--- rpl/lapack/lapack/dpocon.f 2010/08/07 13:22:23 1.5 +++ rpl/lapack/lapack/dpocon.f 2023/08/07 08:39:03 1.18 @@ -1,12 +1,127 @@ +*> \brief \b DPOCON +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DPOCON + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, +* INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, N +* DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION A( LDA, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPOCON estimates the reciprocal of the condition number (in the +*> 1-norm) of a real symmetric positive definite matrix using the +*> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. +*> +*> 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 DOUBLE PRECISION array, dimension (LDA,N) +*> The triangular factor U or L from the Cholesky factorization +*> A = U**T*U or A = L*L**T, as computed by DPOTRF. +*> \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 symmetric 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 DOUBLE PRECISION array, dimension (3*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER 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 doublePOcomputational +* +* ===================================================================== SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, $ 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 DLACN2 in place of DLACON, 5 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER UPLO @@ -18,49 +133,6 @@ DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DPOCON estimates the reciprocal of the condition number (in the -* 1-norm) of a real symmetric positive definite matrix using the -* Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. -* -* 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) DOUBLE PRECISION array, dimension (LDA,N) -* The triangular factor U or L from the Cholesky factorization -* A = U**T*U or A = L*L**T, as computed by DPOTRF. -* -* 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 symmetric 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) DOUBLE PRECISION array, dimension (3*N) -* -* IWORK (workspace) INTEGER array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* * ===================================================================== * * .. Parameters .. @@ -129,7 +201,7 @@ IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * -* Multiply by inv(U'). +* Multiply by inv(U**T). * CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, $ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) @@ -147,7 +219,7 @@ $ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * -* Multiply by inv(L'). +* Multiply by inv(L**T). * CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A, $ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )