NAG FL Interface
f01abf (real_​symm_​posdef_​inv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{a}\left(\mathbf{lda},\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input/Output

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 lower triangle of the inverse matrix $X$ is stored in the elements of the array below the diagonal, in rows $2$ to $n+1$; $x_{ij}$ is stored in $\mathbf{a}\left(i+1,j\right)$ for $i\ge j$. The upper triangle of the original matrix is unchanged.

2: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01abf is called.

Constraint: $\mathbf{lda}\ge \mathbf{n}+1$.

3: $\mathbf{n}$ – Integer Input

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

Constraint: $\mathbf{n}\ge 1$.

4: $\mathbf{b}\left(\mathbf{ldb},\mathbf{n}\right)$ – Real (Kind=nag_wp) array Output

On exit: the lower triangle of the inverse matrix $X$, with $x_{ij}$ stored in $\mathbf{b}\left(i,j\right)$, for $i\ge j$.

5: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f01abf is called.

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

6: $\mathbf{z}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Workspace

7: $\mathbf{ifail}$ – 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

$\mathbf{ifail}=1$

The matrix $A$ is not positive definite, possibly due to rounding errors.

$\mathbf{ifail}=2$

The refinement process failed to converge. The matrix $A$ is ill-conditioned.

$\mathbf{ifail}=3$

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

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

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=-99$

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