208 SUBROUTINE zgsvts3( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
209 $ ldv, q, ldq, alpha, beta, r, ldr, iwork, work,
210 $ lwork, rwork, result )
218 INTEGER LDA, LDB, LDQ, LDR, LDU, LDV, LWORK, M, N, P
222 DOUBLE PRECISION ALPHA( * ), BETA( * ), RESULT( 6 ), RWORK( * )
223 COMPLEX*16 A( lda, * ), AF( lda, * ), B( ldb, * ),
224 $ bf( ldb, * ), q( ldq, * ), r( ldr, * ),
225 $ u( ldu, * ), v( ldv, * ), work( lwork )
231 DOUBLE PRECISION ZERO, ONE
232 parameter ( zero = 0.0d+0, one = 1.0d+0 )
233 COMPLEX*16 CZERO, CONE
234 parameter ( czero = ( 0.0d+0, 0.0d+0 ),
235 $ cone = ( 1.0d+0, 0.0d+0 ) )
238 INTEGER I, INFO, J, K, L
239 DOUBLE PRECISION ANORM, BNORM, RESID, TEMP, ULP, ULPINV, UNFL
242 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
243 EXTERNAL dlamch, zlange, zlanhe
249 INTRINSIC dble, max, min
253 ulp = dlamch(
'Precision' )
255 unfl = dlamch(
'Safe minimum' )
259 CALL zlacpy(
'Full', m, n, a, lda, af, lda )
260 CALL zlacpy(
'Full', p, n, b, ldb, bf, ldb )
262 anorm = max( zlange(
'1', m, n, a, lda, rwork ), unfl )
263 bnorm = max( zlange(
'1', p, n, b, ldb, rwork ), unfl )
267 CALL zggsvd3(
'U',
'V',
'Q', m, n, p, k, l, af, lda, bf, ldb,
268 $ alpha, beta, u, ldu, v, ldv, q, ldq, work, lwork,
269 $ rwork, iwork, info )
273 DO 20 i = 1, min( k+l, m )
275 r( i, j ) = af( i, n-k-l+j )
279 IF( m-k-l.LT.0 )
THEN
280 DO 40 i = m + 1, k + l
282 r( i, j ) = bf( i-k, n-k-l+j )
289 CALL zgemm(
'No transpose',
'No transpose', m, n, n, cone, a, lda,
290 $ q, ldq, czero, work, lda )
292 CALL zgemm(
'Conjugate transpose',
'No transpose', m, n, m, cone,
293 $ u, ldu, work, lda, czero, a, lda )
297 a( i, n-k-l+j ) = a( i, n-k-l+j ) - r( i, j )
301 DO 80 i = k + 1, min( k+l, m )
303 a( i, n-k-l+j ) = a( i, n-k-l+j ) - alpha( i )*r( i, j )
309 resid = zlange(
'1', m, n, a, lda, rwork )
310 IF( anorm.GT.zero )
THEN
311 result( 1 ) = ( ( resid / dble( max( 1, m, n ) ) ) / anorm ) /
319 CALL zgemm(
'No transpose',
'No transpose', p, n, n, cone, b, ldb,
320 $ q, ldq, czero, work, ldb )
322 CALL zgemm(
'Conjugate transpose',
'No transpose', p, n, p, cone,
323 $ v, ldv, work, ldb, czero, b, ldb )
327 b( i, n-l+j ) = b( i, n-l+j ) - beta( k+i )*r( k+i, k+j )
333 resid = zlange(
'1', p, n, b, ldb, rwork )
334 IF( bnorm.GT.zero )
THEN
335 result( 2 ) = ( ( resid / dble( max( 1, p, n ) ) ) / bnorm ) /
343 CALL zlaset(
'Full', m, m, czero, cone, work, ldq )
344 CALL zherk(
'Upper',
'Conjugate transpose', m, m, -one, u, ldu,
349 resid = zlanhe(
'1',
'Upper', m, work, ldu, rwork )
350 result( 3 ) = ( resid / dble( max( 1, m ) ) ) / ulp
354 CALL zlaset(
'Full', p, p, czero, cone, work, ldv )
355 CALL zherk(
'Upper',
'Conjugate transpose', p, p, -one, v, ldv,
360 resid = zlanhe(
'1',
'Upper', p, work, ldv, rwork )
361 result( 4 ) = ( resid / dble( max( 1, p ) ) ) / ulp
365 CALL zlaset(
'Full', n, n, czero, cone, work, ldq )
366 CALL zherk(
'Upper',
'Conjugate transpose', n, n, -one, q, ldq,
371 resid = zlanhe(
'1',
'Upper', n, work, ldq, rwork )
372 result( 5 ) = ( resid / dble( max( 1, n ) ) ) / ulp
376 CALL dcopy( n, alpha, 1, rwork, 1 )
377 DO 110 i = k + 1, min( k+l, m )
381 rwork( i ) = rwork( j )
387 DO 120 i = k + 1, min( k+l, m ) - 1
388 IF( rwork( i ).LT.rwork( i+1 ) )
389 $ result( 6 ) = ulpinv
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
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
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...
subroutine zgsvts3(M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V, LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK, LWORK, RWORK, RESULT)
ZGSVTS3
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK