naginterfaces.library.blas.dtfsm

naginterfaces.library.blas.dtfsm(transr, side, uplo, trans, diag, alpha, a, b)[source]

dtfsm performs one of the matrix-matrix operations

where is a real triangular matrix stored in Rectangular Full Packed (RFP) format, is an real matrix, and is a real scalar. denotes or equivalently .

No test for singularity or near-singularity of is included in this function. Such tests must be performed before calling this function.

For full information please refer to the NAG Library document for f06wb

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06wbf.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.

sidestr, length 1

Specifies whether is operated on from the left or the right, or similarly whether (or its transpose) appears to the left or right of the solution matrix in the linear system to be solved.

is pre-multiplied from the left. The system to be solved has the form or .

is post-multiplied from the right. The system to be solved has the form or .

uplostr, length 1

Specifies whether is upper or lower triangular.

is upper triangular.

is lower triangular.

transstr, length 1

Specifies whether the operation involves or , i.e., whether or not is transposed in the linear system to be solved.

The operation involves , i.e., is not transposed.

The operation involves , i.e., is transposed.

diagstr, length 1

Specifies whether has nonunit or unit diagonal elements.

The diagonal elements of are stored explicitly.

The diagonal elements of are assumed to be , the corresponding elements of are not referenced.

alphafloat

The scalar .

afloat, array-like, shape

Note: the required length for this argument is determined as follows: if : ; if : ; otherwise: .

, the triangular matrix if or the triangular matrix if , stored in RFP format (as specified by ). The storage format is described in detail in the F07 Introduction. If , is not referenced.

bfloat, array-like, shape

The matrix .

If , need not be set.

Returns
bfloat, ndarray, shape

The updated matrix , or similarly 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: or .

(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

No equivalent traditional C interface for this routine exists in the NAG Library.

dtfsm solves (for ) a triangular linear system of one of the forms

where is a real triangular matrix stored in RFP format, , are real matrices, and is a real scalar. The RFP storage format is described in the F07 Introduction.

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)