The routine may be called by the names f06wbf, nagf_blas_dtfsm or its LAPACK name dtfsm.
f06wbf 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 Section 3.3.3 in the F07 Chapter Introduction.
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. Software37, 2
1: – Character(1)Input
On entry: 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.
2: – Character(1)Input
On entry: 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 .
3: – Character(1)Input
On entry: specifies whether is upper or lower triangular.
is upper triangular.
is lower triangular.
4: – Character(1)Input
On entry: 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.
5: – Character(1)Input
On entry: 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 a are not referenced.
6: – IntegerInput
On entry: , the number of rows of the matrix .
7: – IntegerInput
On entry: , the number of columns of the matrix .
8: – Real (Kind=nag_wp)Input
On entry: the scalar .
9: – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array a
must be at least
if and at least if .
On entry: , the triangular matrix if or the triangular matrix if , stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction. If , a is not referenced.
10: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array b
must be at least
On exit: the updated matrix , or similarly the solution matrix .
11: – IntegerInput
On entry: the first dimension of the array b as declared in the (sub)program from which f06wbf is called.
6Error Indicators and Warnings
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f06wbf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
This example reads in the lower triangular part of a symmetric matrix which it converts to RFP format. It also reads in and a matrix and then performs the matrix-matrix operation .