You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
227 lines
5.7 KiB
227 lines
5.7 KiB
*> \brief \b ZQRT12
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK,
|
|
* RWORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION RWORK( * ), S( * )
|
|
* COMPLEX*16 A( LDA, * ), WORK( LWORK )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZQRT12 computes the singular values `svlues' of the upper trapezoid
|
|
*> of A(1:M,1:N) and returns the ratio
|
|
*>
|
|
*> || s - svlues||/(||svlues||*eps*max(M,N))
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is COMPLEX*16 array, dimension (LDA,N)
|
|
*> The M-by-N matrix A. Only the upper trapezoid is referenced.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] S
|
|
*> \verbatim
|
|
*> S is DOUBLE PRECISION array, dimension (min(M,N))
|
|
*> The singular values of the matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is COMPLEX*16 array, dimension (LWORK)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
|
|
*> max(M,N).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RWORK
|
|
*> \verbatim
|
|
*> RWORK is DOUBLE PRECISION array, dimension (2*min(M,N))
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup complex16_lin
|
|
*
|
|
* =====================================================================
|
|
DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK,
|
|
$ RWORK )
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION RWORK( * ), S( * )
|
|
COMPLEX*16 A( LDA, * ), WORK( LWORK )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, INFO, ISCL, J, MN
|
|
DOUBLE PRECISION ANRM, BIGNUM, NRMSVL, SMLNUM
|
|
* ..
|
|
* .. Local Arrays ..
|
|
DOUBLE PRECISION DUMMY( 1 )
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DASUM, DLAMCH, DNRM2, ZLANGE
|
|
EXTERNAL DASUM, DLAMCH, DNRM2, ZLANGE
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DAXPY, DBDSQR, DLASCL, XERBLA, ZGEBD2, ZLASCL,
|
|
$ ZLASET
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DBLE, DCMPLX, MAX, MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
ZQRT12 = ZERO
|
|
*
|
|
* Test that enough workspace is supplied
|
|
*
|
|
IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN
|
|
CALL XERBLA( 'ZQRT12', 7 )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
MN = MIN( M, N )
|
|
IF( MN.LE.ZERO )
|
|
$ RETURN
|
|
*
|
|
NRMSVL = DNRM2( MN, S, 1 )
|
|
*
|
|
* Copy upper triangle of A into work
|
|
*
|
|
CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK,
|
|
$ M )
|
|
DO 20 J = 1, N
|
|
DO 10 I = 1, MIN( J, M )
|
|
WORK( ( J-1 )*M+I ) = A( I, J )
|
|
10 CONTINUE
|
|
20 CONTINUE
|
|
*
|
|
* Get machine parameters
|
|
*
|
|
SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' )
|
|
BIGNUM = ONE / SMLNUM
|
|
*
|
|
* Scale work if max entry outside range [SMLNUM,BIGNUM]
|
|
*
|
|
ANRM = ZLANGE( 'M', M, N, WORK, M, DUMMY )
|
|
ISCL = 0
|
|
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
|
|
*
|
|
* Scale matrix norm up to SMLNUM
|
|
*
|
|
CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO )
|
|
ISCL = 1
|
|
ELSE IF( ANRM.GT.BIGNUM ) THEN
|
|
*
|
|
* Scale matrix norm down to BIGNUM
|
|
*
|
|
CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO )
|
|
ISCL = 1
|
|
END IF
|
|
*
|
|
IF( ANRM.NE.ZERO ) THEN
|
|
*
|
|
* Compute SVD of work
|
|
*
|
|
CALL ZGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ),
|
|
$ WORK( M*N+1 ), WORK( M*N+MN+1 ),
|
|
$ WORK( M*N+2*MN+1 ), INFO )
|
|
CALL DBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ),
|
|
$ DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ),
|
|
$ INFO )
|
|
*
|
|
IF( ISCL.EQ.1 ) THEN
|
|
IF( ANRM.GT.BIGNUM ) THEN
|
|
CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ),
|
|
$ MN, INFO )
|
|
END IF
|
|
IF( ANRM.LT.SMLNUM ) THEN
|
|
CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ),
|
|
$ MN, INFO )
|
|
END IF
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
DO 30 I = 1, MN
|
|
RWORK( I ) = ZERO
|
|
30 CONTINUE
|
|
END IF
|
|
*
|
|
* Compare s and singular values of work
|
|
*
|
|
CALL DAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 )
|
|
ZQRT12 = DASUM( MN, RWORK( 1 ), 1 ) /
|
|
$ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
|
|
IF( NRMSVL.NE.ZERO )
|
|
$ ZQRT12 = ZQRT12 / NRMSVL
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZQRT12
|
|
*
|
|
END
|
|
|