NAG FL Interface
f01buf (real_​symm_​posdef_​fac)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

2: $\mathbf{m1}$ – Integer Input

On entry: $m+1$, where $m$ is the number of nonzero superdiagonals in $A$. Normally $\mathbf{m1}\ll \mathbf{n}$.

3: $\mathbf{k}$ – Integer Input

On entry: $k$, the change-over point in the decomposition.

Constraint: $\mathbf{m1}-1\le \mathbf{k}\le \mathbf{n}$.

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

On entry: the upper triangle of the $n$ by $n$ symmetric band matrix $A$, with the diagonal of the matrix stored in the $\left(m+1\right)$th row of the array, and the $m$ superdiagonals within the band stored in the first $m$ rows of the array. Each column of the matrix is stored in the corresponding column of the array. For example, if $n=6$ and $m=2$, the storage scheme is

$$\begin{array}{llllll}\text{*}& \text{*}& a_{13}& a_{24}& a_{35}& a_{46}\\ \text{*}& a_{12}& a_{23}& a_{34}& a_{45}& a_{56}\\ a_{11}& a_{22}& a_{33}& a_{44}& a_{55}& a_{66}\end{array}$$

Elements in the top left corner of the array are not used. The following code assigns the matrix elements within the band to the correct elements of the array:

   Do 20 j = 1, n
      Do 10 i = max(1,j-m1+1), j
         a(i-j+m1,j) = matrix(i,j)
10    Continue
20 Continue

On exit: $A$ is overwritten by the corresponding elements of $L$, $D$ and $U$.

5: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01buf is called.

Constraint: $\mathbf{lda}\ge \mathbf{m1}$.

6: $\mathbf{w}\left(\mathbf{m1}\right)$ – Real (Kind=nag_wp) array Workspace

7: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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, $\mathbf{k}=〈\mathit{\text{value}}〉$ and $\mathbf{m1}-1=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\ge \mathbf{m1}-1$.

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

$\mathbf{ifail}=2$

The matrix $A$ is not positive definite. This is probably a result of rounding errors, giving an element of $D$ which is zero or negative. The failure occurs in the leading principal sub-matrix of order k.

$\mathbf{ifail}=3$

The matrix $A$ is not positive definite. This is probably a result of rounding errors, giving an element of $D$ which is zero or negative. The failure occurs in the complement.

$\mathbf{ifail}=-99$

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