NAG FL Interface
f11zcf (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: $\mathbf{a}\left(\mathbf{nnz}\right)$ – Real (Kind=nag_wp) array Input/Output

On entry: the nonzero elements of the matrix $A$. If $\mathbf{store}=1$, the elements may be in any order. If $\mathbf{store}=2$, 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 array 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 $\mathit{i}=1,2,\dots ,\mathbf{nnz}$.

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 array Input/Output

On entry: if $\mathbf{store}=1$, the column indices corresponding to the elements supplied in the array a.

If $\mathbf{store}=2$, icol need not be set.

Constraint: if $\mathbf{store}=1$, $1\le \mathbf{icol}\left(\mathit{i}\right)\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnz}$.

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 array Input/Output

On entry: if $\mathbf{store}=2$, the starting address of each column, as supplied in the array a.

If $\mathbf{store}=1$, istc need not be set.

Constraints:

if $\mathbf{store}=2$,

• $\mathbf{istc}\left(1\right)=1$;
• $\mathbf{istc}\left(\mathbf{n}+1\right)=\mathbf{nnz}+1$;
• $\mathbf{istc}\left(\mathit{i}\right)\le \mathbf{istc}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

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

8: $\mathbf{store}$ – Integer Input

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

$\mathbf{store}=1$

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

$\mathbf{store}=2$

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

Constraint: $\mathbf{store}=1$ or $2$.

9: $\mathbf{dup}$ – Character(1) Input

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

$\mathbf{dup}=\text{'R'}$

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

$\mathbf{dup}=\text{'S'}$

The relevant values in a are summed.

$\mathbf{dup}=\text{'F'}$

The routine fails with $\mathbf{ifail}=\mathbf{12}$ on detecting a duplicate.

Constraint: $\mathbf{dup}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.

10: $\mathbf{zer}$ – Character(1) Input

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

$\mathbf{zer}=\text{'R'}$

The entries are removed.

$\mathbf{zer}=\text{'K'}$

The entries are kept.

$\mathbf{zer}=\text{'F'}$

The routine fails with $\mathbf{ifail}=\mathbf{13}$ on detecting a zero.

Constraint: $\mathbf{zer}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.

11: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

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

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

On entry, $\mathbf{store}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{store}=1$ or $2$.

$\mathbf{ifail}=5$

On entry, $\mathbf{dup}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{dup}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.

$\mathbf{ifail}=6$

On entry, $\mathbf{zer}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{zer}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.

$\mathbf{ifail}=7$

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

$\mathbf{ifail}=8$

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left(i\right)=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{store}=1$, then $1\le \mathbf{icol}\left(i\right)\le \mathbf{n}$.

$\mathbf{ifail}=9$

On entry, $\mathbf{istc}\left(1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{istc}\left(1\right)=1$.

$\mathbf{ifail}=10$

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

$\mathbf{ifail}=11$

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

$\mathbf{ifail}=12$

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

$\mathbf{ifail}=13$

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL 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