# naginterfaces.library.lapacklin.zgbtrs¶

naginterfaces.library.lapacklin.zgbtrs(trans, kl, ku, ab, ipiv, b)[source]

zgbtrs solves a complex band system of linear equations with multiple right-hand sides,

where has been factorized by zgbtrf().

For full information please refer to the NAG Library document for f07bs

https://www.nag.com/numeric/nl/nagdoc_29.2/flhtml/f07/f07bsf.html

Parameters
transstr, length 1

Indicates the form of the equations.

is solved for .

is solved for .

is solved for .

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().

bcomplex, array-like, shape

The right-hand side matrix .

Returns
bcomplex, ndarray, shape

The solution matrix .

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

zgbtrs is used to solve a complex band system of linear equations , or , the function must be preceded by a call to zgbtrf() which computes the factorization of as . The solution is computed by forward and backward substitution.

If , the solution is computed by solving and then .

If , the solution is computed by solving and then .

If , the solution is computed by solving and then .

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore