NAG Library Routine Document

f06wbf (dtfsm)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{transr}$ – Character(1)Input

On entry: specifies whether the RFP representation of $A$ is normal or transposed.

$\mathbf{transr}=\text{'N'}$

The matrix $A$ is stored in normal RFP format.

$\mathbf{transr}=\text{'T'}$

The matrix $A$ is stored in transposed RFP format.

Constraint: $\mathbf{transr}=\text{'N'}$ or $\text{'T'}$.

2:     $\mathbf{side}$ – Character(1)Input

On entry: specifies whether $B$ is operated on from the left or the right, or similarly whether $A$ (or its transpose) appears to the left or right of the solution matrix in the linear system to be solved.

$\mathbf{side}=\text{'L'}$

$B$ is pre-multiplied from the left. The system to be solved has the form $AX=\alpha B$ or $A^{\mathrm{T}}X=\alpha B$.

$\mathbf{side}=\text{'R'}$

$B$ is post-multiplied from the right. The system to be solved has the form $XA=\alpha B$ or $X{A}^{\mathrm{T}}=\alpha B$.

Constraint: $\mathbf{side}=\text{'L'}$ or $\text{'R'}$.

3:     $\mathbf{uplo}$ – Character(1)Input

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\text{'U'}$

$A$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

4:     $\mathbf{trans}$ – Character(1)Input

On entry: specifies whether the operation involves $A^{-1}$ or $A^{-\mathrm{T}}$, i.e., whether or not $A$ is transposed in the linear system to be solved.

$\mathbf{trans}=\text{'N'}$

The operation involves $A^{-1}$, i.e., $A$ is not transposed.

$\mathbf{trans}=\text{'T'}$

The operation involves $A^{-\mathrm{T}}$, i.e., $A$ is transposed.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

5:     $\mathbf{diag}$ – Character(1)Input

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\text{'N'}$

The diagonal elements of $A$ are stored explicitly.

$\mathbf{diag}=\text{'U'}$

The diagonal elements of $A$ are assumed to be $1$, the corresponding elements of a are not referenced.

Constraint: $\mathbf{diag}=\text{'N'}$ or $\text{'U'}$.

6:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $B$.

Constraint: $\mathbf{m}\ge 0$.

7:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $B$.

Constraint: $\mathbf{n}\ge 0$.

8:     $\mathbf{alpha}$ – Real (Kind=nag_wp)Input

On entry: the scalar $\alpha$.

9:     $\mathbf{a}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array a must be at least $\max \left(1,\mathbf{m}\times \left(\mathbf{m}+1\right)/2\right)$ if $\mathbf{side}=\text{'L'}$ and at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ if $\mathbf{side}=\text{'R'}$.

On entry: $A$, the $m$ by $m$ triangular matrix $A$ if $\mathbf{side}=\text{'L'}$ or the $n$ by $n$ triangular matrix $A$ if $\mathbf{side}=\text{'R'}$, 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 $\mathbf{alpha}=0.0$, a is not referenced.

10:   $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array b must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $m$ by $n$ matrix $B$.

If $\mathbf{alpha}=0$, b need not be set.

On exit: the updated matrix $B$, or similarly the solution matrix $X$.

11:   $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f06wbf (dtfsm) is called.

Constraint: $\mathbf{ldb}\ge \max \left(1,\mathbf{m}\right)$.

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f06wbfe.f90)

10.2

Program Data

Program Data (f06wbfe.d)

10.3

Program Results

Program Results (f06wbfe.r)