naginterfaces.library.lapacklin.zptcon

naginterfaces.library.lapacklin.zptcon(n, d, e, anorm)[source]

zptcon computes the reciprocal condition number of a complex Hermitian positive definite tridiagonal matrix , using the factorization returned by zpttrf().

For full information please refer to the NAG Library document for f07ju

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07juf.html

Parameters
nint

, the order of the matrix .

dfloat, array-like, shape

Must contain the diagonal elements of the diagonal matrix from the factorization of .

ecomplex, array-like, shape

Must contain the subdiagonal elements of the unit lower bidiagonal matrix . ( can also be regarded as the superdiagonal of the unit upper bidiagonal matrix from the factorization of .)

anormfloat

The -norm of the original matrix , which may be computed by calling blas.zlanht with its argument . must be computed either before calling zpttrf() or else from a copy of the original matrix .

Returns
rcondfloat

The reciprocal condition number, .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zptcon should be preceded by a call to zpttrf(), which computes a modified Cholesky factorization of the matrix as

where is a unit lower bidiagonal matrix and is a diagonal matrix, with positive diagonal elements. zptcon then utilizes the factorization to compute by a direct method, from which the reciprocal of the condition number of , is computed as

is returned, rather than , since when is singular is infinite.

References

Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia