# naginterfaces.library.lapacklin.zgbequ¶

naginterfaces.library.lapacklin.zgbequ(m, kl, ku, ab)[source]

zgbequ computes diagonal scaling matrices and intended to equilibrate a complex band matrix of band width , and reduce its condition number.

For full information please refer to the NAG Library document for f07bt

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f07/f07btf.html

Parameters
mint

, the number of rows of the matrix .

klint

, the number of subdiagonals of the matrix .

kuint

, the number of superdiagonals of the matrix .

abcomplex, array-like, shape

The band matrix whose scaling factors are to be computed.

See Further Comments for further details.

Returns
rfloat, ndarray, shape

If no exception or warning is raised or > , contains the row scale factors, the diagonal elements of . The elements of will be positive.

cfloat, ndarray, shape

If no exception or warning is raised, contains the column scale factors, the diagonal elements of . The elements of will be positive.

rowcndfloat

If no exception or warning is raised or > , contains the ratio of the smallest value of to the largest value of . If and is neither too large nor too small, it is not worth scaling by .

colcndfloat

If no exception or warning is raised, contains the ratio of the smallest value of to the largest value of .

If , it is not worth scaling by .

amaxfloat

. If is very close to overflow or underflow, the matrix should be scaled.

Raises
NagValueError
(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: .

Warns
NagAlgorithmicWarning
(errno )

Row of is exactly zero.

(errno )

Column of is exactly zero.

Notes

zgbequ computes the diagonal scaling matrices. The diagonal scaling matrices are chosen to try to make the elements of largest absolute value in each row and column of the matrix given by

have absolute value . The diagonal elements of and are restricted to lie in the safe range , where is the value returned by function machine.real_safe. Use of these scaling factors is not guaranteed to reduce the condition number of but works well in practice.