NAG Library Routine Document

F03AFF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

2:     EPS – REAL (KIND=nag_wp)Input

On entry: is no longer required by F03AFF but is retained for backwards compatibility.

3:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput/Output

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 $A$.

On exit: $A$ is overwritten by the lower triangular matrix $L$ and the off-diagonal elements of the upper triangular matrix $U$. The unit diagonal elements of $U$ are not stored.

4:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F03AFF is called.

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

5:     D1 – REAL (KIND=nag_wp)Output

6:     ID – INTEGEROutput

On exit: the determinant of $A$ is given by $\mathbf{D1}\times {2.0}^{\mathbf{ID}}$. It is given in this form to avoid overflow or underflow.

7:     P(N) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{P}\left(i\right)$ gives the row index of the $i$th pivot.

8:     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. The factorization could not be completed. D1 and ID are set to zero.

$\mathbf{IFAIL}=2$

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

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f03affe.f90)

9.2  Program Data

Program Data (f03affe.d)

9.3  Program Results

Program Results (f03affe.r)