naginterfaces.library.lapacklin.zpftrs

naginterfaces.library.lapacklin.zpftrs(transr, uplo, n, ar, b)[source]

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

using the Cholesky factorization computed by zpftrf() stored in Rectangular Full Packed (RFP) format.

For full information please refer to the NAG Library document for f07ws

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07wsf.html

Parameters
transrstr, length 1

Specifies whether the normal RFP representation of or its conjugate transpose is stored.

The matrix is stored in normal RFP format.

The conjugate transpose of the RFP representation of the matrix is stored.

uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

nint

, the order of the matrix .

arcomplex, array-like, shape

The Cholesky factorization of stored in RFP format, as returned by zpftrf().

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: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zpftrs is used to solve a complex Hermitian positive definite system of linear equations , the function must be preceded by a call to zpftrf() which computes the Cholesky factorization of , stored in RFP format. The RFP storage format is described in the F07 Introduction. 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

Gustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)