# naginterfaces.library.lapacklin.dpbcon¶

naginterfaces.library.lapacklin.dpbcon(uplo, kd, ab, anorm)[source]

dpbcon estimates the condition number of a real symmetric positive definite band matrix , where has been factorized by dpbtrf().

For full information please refer to the NAG Library document for f07hg

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f07/f07hgf.html

Parameters
uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

kdint

, the number of superdiagonals or subdiagonals of the matrix .

abfloat, array-like, shape

The Cholesky factor of , as returned by dpbtrf().

anormfloat

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

Returns
rcondfloat

An estimate of the reciprocal of the condition number of . is set to zero if exact singularity is detected or the estimate underflows. If is less than machine precision, is singular to working precision.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dpbcon estimates the condition number (in the -norm) of a real symmetric positive definite band matrix :

Since is symmetric, .

Because is infinite if is singular, the function actually returns an estimate of the reciprocal of .

The function should be preceded by a call to blas.dlansb to compute and a call to dpbtrf() to compute the Cholesky factorization of . The function then uses Higham’s implementation of Hager’s method (see Higham (1988)) to estimate .

References

Higham, N J, 1988, FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation, ACM Trans. Math. Software (14), 381–396