NAG Library Function Document

nag_det_real_band_sym (f03bhc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{uplo}$ – Nag_UploTypeInput

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 nag_dpbtrf (f07hdc).

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

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

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

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

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{kd}$ – IntegerInput

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

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

5:    $\mathbf{ab}\left[\mathit{dim}\right]$ – const doubleInput

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

On entry: the Cholesky factor of $A$, as returned by nag_dpbtrf (f07hdc).

6:    $\mathbf{pdab}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) of the matrix in the array ab.

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

7:    $\mathbf{d}$ – double *Output

8:    $\mathbf{id}$ – 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.

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

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

NE_INT_2

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_MAT_NOT_POS_DEF

The matrix $A$ is not positive definite.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 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 (f03bhce.c)

10.2

Program Data

Program Data (f03bhce.d)

10.3

Program Results

Program Results (f03bhce.r)