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# spocon

```
NAME
SPOCON - 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 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
= '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) REAL array, dimension (LDA,N)
The triangular factor U or L from the Cholesky fac-
torization 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) com-
puted 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
```