# naginterfaces.library.lapacklin.zgbcon¶

naginterfaces.library.lapacklin.zgbcon(norm, kl, ku, ab, ipiv, anorm)[source]

zgbcon estimates the condition number of a complex band matrix , where has been factorized by zgbtrf().

For full information please refer to the NAG Library document for f07bu

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f07/f07buf.html

Parameters
normstr, length 1

Indicates whether or is estimated.

or

is estimated.

is estimated.

klint

, the number of subdiagonals within the band of the matrix .

kuint

, the number of superdiagonals within the band of the matrix .

abcomplex, array-like, shape

The factorization of , as returned by zgbtrf().

ipivint, array-like, shape

The pivot indices, as returned by zgbtrf().

anormfloat

If or , the -norm of the original matrix .

If , the -norm of the original matrix .

may be computed by calling blas.zlangb with the same value for the argument .

must be computed either before calling zgbtrf() 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: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zgbcon estimates the condition number of a complex band matrix , in either the -norm or the -norm:

Note that .

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

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

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