---
name: "spocon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/spocon/3lapack"
---

# spocon(3lapack)

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

## 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

  \= '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 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