# spocon (l) - Linux Manuals

## NAME

SPOCON - 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 SPOTRF

## SYNOPSIS

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

CHARACTER UPLO

INTEGER INFO, LDA, N

REAL ANORM, RCOND

INTEGER IWORK( * )

REAL A( LDA, * ), WORK( * )

## PURPOSE

SPOCON 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 SPOTRF. 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
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) REAL 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 SPOTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM (input) REAL
The 1-norm (or infinity-norm) of the symmetric matrix A.
RCOND (output) REAL
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) REAL 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