# naginterfaces.library.lapacklin.dtbcon¶

naginterfaces.library.lapacklin.dtbcon(norm, uplo, diag, kd, ab)[source]

dtbcon estimates the condition number of a real triangular band matrix.

For full information please refer to the NAG Library document for f07vg

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f07/f07vgf.html

Parameters
normstr, length 1

Indicates whether or is estimated.

or

is estimated.

is estimated.

uplostr, length 1

Specifies whether is upper or lower triangular.

is upper triangular.

is lower triangular.

diagstr, length 1

Indicates whether is a nonunit or unit triangular matrix.

is a nonunit triangular matrix.

is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .

kdint

, the number of superdiagonals of the matrix if , or the number of subdiagonals if .

abfloat, array-like, shape

The triangular band 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: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dtbcon estimates the condition number of a real triangular 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 computes or exactly, and 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