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Updated: June 2017
 
 

cptcon (3p)

Name

cptcon - 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 CPTTRF

Synopsis

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

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

SUBROUTINE CPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




C INTERFACE
#include <sunperf.h>

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

void cptcon_64(long n, float *d, complex *e, float anorm, float *rcond,
long *info);

Description

Oracle Solaris Studio Performance Library                           cptcon(3P)



NAME
       cptcon - 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 CPTTRF


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

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

       SUBROUTINE CPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO)

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




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

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

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

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




   C INTERFACE
       #include <sunperf.h>

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

       void cptcon_64(long n, float *d, complex *e, float anorm, float *rcond,
                 long *info);



PURPOSE
       cptcon  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 CPTTRF.

       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 CPTTRF.


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


       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                        cptcon(3P)