numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| .. | |||
| lapack/TESTING/LIN/sqrt12.f | 5606B | -rw-r--r-- |
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*> \brief \b SQRT12 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * REAL A( LDA, * ), S( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SQRT12 computes the singular values `svlues' of the upper trapezoid *> of A(1:M,1:N) and returns the ratio *> *> || svlues - s ||/(||s||*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 REAL 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 REAL array, dimension (min(M,N)) *> The singular values of the matrix A. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) + *> max(M,N), M*N+2*MIN( M, N )+4*N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK ) * * -- 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 .. REAL A( LDA, * ), S( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, INFO, ISCL, J, MN REAL ANRM, BIGNUM, NRMSVL, SMLNUM * .. * .. External Functions .. REAL SASUM, SLAMCH, SLANGE, SNRM2 EXTERNAL SASUM, SLAMCH, SLANGE, SNRM2 * .. * .. External Subroutines .. EXTERNAL SAXPY, SBDSQR, SGEBD2, SLASCL, SLASET, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Local Arrays .. REAL DUMMY( 1 ) * .. * .. Executable Statements .. * SQRT12 = ZERO * * Test that enough workspace is supplied * IF( LWORK.LT.MAX( M*N+4*MIN( M, N )+MAX( M, N ), $ M*N+2*MIN( M, N )+4*N) ) THEN CALL XERBLA( 'SQRT12', 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 SLASET( 'Full', M, N, ZERO, ZERO, WORK, M ) DO J = 1, N DO I = 1, MIN( J, M ) WORK( ( J-1 )*M+I ) = A( I, J ) END DO END DO * * Get machine parameters * SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' ) BIGNUM = ONE / SMLNUM * * Scale work if max entry outside range [SMLNUM,BIGNUM] * ANRM = SLANGE( 'M', M, N, WORK, M, DUMMY ) ISCL = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN * * Scale matrix norm up to SMLNUM * CALL SLASCL( '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 SLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO ) ISCL = 1 END IF * IF( ANRM.NE.ZERO ) THEN * * Compute SVD of work * CALL SGEBD2( M, N, WORK, M, WORK( M*N+1 ), WORK( M*N+MN+1 ), $ WORK( M*N+2*MN+1 ), WORK( M*N+3*MN+1 ), $ WORK( M*N+4*MN+1 ), INFO ) CALL SBDSQR( 'Upper', MN, 0, 0, 0, WORK( M*N+1 ), $ WORK( M*N+MN+1 ), DUMMY, MN, DUMMY, 1, DUMMY, MN, $ WORK( M*N+2*MN+1 ), INFO ) * IF( ISCL.EQ.1 ) THEN IF( ANRM.GT.BIGNUM ) THEN CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, $ WORK( M*N+1 ), MN, INFO ) END IF IF( ANRM.LT.SMLNUM ) THEN CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, $ WORK( M*N+1 ), MN, INFO ) END IF END IF * ELSE * DO I = 1, MN WORK( M*N+I ) = ZERO END DO END IF * * Compare s and singular values of work * CALL SAXPY( MN, -ONE, S, 1, WORK( M*N+1 ), 1 ) SQRT12 = SASUM( MN, WORK( M*N+1 ), 1 ) / $ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) IF( NRMSVL.NE.ZERO ) $ SQRT12 = SQRT12 / NRMSVL * RETURN * * End of SQRT12 * END