NAG CL Interface
f11mkc (direct_​real_​gen_​matmul)

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: $\mathbf{trans}$ – Nag_TransType Input

On entry: specifies whether or not the matrix $A$ is transposed.

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

$\alpha AB+\beta C$ is computed.

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

$\alpha A^{\mathrm{T}}B+\beta C$ is computed.

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

3: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $A$.

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

4: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of columns of matrices $B$ and $C$.

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

5: $\mathbf{alpha}$ – double Input

On entry: $\alpha$, the scalar factor in the matrix multiplication.

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

Note: the dimension, dim, of the array icolzp must be at least $\mathbf{n}+1$.

On entry: the new column index array of sparse matrix $A$. See Section 2.1.3 in the F11 Chapter Introduction.

7: $\mathbf{irowix}\left[\mathit{dim}\right]$ – const Integer Input

Note: the dimension, dim, of the array irowix must be at least $\mathbf{icolzp}\left[\mathbf{n}\right]-1$, the number of nonzeros of the sparse matrix $A$.

On entry: the row index array of sparse matrix $A$. See Section 2.1.3 in the F11 Chapter Introduction.

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

Note: the dimension, dim, of the array a must be at least $\mathbf{icolzp}\left[\mathbf{n}\right]-1$, the number of nonzeros of the sparse matrix $A$.

On entry: the array of nonzero values in the sparse matrix $A$.

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

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

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

The $\left(i,j\right)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $m$ matrix $B$.

10: $\mathbf{pdb}$ – Integer Input

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

Constraints:

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

11: $\mathbf{beta}$ – double Input

On entry: the scalar factor $\beta$.

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

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

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

The $\left(i,j\right)$th element of the matrix $C$ is stored in

• $\mathbf{c}\left[\left(j-1\right)\times \mathbf{pdc}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{c}\left[\left(i-1\right)\times \mathbf{pdc}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $m$ matrix $C$.

On exit: $C$ is overwritten by $\alpha AB+\beta C$ or $\alpha A^{\mathrm{T}}B+\beta C$ depending on the value of trans.

13: $\mathbf{pdc}$ – Integer Input

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

Constraints:

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

14: $\mathbf{fail}$ – 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: $\mathbf{n}\ge 0$.

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

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

NE_INT_2

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

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

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

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

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