NAG Library Routine Document

f11dbf (real_gen_precon_ilu_solve)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

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

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

$Mx=y$ is solved.

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

$M^{\mathrm{T}}x=y$ is solved.

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

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $M$. This must be the same value as was supplied in the preceding call to f11daf.

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

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

On entry: the values returned in the array a by a previous call to f11daf.

4:     $\mathbf{la}$ – IntegerInput

On entry: the dimension of the arrays a, irow and icol as declared in the (sub)program from which f11dbf is called. This must be the same value returned by the preceding call to f11daf.

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

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

7:     $\mathbf{ipivp}\left(\mathbf{n}\right)$ – Integer arrayInput

8:     $\mathbf{ipivq}\left(\mathbf{n}\right)$ – Integer arrayInput

9:     $\mathbf{istr}\left(\mathbf{n}+1\right)$ – Integer arrayInput

10:   $\mathbf{idiag}\left(\mathbf{n}\right)$ – Integer arrayInput

On entry: the values returned in arrays irow, icol, ipivp, ipivq, istr and idiag by a previous call to f11daf.

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

On entry: specifies whether or not the CS representation of the matrix $M$ should be checked.

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

Checks are carried on the values of n, irow, icol, ipivp, ipivq, istr and idiag.

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

None of these checks are carried out.

See also Section 9.2.

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

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

On entry: the right-hand side vector $y$.

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

On exit: the solution vector $x$.

14:   $\mathbf{ifail}$ – 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, $\mathbf{check}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{check}=\text{'C'}$ or $\text{'N'}$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, $\mathbf{a}\left(i\right)$ is out of order: $i=〈\mathit{\text{value}}〉$.

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

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

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

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

On entry, $\mathbf{idiag}\left(i\right)$ appears to be incorrect: $i=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{ipivp}\left(i\right)$ is a repeated value: $i=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{ipivq}\left(i\right)$ is a repeated value: $i=〈\mathit{\text{value}}〉$.

On entry, istr appears to be invalid.

On entry, $\mathbf{istr}\left(i\right)$ is inconsistent with irow: $i=〈\mathit{\text{value}}〉$.

On entry, the location ($\mathbf{irow}\left(i\right),\mathbf{icol}\left(i\right)$) is a duplicate: $i=〈\mathit{\text{value}}〉$.

Check that a, irow, icol, ipivp, ipivq, istr and idiag have not been corrupted between calls to f11dbf and f11daf.

$\mathbf{ifail}=-99$

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 (f11dbfe.f90)

10.2

Program Data

Program Data (f11dbfe.d)

10.3

Program Results

Program Results (f11dbfe.r)