naginterfaces.library.lapacklin.dpftrs

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

dpftrs solves a real symmetric positive definite system of linear equations with multiple right-hand sides,

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

For full information please refer to the NAG Library document for f07we

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07wef.html

Parameters
transrstr, length 1

Specifies whether the RFP representation of is normal or transposed.

The matrix is stored in normal RFP format.

The matrix is stored in transposed RFP format.

uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

nint

, the order of the matrix .

arfloat, array-like, shape

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

bfloat, array-like, shape

The right-hand side matrix .

Returns
bfloat, 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

dpftrs is used to solve a real symmetric positive definite system of linear equations , the function must be preceded by a call to dpftrf() 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)