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, RWORK, INFO )

void cptcon(long int n, float ∗d, complex ∗e, float anorm,
float ∗srcond, long int ∗info)

INTEGER INFO, N

REAL ANORM, RCOND

REAL D( ∗ ), RWORK( ∗ )

COMPLEX E( ∗ )

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) INTEGER
The order of the matrix A. N >= 0.

D (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by CPTTRF.

E (input) COMPLEX array, dimension (N-1)
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) REAL
The 1-norm of the original matrix A.

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

RWORK (workspace) REAL array, dimension (N)

INFO (output) INTEGER
= 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 Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.