NAG CL Interface
f16zlc (ztfsm)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2: $\mathbf{transr}$ – Nag_RFP_Store Input

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

$\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$

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

$\mathbf{transr}=\mathrm{Nag\_RFP\_ConjTrans}$

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

Constraint: $\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$ or $\mathrm{Nag\_RFP\_ConjTrans}$.

3: $\mathbf{side}$ – Nag_SideType 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.

$\mathbf{side}=\mathrm{Nag\_LeftSide}$

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

$\mathbf{side}=\mathrm{Nag\_RightSide}$

$B$ 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: $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$.

4: $\mathbf{uplo}$ – Nag_UploType Input

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

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

$A$ is upper triangular.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

5: $\mathbf{trans}$ – Nag_TransType 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.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

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

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$

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

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_ConjTrans}$.

6: $\mathbf{diag}$ – Nag_DiagType Input

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

$\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$

The diagonal elements of $A$ are stored explicitly.

$\mathbf{diag}=\mathrm{Nag\_UnitDiag}$

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

Constraint: $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathrm{Nag\_UnitDiag}$.

7: $\mathbf{m}$ – Integer Input

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

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

8: $\mathbf{n}$ – Integer Input

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

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

9: $\mathbf{alpha}$ – Complex Input

On entry: the scalar $\alpha$.

10: $\mathbf{ar}\left[\mathit{dim}\right]$ – const Complex Input

Note: the dimension, dim, of the array ar must be at least

• $\max \left(1,\mathbf{m}\times \left(\mathbf{m}+1\right)/2\right)$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$;
• $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$.

On entry: the $m$ by $m$ triangular matrix $A$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or the $n$ by $n$ triangular matrix $A$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$, stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.4.3 in the F07 Chapter Introduction. If $\mathbf{alpha}=0.0$, ar is not referenced.

11: $\mathbf{b}\left[\mathit{dim}\right]$ – Complex Input/Output

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{n}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{m}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

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 $X$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $B_{ij}$ is stored in $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $B_{ij}$ is stored in $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$.

12: $\mathbf{pdb}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

13: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INT_2

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results