NAG CL Interface
f01dfc (real_​tri_​matmul)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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

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

$C$ is upper triangular.

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

$C$ is lower triangular.

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

2: $\mathbf{transa}$ – Nag_TransType Input

On entry: specifies whether the operation involves $A$ or $A^{\mathrm{T}}$.

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

The operation involves $A$.

$\mathbf{transa}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$

The operation involves $A^{\mathrm{T}}$.

Constraint: $\mathbf{transa}=\mathrm{Nag\_NoTrans}$, $\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

3: $\mathbf{transb}$ – Nag_TransType Input

On entry: specifies whether the operation involves $B$ or $B^{\mathrm{T}}$.

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

The operation involves $B$.

$\mathbf{transb}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$

The operation involves $B^{\mathrm{T}}$.

Constraint: $\mathbf{transb}=\mathrm{Nag\_NoTrans}$, $\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

4: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the triangular matrices $A$, $B$, and $C$.

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

5: $\mathbf{alpha}$ – double Input

On entry: the scalar $\alpha$.

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

Note: the dimension, dim, of the array a must be at least $\max (1,\mathbf{pda}\times \mathbf{n})$.

On entry: the $n\times n$ triangular matrix $A$.

$A_{ij}$ is stored in $\mathbf{a}\left[(j-1)\times \mathbf{pda}+i-1\right]$.

• If $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
  • if $\mathbf{transa}=\mathrm{Nag\_NoTrans}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced;
  • if $\mathbf{transa}=\mathrm{Nag\_Trans}$ or $\mathbf{transa}=\mathrm{Nag\_ConjTrans}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{uplo}=\mathrm{Nag\_Lower}$
  • if $\mathbf{transa}=\mathrm{Nag\_NoTrans}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced;
  • if $\mathbf{transa}=\mathrm{Nag\_Trans}$ or $\mathbf{transa}=\mathrm{Nag\_ConjTrans}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.

7: $\mathbf{pda}$ – Integer Input

On entry: the stride separating row elements of the matrix $A$ in the array a.

Constraint: $\mathbf{pda}\ge \max (1,\mathbf{n})$.

8: $\mathbf{b}\left[\mathit{dim}\right]$ – const double Input

Note: the dimension, dim, of the array b must be at least $\max (1,\mathbf{pdb}\times \mathbf{n})$.

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

$B_{ij}$ is stored in $\mathbf{b}\left[(j-1)\times \mathbf{pdb}+i-1\right]$.

• If $\mathbf{uplo}=\mathrm{Nag\_Upper}$,
  • if $\mathbf{transa}=\mathrm{Nag\_NoTrans}$, $B$ is upper triangular and the elements of the array below the diagonal are not referenced;
  • if $\mathbf{transa}=\mathrm{Nag\_Trans}$ or $\mathbf{transa}=\mathrm{Nag\_ConjTrans}$, $B$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{uplo}=\mathrm{Nag\_Lower}$
  • if $\mathbf{transa}=\mathrm{Nag\_NoTrans}$, $B$ is lower triangular and the elements of the array above the diagonal are not referenced;
  • if $\mathbf{transa}=\mathrm{Nag\_Trans}$ or $\mathbf{transa}=\mathrm{Nag\_ConjTrans}$, $B$ is upper triangular and the elements of the array below the diagonal are not referenced.

9: $\mathbf{pdb}$ – Integer Input

On entry: the stride separating row elements of the matrix $B$ in the array b.

Constraint: $\mathbf{pdb}\ge \max (1,\mathbf{n})$.

10: $\mathbf{beta}$ – double Input

On entry: the scalar $\beta$.

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

Note: the dimension, dim, of the array c must be at least $\max (1,\mathbf{pdc}\times \mathbf{n})$.

$C_{ij}$ is stored in $\mathbf{c}\left[(j-1)\times \mathbf{pdc}+i-1\right]$.

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

On entry: the $n\times n$ matrix $C$.

If $\mathbf{beta}=0$, c need not be set.

On exit: the triangular part of $C$, as specified by uplo, is updated.

12: $\mathbf{pdc}$ – Integer Input

On entry: the stride separating row elements of the matrix $C$ in the array c.

Constraint: $\mathbf{pdc}\ge \max (1,\mathbf{n})$.

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_INT

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

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

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.
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