numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/dlaqsp.f | 5719B | -rw-r--r-- |
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*> \brief \b DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAQSP + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsp.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsp.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsp.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) * * .. Scalar Arguments .. * CHARACTER EQUED, UPLO * INTEGER N * DOUBLE PRECISION AMAX, SCOND * .. * .. Array Arguments .. * DOUBLE PRECISION AP( * ), S( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAQSP equilibrates a symmetric matrix A using the scaling factors *> in the vector S. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the symmetric matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (N) *> The scale factors for A. *> \endverbatim *> *> \param[in] SCOND *> \verbatim *> SCOND is DOUBLE PRECISION *> Ratio of the smallest S(i) to the largest S(i). *> \endverbatim *> *> \param[in] AMAX *> \verbatim *> AMAX is DOUBLE PRECISION *> Absolute value of largest matrix entry. *> \endverbatim *> *> \param[out] EQUED *> \verbatim *> EQUED is CHARACTER*1 *> Specifies whether or not equilibration was done. *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. *> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup laqhp * * ===================================================================== SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER EQUED, UPLO INTEGER N DOUBLE PRECISION AMAX, SCOND * .. * .. Array Arguments .. DOUBLE PRECISION AP( * ), S( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, THRESH PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) * .. * .. Local Scalars .. INTEGER I, J, JC DOUBLE PRECISION CJ, LARGE, SMALL * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH EXTERNAL LSAME, DLAMCH * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN EQUED = 'N' RETURN END IF * * Initialize LARGE and SMALL. * SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) LARGE = ONE / SMALL * IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN * * No equilibration * EQUED = 'N' ELSE * * Replace A by diag(S) * A * diag(S). * IF( LSAME( UPLO, 'U' ) ) THEN * * Upper triangle of A is stored. * JC = 1 DO 20 J = 1, N CJ = S( J ) DO 10 I = 1, J AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 ) 10 CONTINUE JC = JC + J 20 CONTINUE ELSE * * Lower triangle of A is stored. * JC = 1 DO 40 J = 1, N CJ = S( J ) DO 30 I = J, N AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J ) 30 CONTINUE JC = JC + N - J + 1 40 CONTINUE END IF EQUED = 'Y' END IF * RETURN * * End of DLAQSP * END