--- rpl/lapack/lapack/zlaqsp.f 2010/12/21 13:53:51 1.7 +++ rpl/lapack/lapack/zlaqsp.f 2011/11/21 20:43:16 1.8 @@ -1,9 +1,135 @@ +*> \brief \b ZLAQSP +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLAQSP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) +* +* .. Scalar Arguments .. +* CHARACTER EQUED, UPLO +* INTEGER N +* DOUBLE PRECISION AMAX, SCOND +* .. +* .. Array Arguments .. +* DOUBLE PRECISION S( * ) +* COMPLEX*16 AP( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLAQSP 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 COMPLEX*16 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 = 'Y': Equilibration was done, i.e., A has been replaced by +*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. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER EQUED, UPLO @@ -15,60 +141,6 @@ COMPLEX*16 AP( * ) * .. * -* Purpose -* ======= -* -* ZLAQSP equilibrates a symmetric matrix A using the scaling factors -* in the vector S. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* Specifies whether the upper or lower triangular part of the -* symmetric matrix A is stored. -* = 'U': Upper triangular -* = 'L': Lower triangular -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* AP (input/output) COMPLEX*16 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. -* -* S (input) DOUBLE PRECISION array, dimension (N) -* The scale factors for A. -* -* SCOND (input) DOUBLE PRECISION -* Ratio of the smallest S(i) to the largest S(i). -* -* AMAX (input) DOUBLE PRECISION -* Absolute value of largest matrix entry. -* -* EQUED (output) 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). -* -* Internal Parameters -* =================== -* -* 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. -* * ===================================================================== * * .. Parameters ..