DPOCON(3)

NAME
DPOCON - 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

SYNOPSIS

SUBROUTINE DPOCON(
    UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER
    UPLO

INTEGER
    INFO, LDA, N

DOUBLE
    PRECISION ANORM, RCOND

INTEGER
    IWORK( * )

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