dspcon(3)

NAME

DSPCON - estimate the reciprocal of the condition number

(in the 1-norm) of a real symmetric packed matrix A using the

factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF

SYNOPSIS

SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND,  WORK,
IWORK, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, N
    DOUBLE         PRECISION ANORM, RCOND
    INTEGER        IPIV( * ), IWORK( * )
    DOUBLE         PRECISION AP( * ), WORK( * )

PURPOSE

DSPCON estimates the reciprocal of the condition number

(in the 1-norm) of a real symmetric packed matrix A using the

factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF.

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.

AP (input) DOUBLE PRECISION array, dimension

(N*(N+1)/2)

The block diagonal matrix D and the multipliers

used to obtain the factor U or L as computed by DSPTRF, stored as

a packed triangular matrix.

IPIV (input) INTEGER array, dimension (N)

Details of the interchanges and the block struc

ture of D as determined by DSPTRF.

ANORM (input) DOUBLE PRECISION

The 1-norm of the original matrix A.

RCOND (output) DOUBLE PRECISION

The reciprocal of the condition number of the ma

trix 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 ille

gal value

LAPACK version 3.0 15 June 2000

DSPCON(3)