cptcon-f(3)

cptcon.f –

Synopsis

Functions/Subroutines

subroutine cptcon (N, D, E, ANORM, RCOND, RWORK, INFO)
CPTCON

Function/Subroutine Documentation

subroutine cptcon (integerN, real, dimension( * )D, complex, dimension( * )E, realANORM, realRCOND, real, dimension( * )RWORK, integerINFO)

CPTCON

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))).

Parameters:

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

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

 E is 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

 ANORM is REAL
 The 1-norm of the original matrix A.

RCOND

 RCOND is 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

 RWORK is REAL array, dimension (N)

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

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.

Definition at line 120 of file cptcon.f.

Author

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