naginterfaces.library.lapacklin.zpbtrs

naginterfaces.library.lapacklin.zpbtrs(uplo, kd, ab, b)[source]

zpbtrs solves a complex Hermitian positive definite band system of linear equations with multiple right-hand sides,

where has been factorized by zpbtrf().

For full information please refer to the NAG Library document for f07hs

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07hsf.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 .

abcomplex, array-like, shape

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

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: .

Notes

zpbtrs is used to solve a complex Hermitian positive definite band system of linear equations , the function must be preceded by a call to zpbtrf() which computes the Cholesky factorization of . The solution is computed by forward and backward substitution.

If , , where is upper triangular; the solution is computed by solving and then .

If , , where is lower triangular; 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