NAG Library Function Document

nag_superlu_matrix_product (f11mkc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     trans – Nag_TransTypeInput

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:     n – IntegerInput

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

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

4:     m – IntegerInput

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

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

5:     alpha – doubleInput

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

6:     icolzp[$\mathit{dim}$] – const IntegerInput

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

On entry: $\mathbf{icolzp}\left[i-1\right]$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the f11 Chapter Introduction.

7:     irowix[$\mathit{dim}$] – const IntegerInput

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 the sparse matrix $A$.

8:     a[$\mathit{dim}$] – const doubleInput

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:     b[$\mathit{dim}$] – const doubleInput

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:   pdb – IntegerInput

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:   beta – doubleInput

On entry: the scalar factor $\beta$.

12:   c[$\mathit{dim}$] – doubleInput/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:   pdc – IntegerInput

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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

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

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.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11mkce.c)

9.2  Program Data

Program Data (f11mkce.d)

9.3  Program Results

Program Results (f11mkce.r)