NAG Library Routine Document

F03AAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

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

2:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F03AAF is called.

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

3:     N – INTEGERInput

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

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

4:     DET – REAL (KIND=nag_wp)Output

On exit: the determinant of $A$.

5:     WKSPCE(N) – REAL (KIND=nag_wp) arrayWorkspace

6:     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. DET is set to $0.0$.

$\mathbf{IFAIL}=2$

Overflow. The value of the determinant is too large to be held in the computer.

$\mathbf{IFAIL}=3$

Underflow. The value of the determinant is too small to be held in the computer.

$\mathbf{IFAIL}=4$

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 (f03aafe.f90)

9.2  Program Data

Program Data (f03aafe.d)

9.3  Program Results

Program Results (f03aafe.r)