zptcon (3p)

Name

zptcon - norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF

Synopsis

SUBROUTINE ZPTCON(N, D, E, ANORM, RCOND, WORK, INFO)

DOUBLE COMPLEX E(*)
INTEGER N, INFO
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D(*), WORK(*)

SUBROUTINE ZPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

DOUBLE COMPLEX E(*)
INTEGER*8 N, INFO
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D(*), WORK(*)




F95 INTERFACE
SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO)

COMPLEX(8), DIMENSION(:) :: E
INTEGER :: N, INFO
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: D, WORK

SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

COMPLEX(8), DIMENSION(:) :: E
INTEGER(8) :: N, INFO
REAL(8) :: ANORM, RCOND
REAL(8), DIMENSION(:) :: D, WORK




C INTERFACE
#include <sunperf.h>

void  zptcon(int  n,  double *d, doublecomplex *e, double anorm, double
*rcond, int *info);

void zptcon_64(long n, double *d, doublecomplex *e, double anorm,  dou-
ble *rcond, long *info);

Description

Oracle Solaris Studio Performance Library                           zptcon(3P)



NAME
       zptcon - compute the reciprocal of the condition number (in the 1-norm)
       of a complex Hermitian positive definite tridiagonal matrix  using  the
       factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF


SYNOPSIS
       SUBROUTINE ZPTCON(N, D, E, ANORM, RCOND, WORK, INFO)

       DOUBLE COMPLEX E(*)
       INTEGER N, INFO
       DOUBLE PRECISION ANORM, RCOND
       DOUBLE PRECISION D(*), WORK(*)

       SUBROUTINE ZPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

       DOUBLE COMPLEX E(*)
       INTEGER*8 N, INFO
       DOUBLE PRECISION ANORM, RCOND
       DOUBLE PRECISION D(*), WORK(*)




   F95 INTERFACE
       SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO)

       COMPLEX(8), DIMENSION(:) :: E
       INTEGER :: N, INFO
       REAL(8) :: ANORM, RCOND
       REAL(8), DIMENSION(:) :: D, WORK

       SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

       COMPLEX(8), DIMENSION(:) :: E
       INTEGER(8) :: N, INFO
       REAL(8) :: ANORM, RCOND
       REAL(8), DIMENSION(:) :: D, WORK




   C INTERFACE
       #include <sunperf.h>

       void  zptcon(int  n,  double *d, doublecomplex *e, double anorm, double
                 *rcond, int *info);

       void zptcon_64(long n, double *d, doublecomplex *e, double anorm,  dou-
                 ble *rcond, long *info);



PURPOSE
       zptcon  computes the reciprocal of the condition number (in the 1-norm)
       of a complex Hermitian positive definite tridiagonal matrix  using  the
       factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF.

       Norm(inv(A))  is computed by a direct method, and the reciprocal of the
       condition number is computed as
                        RCOND = 1 / (ANORM * norm(inv(A))).


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


       D (input) The n diagonal elements of the diagonal  matrix  D  from  the
                 factorization of A, as computed by ZPTTRF.


       E (input) The (n-1) off-diagonal elements of the unit bidiagonal factor
                 U or L from the factorization of A, as computed by ZPTTRF.


       ANORM (input)
                 The 1-norm of the original matrix A.


       RCOND (output)
                 The reciprocal of the condition number of the matrix A,  com-
                 puted  as  RCOND  =  1/(ANORM  * AINVNM), where AINVNM is the
                 1-norm of inv(A) computed in this routine.


       WORK (workspace)


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       The method used is described in Nicholas J.  Higham,  "Efficient  Algo-
       rithms  for  Computing  the  Condition Number of a Tridiagonal Matrix",
       SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.




                                  7 Nov 2015                        zptcon(3P)