NAG Library Routine Document

f11xaf  (real_gen_matvec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

On entry: specifies whether or not the matrix $A$ is transposed.

$\mathbf{trans}=\text{'N'}$

$y=Ax$ is computed.

$\mathbf{trans}=\text{'T'}$

$y=A^{\mathrm{T}}x$ is computed.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

2:     $\mathbf{n}$ – IntegerInput

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

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

3:     $\mathbf{nnz}$ – IntegerInput

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

Constraint: $1\le \mathbf{nnz}\le {\mathbf{n}}^2$.

4:     $\mathbf{a}\left(\mathbf{nnz}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the nonzero elements in the matrix $A$, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The routine f11zaf may be used to order the elements in this way.

5:     $\mathbf{irow}\left(\mathbf{nnz}\right)$ – Integer arrayInput

6:     $\mathbf{icol}\left(\mathbf{nnz}\right)$ – Integer arrayInput

On entry: the row and column indices of the nonzero elements supplied in array a.

Constraints:

irow and icol must satisfy the following constraints (which may be imposed by a call to f11zaf):

• $1\le \mathbf{irow}\left(\mathit{i}\right)\le \mathbf{n}$ and $1\le \mathbf{icol}\left(\mathit{i}\right)\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnz}$;
• $\mathbf{irow}\left(\mathit{i}-1\right)<\mathbf{irow}\left(\mathit{i}\right)$ or $\mathbf{irow}\left(\mathit{i}-1\right)=\mathbf{irow}\left(\mathit{i}\right)$ and $\mathbf{icol}\left(\mathit{i}-1\right)<\mathbf{icol}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{nnz}$.

7:     $\mathbf{check}$ – Character(1)Input

On entry: specifies whether or not the CS representation of the matrix $A$, values of n, nnz, irow and icol should be checked.

$\mathbf{check}=\text{'C'}$

Checks are carried on the values of n, nnz, irow and icol.

$\mathbf{check}=\text{'N'}$

None of these checks are carried out.

See also Section 9.2.

Constraint: $\mathbf{check}=\text{'C'}$ or $\text{'N'}$.

8:     $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the vector $x$.

9:     $\mathbf{y}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the vector $y$.

10:   $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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,	$\mathbf{trans}\ne \text{'N'}$ or $\text{'T'}$,
or	$\mathbf{check}\ne \text{'C'}$ or $\text{'N'}$.

$\mathbf{ifail}=2$

On entry,	$\mathbf{n}<1$,
or	$\mathbf{nnz}<1$,
or	$\mathbf{nnz}>{\mathbf{n}}^2$.

$\mathbf{ifail}=3$

On entry, the arrays irow and icol fail to satisfy the following constraints:

• $1\le \mathbf{irow}\left(i\right)\le \mathbf{n}$ and $1\le \mathbf{icol}\left(i\right)\le \mathbf{n}$, for $i=1,2,\dots ,\mathbf{nnz}$;
• $\mathbf{irow}\left(i-1\right)<\mathbf{irow}\left(i\right)$, or $\mathbf{irow}\left(i-1\right)=\mathbf{irow}\left(i\right)$ and $\mathbf{icol}\left(i-1\right)<\mathbf{icol}\left(i\right)$, for $i=2,3,\dots ,\mathbf{nnz}$.

Therefore a nonzero element has been supplied which does not lie within the matrix $A$, is out of order, or has duplicate row and column indices. Call f11zaf to reorder and sum or remove duplicates.

$\mathbf{ifail}=-99$

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

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

9.1

Timing

9.2

Use of check

10

Example

10.1

Program Text

Program Text (f11xafe.f90)

10.2

Program Data

Program Data (f11xafe.d)

10.3

Program Results

Program Results (f11xafe.r)