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://support.nag.com/numeric/nl/nagdoc_30.3/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 tozpftrf()
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)