SYNOPSIS

SUBROUTINE DSYCON(

UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, LDA, N

    

DOUBLE PRECISION ANORM, RCOND

    

INTEGER IPIV( * ), IWORK( * )

    

DOUBLE PRECISION A( LDA, * ), WORK( * )

PURPOSE

DSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF. 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

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.

N (input) INTEGER

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

A (input) DOUBLE PRECISION array, dimension (LDA,N)

The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.

LDA (input) INTEGER

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

IPIV (input) INTEGER array, dimension (N)

Details of the interchanges and the block structure of D as determined by DSYTRF.

ANORM (input) DOUBLE PRECISION

The 1-norm of the original 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 (2*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