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217 lines
5.5 KiB
217 lines
5.5 KiB
*> \brief \b SQRT12
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), S( * ), WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SQRT12 computes the singular values `svlues' of the upper trapezoid
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*> of A(1:M,1:N) and returns the ratio
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*>
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*> || s - svlues||/(||svlues||*eps*max(M,N))
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The M-by-N matrix A. Only the upper trapezoid is referenced.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A.
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*> \endverbatim
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*>
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*> \param[in] S
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*> \verbatim
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*> S is REAL array, dimension (min(M,N))
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*> The singular values of the matrix A.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
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*> max(M,N), M*N+2*MIN( M, N )+4*N).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), S( * ), WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, ISCL, J, MN
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REAL ANRM, BIGNUM, NRMSVL, SMLNUM
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* ..
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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANGE, SNRM2
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EXTERNAL SASUM, SLAMCH, SLANGE, SNRM2
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SBDSQR, SGEBD2, SLASCL, SLASET, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, REAL
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* ..
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* .. Local Arrays ..
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REAL DUMMY( 1 )
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* ..
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* .. Executable Statements ..
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*
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SQRT12 = ZERO
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*
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* Test that enough workspace is supplied
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*
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IF( LWORK.LT.MAX( M*N+4*MIN( M, N )+MAX( M, N ),
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$ M*N+2*MIN( M, N )+4*N) ) THEN
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CALL XERBLA( 'SQRT12', 7 )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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MN = MIN( M, N )
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IF( MN.LE.ZERO )
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$ RETURN
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*
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NRMSVL = SNRM2( MN, S, 1 )
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*
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* Copy upper triangle of A into work
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*
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CALL SLASET( 'Full', M, N, ZERO, ZERO, WORK, M )
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DO 20 J = 1, N
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DO 10 I = 1, MIN( J, M )
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WORK( ( J-1 )*M+I ) = A( I, J )
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10 CONTINUE
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20 CONTINUE
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*
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* Get machine parameters
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*
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SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
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BIGNUM = ONE / SMLNUM
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*
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* Scale work if max entry outside range [SMLNUM,BIGNUM]
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*
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ANRM = SLANGE( 'M', M, N, WORK, M, DUMMY )
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ISCL = 0
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IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
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*
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* Scale matrix norm up to SMLNUM
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*
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CALL SLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO )
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ISCL = 1
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ELSE IF( ANRM.GT.BIGNUM ) THEN
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*
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* Scale matrix norm down to BIGNUM
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*
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CALL SLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO )
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ISCL = 1
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END IF
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*
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IF( ANRM.NE.ZERO ) THEN
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*
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* Compute SVD of work
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*
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CALL SGEBD2( M, N, WORK, M, WORK( M*N+1 ), WORK( M*N+MN+1 ),
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$ WORK( M*N+2*MN+1 ), WORK( M*N+3*MN+1 ),
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$ WORK( M*N+4*MN+1 ), INFO )
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CALL SBDSQR( 'Upper', MN, 0, 0, 0, WORK( M*N+1 ),
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$ WORK( M*N+MN+1 ), DUMMY, MN, DUMMY, 1, DUMMY, MN,
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$ WORK( M*N+2*MN+1 ), INFO )
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*
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IF( ISCL.EQ.1 ) THEN
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IF( ANRM.GT.BIGNUM ) THEN
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CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1,
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$ WORK( M*N+1 ), MN, INFO )
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END IF
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IF( ANRM.LT.SMLNUM ) THEN
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CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1,
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$ WORK( M*N+1 ), MN, INFO )
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END IF
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END IF
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*
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ELSE
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*
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DO 30 I = 1, MN
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WORK( M*N+I ) = ZERO
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30 CONTINUE
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END IF
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*
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* Compare s and singular values of work
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*
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CALL SAXPY( MN, -ONE, S, 1, WORK( M*N+1 ), 1 )
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SQRT12 = SASUM( MN, WORK( M*N+1 ), 1 ) /
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$ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
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IF( NRMSVL.NE.ZERO )
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$ SQRT12 = SQRT12 / NRMSVL
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*
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RETURN
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*
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* End of SQRT12
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*
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END
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