SYNOPSIS

SUBROUTINE SGECON(

NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )

    

CHARACTER NORM

    

INTEGER INFO, LDA, N

    

REAL ANORM, RCOND

    

INTEGER IWORK( * )

    

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

PURPOSE

SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as

   RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

NORM (input) CHARACTER*1

Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input) REAL array, dimension (LDA,N)

The factors L and U from the factorization A = P*L*U as computed by SGETRF.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

ANORM (input) REAL

If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.

RCOND (output) REAL

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK (workspace) REAL array, dimension (4*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