SVD) for OTHER matrices
Definition zggsvd3.f:351
zherk
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
zlacpy
subroutine zlacpy(uplo, m, n, a, lda, b, ldb)
ZLACPY copies all or part of one two-dimensional array to another.
Definition zlacpy.f:101
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:113
zlanhe
double precision function zlanhe(norm, uplo, n, a, lda, work)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhe.f:122
zlaset
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:104
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