DSYCON(3)                  MathKeisan LAPACK routine                 DSYCON(3)



NAME
       DSYCON  -  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

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 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.

       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, 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                       DSYCON(3)