dptcon (3p)

Name

dptcon - norm) of a real symmetric positive definite tridiagonal matrix using the fac- torization A = L*D*L**T or A = U**T*D*U computed by DPTTRF

Synopsis

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

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

SUBROUTINE DPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




C INTERFACE
#include <sunperf.h>

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

void dptcon_64(long n, double  *d,  double  *e,  double  anorm,  double
*rcond, long *info);

Description

Oracle Solaris Studio Performance Library                           dptcon(3P)



NAME
       dptcon - compute the reciprocal of the condition number (in the 1-norm)
       of a real symmetric positive definite tridiagonal matrix using the fac-
       torization A = L*D*L**T or A = U**T*D*U computed by DPTTRF


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

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

       SUBROUTINE DPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




   C INTERFACE
       #include <sunperf.h>

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

       void dptcon_64(long n, double  *d,  double  *e,  double  anorm,  double
                 *rcond, long *info);



PURPOSE
       dptcon  computes the reciprocal of the condition number (in the 1-norm)
       of a real symmetric positive definite tridiagonal matrix using the fac-
       torization A = L*D*L**T or A = U**T*D*U computed by DPTTRF.

       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 DPTTRF.


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


       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)
                 dimension(N)

       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                        dptcon(3P)