NAG Library Routine Document

F03AEF

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:     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 upper triangle of the $n$ by $n$ positive definite symmetric matrix $A$. The elements of the array below the diagonal need not be set.

On exit: the subdiagonal elements of the lower triangular matrix $L$. The upper triangle of $A$ is unchanged.

3:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F03AEF is called.

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

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

On exit: the reciprocals of the diagonal elements of $L$.

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:     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 not positive definite, 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 (f03aefe.f90)

9.2  Program Data

Program Data (f03aefe.d)

9.3  Program Results

Program Results (f03aefe.r)