NAG Library Routine Document

F06WPF (ZTFSM)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TRANSR – CHARACTER(1)Input

On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

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

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

$\mathbf{TRANSR}=\text{'C'}$

The conjugate transpose of the RFP representation of the matrix $A$ is stored.

Constraint: $\mathbf{TRANSR}=\text{'N'}$ or $\text{'C'}$.

2:     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 $A^{\mathrm{H}}X=\alpha B$.

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

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

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

3:     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:     TRANS – CHARACTER(1)Input

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

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

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

$\mathbf{TRANS}=\text{'C'}$

The operation involves $A^{-\mathrm{H}}$, i.e., $A$ is transpose conjugated.

Constraint: $\mathbf{TRANS}=\text{'N'}$ or $\text{'C'}$.

5:     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:     M – INTEGERInput

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

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

7:     N – INTEGERInput

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

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

8:     ALPHA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

9:     A($*$) – COMPLEX (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 described in Section 3.3.3 in the F07 Chapter Introduction.

10:   B(LDB,$*$) – COMPLEX (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:   LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F06WPF (ZTFSM) is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f06wpfe.f90)

9.2  Program Data

Program Data (f06wpfe.d)

9.3  Program Results

Program Results (f06wpfe.r)