sptcon (3p)

Name

sptcon - 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 SPTTRF

Synopsis

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

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

SUBROUTINE SPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




C INTERFACE
#include <sunperf.h>

void  sptcon(int  n, float *d, float *e, float anorm, float *rcond, int
*info);

void sptcon_64(long n, float *d, float *e, float anorm,  float  *rcond,
long *info);

Description

Oracle Solaris Studio Performance Library                           sptcon(3P)



NAME
       sptcon - 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 SPTTRF


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

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

       SUBROUTINE SPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




   C INTERFACE
       #include <sunperf.h>

       void  sptcon(int  n, float *d, float *e, float anorm, float *rcond, int
                 *info);

       void sptcon_64(long n, float *d, float *e, float anorm,  float  *rcond,
                 long *info);



PURPOSE
       sptcon  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 SPTTRF.

       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 SPTTRF.


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


       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                        sptcon(3P)