NAG FL Interface
f03bff (real_​sym)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

Constraint: $\mathbf{n}>0$.

2: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array a must be at least $\mathbf{n}$.

On entry: the lower or upper triangle of the Cholesky factorized form of the $n$ by $n$ positive definite symmetric matrix $A$. Only the diagonal elements are referenced.

3: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f03bff is called.

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

4: $\mathbf{d}$ – Real (Kind=nag_wp) Output

5: $\mathbf{id}$ – Integer Output

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

6: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

The matrix $A$ is not positive definite.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results