NAG Library Routine Document

F01ABF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     A(LDA,N) – REAL (KIND=nag_wp) arrayInput/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:     LDA – INTEGERInput

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:     N – INTEGERInput

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

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

4:     B(LDB,N) – REAL (KIND=nag_wp) arrayOutput

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:     LDB – INTEGERInput

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:     Z(N) – REAL (KIND=nag_wp) arrayWorkspace

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.

$\mathbf{IFAIL}=2$

The refinement process fails to converge, i.e., the matrix $A$ is ill-conditioned.

$\mathbf{IFAIL}=3$

$\mathbf{N}<1$, or $\mathbf{LDA}<\mathbf{N}+1$, or $\mathbf{LDB}<\mathbf{N}$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01abfe.f90)

9.2  Program Data

Program Data (f01abfe.d)

9.3  Program Results

Program Results (f01abfe.r)