NAG Library Routine Document

f03bff (real_sym)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

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

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:     $\mathbf{lda}$ – IntegerInput

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:     $\mathbf{id}$ – IntegerOutput

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:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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

$\mathbf{ifail}=1$

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 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f03bffe.f90)

10.2

Program Data

Program Data (f03bffe.d)

10.3

Program Results

Program Results (f03bffe.r)