--- rpl/lapack/lapack/zpocon.f 2010/08/06 15:32:48 1.4 +++ rpl/lapack/lapack/zpocon.f 2023/08/07 08:39:33 1.18 @@ -1,12 +1,127 @@ +*> \brief \b ZPOCON +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZPOCON + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, +* INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, N +* DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. +* DOUBLE PRECISION RWORK( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZPOCON estimates the reciprocal of the condition number (in the +*> 1-norm) of a complex Hermitian positive definite matrix using the +*> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. +*> +*> An estimate is obtained for norm(inv(A)), and the reciprocal of the +*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The triangular factor U or L from the Cholesky factorization +*> A = U**H*U or A = L*L**H, as computed by ZPOTRF. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> The 1-norm (or infinity-norm) of the Hermitian matrix A. +*> \endverbatim +*> +*> \param[out] RCOND +*> \verbatim +*> RCOND is DOUBLE PRECISION +*> The reciprocal of the condition number of the matrix A, +*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an +*> estimate of the 1-norm of inv(A) computed in this routine. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup complex16POcomputational +* +* ===================================================================== SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, $ INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 -* -* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER UPLO @@ -18,49 +133,6 @@ COMPLEX*16 A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZPOCON estimates the reciprocal of the condition number (in the -* 1-norm) of a complex Hermitian positive definite matrix using the -* Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. -* -* An estimate is obtained for norm(inv(A)), and the reciprocal of the -* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* A (input) COMPLEX*16 array, dimension (LDA,N) -* The triangular factor U or L from the Cholesky factorization -* A = U**H*U or A = L*L**H, as computed by ZPOTRF. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* ANORM (input) DOUBLE PRECISION -* The 1-norm (or infinity-norm) of the Hermitian matrix A. -* -* RCOND (output) DOUBLE PRECISION -* The reciprocal of the condition number of the matrix A, -* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an -* estimate of the 1-norm of inv(A) computed in this routine. -* -* WORK (workspace) COMPLEX*16 array, dimension (2*N) -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* * ===================================================================== * * .. Parameters .. @@ -136,7 +208,7 @@ IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * -* Multiply by inv(U'). +* Multiply by inv(U**H). * CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit', $ NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO ) @@ -154,7 +226,7 @@ $ A, LDA, WORK, SCALEL, RWORK, INFO ) NORMIN = 'Y' * -* Multiply by inv(L'). +* Multiply by inv(L**H). * CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit', $ NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )