NAG Library Routine Document

F04ATF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – REAL (KIND=nag_wp) arrayInput

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

On entry: the $n$ by $n$ matrix $A$.

2:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F04ATF is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

3:     $\mathrm{B}\left(*\right)$ – REAL (KIND=nag_wp) arrayInput

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

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

4:     $\mathrm{N}$ – INTEGERInput

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

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

5:     $\mathrm{C}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the solution vector $x$.

6:     $\mathrm{AA}\left(\mathbf{LDAA},\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayOutput

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

On exit: the triangular factors $L$ and $U$, except that the unit diagonal elements of $U$ are not stored.

7:     $\mathrm{LDAA}$ – INTEGERInput

On entry: the first dimension of the array AA as declared in the (sub)program from which F04ATF is called.

Constraint: $\mathbf{LDAA}\ge \max \left(1,\mathbf{N}\right)$.

8:     $\mathrm{WKS1}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayWorkspace

9:     $\mathrm{WKS2}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) 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

$\mathbf{IFAIL}=1$

The matrix $A$ is singular, possibly due to rounding errors.

$\mathbf{IFAIL}=2$

Iterative refinement fails to improve the solution, i.e., the matrix $A$ is too ill-conditioned.

$\mathbf{IFAIL}=3$

On entry,	$\mathbf{N}<0$,
or	$\mathbf{LDA}<\max \left(1,\mathbf{N}\right)$,
or	$\mathbf{LDAA}<\max \left(1,\mathbf{N}\right)$.

$\mathbf{IFAIL}=-99$

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 (f04atfe.f90)

10.2  Program Data

Program Data (f04atfe.d)

10.3  Program Results

Program Results (f04atfe.r)