NAG FL Interface
f11zbf (real_​symm_​sort)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

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

2: $\mathbf{nnz}$ – 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.

3: $\mathbf{a}\left(*\right)$ – Real (Kind=nag_wp) array Input/Output

Note: the dimension of the array a must be at least $\max \left(1,\mathbf{nnz}\right)$.

On entry: the nonzero elements of the lower triangular part of the real matrix $A$. These may be in any order and there may be multiple nonzero elements with the same row and column indices.

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

4: $\mathbf{irow}\left(*\right)$ – Integer array Input/Output

Note: the dimension of the array irow must be at least $\max \left(1,\mathbf{nnz}\right)$.

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

Constraint: $1\le \mathbf{irow}\left(\mathit{i}\right)\le \mathbf{n}$, 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.

5: $\mathbf{icol}\left(*\right)$ – Integer array Input/Output

Note: the dimension of the array icol must be at least $\max \left(1,\mathbf{nnz}\right)$.

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

Constraint: $1\le \mathbf{icol}\left(\mathit{i}\right)\le \mathbf{irow}\left(\mathit{i}\right)$, 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.

6: $\mathbf{dup}$ – 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 $\mathbf{ifail}=\mathbf{3}$ on detecting a duplicate.

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

7: $\mathbf{zer}$ – 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 $\mathbf{ifail}=\mathbf{4}$ on detecting a zero.

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

8: $\mathbf{istr}\left(\mathbf{n}+1\right)$ – Integer array Output

On exit: $\mathbf{istr}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$, is the starting address in the arrays a, irow and icol of row $i$ of the matrix $A$. $\mathbf{istr}\left(\mathbf{n}+1\right)$ is the address of the last element in a plus one.

9: $\mathbf{iwork}\left(\mathbf{n}\right)$ – Integer array Workspace

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

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\mathbf{dup}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{dup}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.

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

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

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

$\mathbf{ifail}=2$

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

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=-99$

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