cptcon(3P) Sun Performance Library cptcon(3P)NAMEcptcon - 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);
PURPOSEcptcon 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.
6 Mar 2009 cptcon(3P)
