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REAL FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
$ RWORK )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL RWORK( * ), S( * )
COMPLEX A( LDA, * ), WORK( LWORK )
* ..
*
* Purpose
* =======
*
* CQRT12 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 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) REAL array, dimension (min(M,N))
* The singular values of the matrix A.
*
* WORK (workspace) COMPLEX array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
* max(M,N).
*
* RWORK (workspace) REAL array, dimension (4*min(M,N))
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, ISCL, J, MN
REAL ANRM, BIGNUM, NRMSVL, SMLNUM
* ..
* .. Local Arrays ..
REAL DUMMY( 1 )
* ..
* .. External Functions ..
REAL CLANGE, SASUM, SLAMCH, SNRM2
EXTERNAL CLANGE, SASUM, SLAMCH, SNRM2
* ..
* .. External Subroutines ..
EXTERNAL CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLABAD,
$ SLASCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
CQRT12 = ZERO
*
* Test that enough workspace is supplied
*
IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN
CALL XERBLA( 'CQRT12', 7 )
RETURN
END IF
*
* Quick return if possible
*
MN = MIN( M, N )
IF( MN.LE.ZERO )
$ RETURN
*
NRMSVL = SNRM2( MN, S, 1 )
*
* Copy upper triangle of A into work
*
CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( 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 = SLAMCH( 'S' ) / SLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* Scale work if max entry outside range [SMLNUM,BIGNUM]
*
ANRM = CLANGE( 'M', M, N, WORK, M, DUMMY )
ISCL = 0
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
*
* Scale matrix norm up to SMLNUM
*
CALL CLASCL( '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 CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO )
ISCL = 1
END IF
*
IF( ANRM.NE.ZERO ) THEN
*
* Compute SVD of work
*
CALL CGEBD2( 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 SBDSQR( '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 SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ),
$ MN, INFO )
END IF
IF( ANRM.LT.SMLNUM ) THEN
CALL SLASCL( '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 SAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 )
CQRT12 = SASUM( MN, RWORK( 1 ), 1 ) /
$ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
IF( NRMSVL.NE.ZERO )
$ CQRT12 = CQRT12 / NRMSVL
*
RETURN
*
* End of CQRT12
*
END
|
