169 lines
4.5 KiB
FortranFixed
169 lines
4.5 KiB
FortranFixed
DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK,
|
|
$ RWORK )
|
|
*
|
|
* -- LAPACK test routine (version 3.1) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION RWORK( * ), S( * )
|
|
COMPLEX*16 A( LDA, * ), WORK( LWORK )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* 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))
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* M (input) INTEGER
|
|
* The number of rows of the matrix A.
|
|
*
|
|
* N (input) INTEGER
|
|
* The number of columns of the matrix A.
|
|
*
|
|
* A (input) COMPLEX*16 array, dimension (LDA,N)
|
|
* The M-by-N matrix A. Only the upper trapezoid is referenced.
|
|
*
|
|
* LDA (input) INTEGER
|
|
* The leading dimension of the array A.
|
|
*
|
|
* S (input) DOUBLE PRECISION array, dimension (min(M,N))
|
|
* The singular values of the matrix A.
|
|
*
|
|
* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
|
|
*
|
|
* LWORK (input) INTEGER
|
|
* The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
|
|
* max(M,N).
|
|
*
|
|
* RWORK (workspace) DOUBLE PRECISION array, dimension (2*min(M,N))
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. 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, DLABAD, 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
|
|
CALL DLABAD( SMLNUM, BIGNUM )
|
|
*
|
|
* 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
|