NAG CL Interface
f16zjc (ztrsm)

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: $\mathbf{side}$ – Nag_SideType Input

On entry: specifies whether $B$ is operated on from the left or the right.

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

$B$ is pre-multiplied from the left.

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

$B$ is post-multiplied from the right.

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

3: $\mathbf{uplo}$ – 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 $\mathrm{Nag\_Lower}$.

4: $\mathbf{trans}$ – Nag_TransType Input

On entry: specifies the operation to be performed.

$\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{side}=\mathrm{Nag\_LeftSide}$

$B\leftarrow \alpha A^{-\mathrm{T}}B$.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{side}=\mathrm{Nag\_LeftSide}$

$B\leftarrow \alpha A^{-1}B$.

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$ and $\mathbf{side}=\mathrm{Nag\_LeftSide}$

$B\leftarrow \alpha A^{-\mathrm{H}}B$.

$\mathbf{trans}=\mathrm{Nag\_Trans}$ and $\mathbf{side}=\mathrm{Nag\_RightSide}$

$B\leftarrow \alpha B{A}^{-\mathrm{T}}$.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{side}=\mathrm{Nag\_RightSide}$

$B\leftarrow \alpha B{A}^{-1}$.

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$ and $\mathbf{side}=\mathrm{Nag\_RightSide}$

$B\leftarrow \alpha B{A}^{-\mathrm{H}}$.

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

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

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

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

The diagonal elements are stored explicitly.

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

The diagonal elements are assumed to be $1$ and are not referenced.

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

6: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of rows of the matrix $B$; the order of $A$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$.

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

7: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of columns of the matrix $B$; the order of $A$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$.

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

8: $\mathbf{alpha}$ – Complex Input

On entry: the scalar $\alpha$.

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

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

• $\max (1,\mathbf{pda}\times \mathbf{m})$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$;
• $\max (1,\mathbf{pda}\times \mathbf{n})$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$.

On entry: the triangular matrix $A$; $A$ is $m\times m$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, or $n\times n$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$.

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

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

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, $A$ is upper triangular and the elements of the array corresponding to the lower triangular part of $A$ are not referenced.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, $A$ is lower triangular and the elements of the array corresponding to the upper triangular part of $A$ are not referenced.

If $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

10: $\mathbf{pda}$ – Integer Input

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

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{pda}\ge \max (1,\mathbf{m})$;
• if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max (1,\mathbf{n})$.

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

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

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

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

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

On entry: the $m\times n$ matrix $B$.

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

On exit: the updated matrix $B$.

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

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_ENUM_INT_2

On entry, $\mathbf{side}=⟨\mathit{\text{value}}⟩$, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{pda}\ge \max (1,\mathbf{m})$.

On entry, $\mathbf{side}=⟨\mathit{\text{value}}⟩$, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max (1,\mathbf{n})$.

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, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$; $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pda}\ge \max (1,\mathbf{n})$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$; $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{m})$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{m})$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{n})$.

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.

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