NAME

DPOCON - estimate 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

  —  LAPACK version 2.0  —  08 October 1994