NAG FL Interface
f03bhf (real_​band_​sym)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – Character(1) Input

On entry: indicates whether the upper or lower triangular part of $A$ was stored and how it was factorized. This should not be altered following a call to f07hdf.

$\mathbf{uplo}=\text{'U'}$

The upper triangular part of $A$ was originally stored and $A$ was factorized as $U^{\mathrm{T}}U$ where $U$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

The lower triangular part of $A$ was originally stored and $A$ was factorized as $L{L}^{\mathrm{T}}$ where $L$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

2: $\mathbf{n}$ – Integer Input

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

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

3: $\mathbf{kd}$ – Integer Input

On entry: $k_d$, the number of superdiagonals or subdiagonals of the matrix $A$.

Constraint: $\mathbf{kd}\ge 0$.

4: $\mathbf{ab}\left(\mathbf{ldab},*\right)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array ab must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the Cholesky factor of $A$, as returned by f07hdf.

5: $\mathbf{ldab}$ – Integer Input

On entry: the first dimension of the array ab as declared in the subprogram from which f03bhf is called.

Constraint: $\mathbf{ldab}\ge \mathbf{kd}+1$.

6: $\mathbf{d}$ – Real (Kind=nag_wp) Output

7: $\mathbf{id}$ – Integer Output

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.

8: $\mathbf{ifail}$ – 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, $\mathbf{uplo}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{uplo}=\text{'L'}$ or $\text{'U'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

$\mathbf{ifail}=3$

On entry, $\mathbf{kd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{kd}\ge 0$.

$\mathbf{ifail}=5$

On entry, $\mathbf{ldab}=〈\mathit{\text{value}}〉$ and $\mathbf{kd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldab}\ge \mathbf{kd}+1$.

$\mathbf{ifail}=6$

The matrix $A$ is not positive definite.

$\mathbf{ifail}=-99$

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