ZSPCON(3)                  MathKeisan LAPACK routine                 ZSPCON(3)



NAME
       ZSPCON  -  the  reciprocal of the condition number (in the 1-norm) of a
       complex symmetric packed matrix A using the factorization A =  U*D*U**T
       or A = L*D*L**T computed by ZSPTRF

SYNOPSIS
       SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, N

           DOUBLE         PRECISION ANORM, RCOND

           INTEGER        IPIV( * )

           COMPLEX*16     AP( * ), WORK( * )

PURPOSE
       ZSPCON estimates the reciprocal of the condition number (in the 1-norm)
       of a complex symmetric packed matrix A  using  the  factorization  A  =
       U*D*U**T or A = L*D*L**T computed by ZSPTRF.

       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) COMPLEX*16 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 ZSPTRF, 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 ZSPTRF.

       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) COMPLEX*16 array, dimension (2*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                       ZSPCON(3)