NAG Library Function Document

nag_det_real_band_sym (f03bhc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     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:     n – IntegerInput

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

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

4:     kd – IntegerInput

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

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

5:     ab[$\mathit{dim}$] – 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:     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:     d – double *Output

8:     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:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

NE_MAT_NOT_POS_DEF

The matrix $A$ is not positive definite.

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)