NAG Library Routine Document

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 (dpbtrf).

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

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:     $\mathbf{n}$ – IntegerInput

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

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

3:     $\mathbf{kd}$ – IntegerInput

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) arrayInput

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 (dpbtrf).

5:     $\mathbf{ldab}$ – IntegerInput

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:     $\mathbf{id}$ – IntegerOutput

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:     $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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, $\mathbf{uplo}=〈\mathit{\text{value}}〉$.
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 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f03bhfe.f90)

10.2

Program Data

Program Data (f03bhfe.d)

10.3

Program Results

Program Results (f03bhfe.r)