NAG Library Routine Document

F11ZBF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

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

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

2:     $\mathrm{NNZ}$ – INTEGERInput/Output

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

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

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

3:     $\mathrm{A}\left(*\right)$ – 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 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:     $\mathrm{IROW}\left(*\right)$ – 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:     $\mathrm{ICOL}\left(*\right)$ – 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: $1\le \mathbf{ICOL}\left(\mathit{i}\right)\le \mathbf{IROW}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NNZ}$.

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

6:     $\mathrm{DUP}$ – 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.

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

7:     $\mathrm{ZER}$ – 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.

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

8:     $\mathrm{ISTR}\left(\mathbf{N}+1\right)$ – 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:     $\mathrm{IWORK}\left(\mathbf{N}\right)$ – INTEGER arrayWorkspace

10:   $\mathrm{IFAIL}$ – 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	$\mathbf{DUP}\ne \text{'R'}$ or $\text{'S'}$.
or	$\mathbf{ZER}\ne \text{'R'}$ or $\text{'K'}$.

$\mathbf{IFAIL}=2$

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

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

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

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f11zbfe.f90)

10.2  Program Data

Program Data (f11zbfe.d)

10.3  Program Results

Program Results (f11zbfe.r)