NAG CL Interface
f11zcc (real_​rect_​sort)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

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

Constraint: $\mathbf{m}\ge 1$.

2: $\mathbf{n}$ – Integer Input

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

Constraint: $\mathbf{n}\ge 1$.

3: $\mathbf{nnz}$ – Integer * Input/Output

On entry: the number of elements supplied in the array a.

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

On exit: the number of elements with unique row and column indices.

4: $\mathbf{a}\left[\mathbf{nnz}\right]$ – double Input/Output

On entry: the nonzero elements of the matrix $A$. If $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$, the elements may be in any order. If $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCCS}$, the elements must be ordered by increasing column index. There may be multiple nonzero elements with the same row and column indices.

On exit: the nonzero elements ordered by increasing column index, and by increasing row index within each column. Each nonzero element has a unique row and column index.

5: $\mathbf{irow}\left[\mathbf{nnz}\right]$ – Integer Input/Output

On entry: the row indices corresponding to the elements supplied in the array a.

Constraint: $1\le \mathbf{irow}\left[\mathit{i}\right]\le \mathbf{m}$, for $\mathit{i}=0,1,\dots ,\mathbf{nnz}-1$.

On exit: the first nnz elements contain the row indices corresponding to the elements returned in the array a.

6: $\mathbf{icol}\left[\mathbf{nnz}\right]$ – Integer Input/Output

On entry: if $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$, the column indices corresponding to the elements supplied in the array a.

If $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCCS}$, icol need not be set.

Constraint: if $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$, $1\le \mathbf{icol}\left[\mathit{i}\right]\le \mathbf{n}$, for $\mathit{i}=0,1,\dots ,\mathbf{nnz}-1$.

On exit: the first nnz elements contain the column indices corresponding to the elements returned in the array a.

7: $\mathbf{istc}\left[\mathbf{n}+1\right]$ – Integer Input/Output

On entry: if $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCCS}$, the starting address of each column, as supplied in the array a.

If $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$, istc need not be set.

Constraints:

if $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCCS}$,

• $\mathbf{istc}\left[0\right]=1$;
• $\mathbf{istc}\left[\mathbf{n}\right]=\mathbf{nnz}+1$;
• $\mathbf{istc}\left[\mathit{i}-1\right]\le \mathbf{istc}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

On exit: the starting address of each column, as returned in the array a. $\mathbf{istc}\left[\mathbf{n}\right]-1$ is the address of the last element in a plus one.

8: $\mathbf{store}$ – Nag_SparseNsym_Store Input

On entry: indicates which storage format the matrix $A$ is represented with on entry.

$\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$

$A$ is represented in coordinate storage (CS) format using a, irow and icol.

$\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCCS}$

$A$ is represented in compressed column storage (CCS) format using a, irow and istc.

Constraint: $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$ or $\mathrm{Nag\_SparseNsym\_StoreCCS}$.

9: $\mathbf{dup}$ – Nag_SparseNsym_Dups Input

On entry: indicates how elements in a with duplicate row and column indices are to be treated.

$\mathbf{dup}=\mathrm{Nag\_SparseNsym\_RemoveDups}$

Duplicate entries are removed, only the first entry is kept.

$\mathbf{dup}=\mathrm{Nag\_SparseNsym\_SumDups}$

The relevant values in a are summed.

$\mathbf{dup}=\mathrm{Nag\_SparseNsym\_FailDups}$

The function fails with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NON_ZERO_DUP on detecting a duplicate.

Constraint: $\mathbf{dup}=\mathrm{Nag\_SparseNsym\_RemoveDups}$, $\mathrm{Nag\_SparseNsym\_SumDups}$ or $\mathrm{Nag\_SparseNsym\_FailDups}$.

10: $\mathbf{zero}$ – Nag_SparseNsym_Zeros Input

On entry: indicates how elements in a with zero values are to be treated.

$\mathbf{zero}=\mathrm{Nag\_SparseNsym\_RemoveZeros}$

The entries are removed.

$\mathbf{zero}=\mathrm{Nag\_SparseNsym\_KeepZeros}$

The entries are kept.

$\mathbf{zero}=\mathrm{Nag\_SparseNsym\_FailZeros}$

The function fails with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_ZERO_COEFF on detecting a zero.

Constraint: $\mathbf{zero}=\mathrm{Nag\_SparseNsym\_RemoveZeros}$, $\mathrm{Nag\_SparseNsym\_KeepZeros}$ or $\mathrm{Nag\_SparseNsym\_FailZeros}$.

11: $\mathbf{fail}$ – 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, $\mathbf{istc}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{istc}\left[0\right]=1$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

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

NE_INT_3

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left[i-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{store}=\mathrm{Nag\_SparseNsym\_StoreCS}$, then $1\le \mathbf{icol}\left[i-1\right]\le \mathbf{n}$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irow}\left[i-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{irow}\left[i-1\right]\le \mathbf{m}$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{istc}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{istc}\left[\mathit{i}\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{istc}\left[\mathit{i}-1\right]\le \mathbf{istc}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{istc}\left[\mathbf{n}\right]=〈\mathit{\text{value}}〉$ and $\mathbf{nnz}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{istc}\left[\mathbf{n}\right]=\mathbf{nnz}+1$.

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.

NE_NON_ZERO_DUP

On entry, a duplicate entry has been found in row $〈\mathit{\text{value}}〉$ and column $〈\mathit{\text{value}}〉$.

NE_ZERO_COEFF

On entry, a zero entry has been found in row $〈\mathit{\text{value}}〉$ and column $〈\mathit{\text{value}}〉$.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results