ZTPCON(3)                  MathKeisan LAPACK routine                 ZTPCON(3)



NAME
       ZTPCON  - the reciprocal of the condition number of a packed triangular
       matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS
       SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO )

           CHARACTER      DIAG, NORM, UPLO

           INTEGER        INFO, N

           DOUBLE         PRECISION RCOND

           DOUBLE         PRECISION RWORK( * )

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

PURPOSE
       ZTPCON estimates the reciprocal of the condition  number  of  a  packed
       triangular matrix A, in either the 1-norm or the infinity-norm.

       The norm of A is computed and an estimate is obtained for norm(inv(A)),
       then the reciprocal of the condition number is computed as
          RCOND = 1 / ( norm(A) * norm(inv(A)) ).


ARGUMENTS
       NORM    (input) CHARACTER*1
               Specifies whether the 1-norm condition number or the  infinity-
               norm condition number is required:
               = '1' or 'O':  1-norm;
               = 'I':         Infinity-norm.

       UPLO    (input) CHARACTER*1
               = 'U':  A is upper triangular;
               = 'L':  A is lower triangular.

       DIAG    (input) CHARACTER*1
               = 'N':  A is non-unit triangular;
               = 'U':  A is unit triangular.

       N       (input) INTEGER
               The order of the matrix A.  N >= 0.

       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
               The  upper or lower triangular matrix A, packed columnwise in a
               linear array.  The j-th column of A is stored in the  array  AP
               as  follows:  if  UPLO  =  'U',  AP(i + (j-1)*j/2) = A(i,j) for
               1<=i<=j; if UPLO = 'L', AP(i +  (j-1)*(2n-j)/2)  =  A(i,j)  for
               j<=i<=n.   If  DIAG  =  'U', the diagonal elements of A are not
               referenced and are assumed to be 1.

       RCOND   (output) DOUBLE PRECISION
               The reciprocal of the condition number of the  matrix  A,  com-
               puted as RCOND = 1/(norm(A) * norm(inv(A))).

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION 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                       ZTPCON(3)