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

On entry: the upper triangle of the $n\times n$ symmetric band matrix $A$, with the diagonal of the matrix stored in the $(m+1)$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 matrix elements within the band can be assigned to the correct elements of the array using the following code:

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

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 $0$, $-1$ 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, $\mathbf{k}=⟨\mathit{\text{value}}⟩$ 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