NAG Library Routine Document

F11ZAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

2:     NNZ – INTEGERInput/Output

On entry: the number of nonzero elements in the matrix $A$.

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

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

3:     A($*$) – REAL (KIND=nag_wp) arrayInput/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 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 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:     IROW($*$) – INTEGER arrayInput/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 nonzero 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 nonzero elements returned in the array A.

5:     ICOL($*$) – INTEGER arrayInput/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 nonzero elements supplied in the array A.

Constraint: $1\le \mathbf{ICOL}\left(\mathit{i}\right)\le \mathbf{N}$, for $\mathit{i}=1,2,\dots ,\mathbf{NNZ}$.

On exit: the first NNZ elements contain the row indices corresponding to the nonzero elements returned in the array A.

6:     DUP – CHARACTER(1)Input

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

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

The entries are removed.

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

The relevant values in A are summed.

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

The routine fails on detecting a duplicate, with $\mathbf{IFAIL}=\mathbf{3}$.

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

7:     ZER – CHARACTER(1)Input

On entry: indicates how any elements with zero values in A 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 on detecting a zero, with $\mathbf{IFAIL}=\mathbf{4}$.

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

8:     ISTR($\mathbf{N}+1$) – INTEGER arrayOutput

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 nonzero element in $A$ plus one.

9:     IWORK(N) – INTEGER arrayWorkspace

10:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{N}<1$,
or	$\mathbf{NNZ}<0$,
or	$\mathbf{DUP}\ne \text{'R'},\text{'S'}$, or 'F',
or	$\mathbf{ZER}\ne \text{'R'},\text{'K'}$, or 'F'.

$\mathbf{IFAIL}=2$

On entry, a nonzero element has been supplied which does not lie within the matrix $A$, i.e., one or more of the following constraints has been violated:

• $1\le \mathbf{IROW}\left(i\right)\le \mathbf{N}$,
• $1\le \mathbf{ICOL}\left(i\right)\le \mathbf{N}$,

for $i=1,2,\dots ,\mathbf{NNZ}$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{DUP}=\text{'F'}$ and nonzero elements have been supplied which have duplicate row and column indices.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{ZER}=\text{'F'}$ and at least one matrix element has been supplied with a zero coefficient value.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11zafe.f90)

9.2  Program Data

Program Data (f11zafe.d)

9.3  Program Results

Program Results (f11zafe.r)