DSPCON(3)                  MathKeisan LAPACK routine                 DSPCON(3)



NAME
       DSPCON  -  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 triangu-
               lar, 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 structure 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  matrix  A,  com-
               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti-
               mate 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



 LAPACK routine (version 3.1)    November 2006                       DSPCON(3)