NAG Library Function Document

nag_det_complex_gen (f03bnc)

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:    $\mathbf{n}$ – IntegerInput

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

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

3:    $\mathbf{a}\left[\mathit{dim}\right]$ – const ComplexInput

Note: the dimension, dim, of the array a must be at least $\mathbf{pda}\times \mathbf{n}$.

The $\left(i,j\right)$th element of the factorized form of the matrix $A$ is stored in

• $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $n$ matrix $A$ in factorized form as returned by nag_zgetrf (f07arc).

4:    $\mathbf{pda}$ – IntegerInput

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

Constraint: $\mathbf{pda}\ge \mathbf{n}$.

5:    $\mathbf{ipiv}\left[\mathbf{n}\right]$ – const IntegerInput

On entry: the row interchanges used to factorize matrix $A$ as returned by nag_zgetrf (f07arc).

6:    $\mathbf{d}$ – Complex *Output

On exit: the mantissa of the real and imaginary parts of the determinant.

7:    $\mathbf{id}\left[2\right]$ – IntegerOutput

On exit: the exponents for the real and imaginary parts of the determinant. The determinant, $d=\left(d_r,d_i\right)$, is returned as $d_r=D_r\times 2^j$ and $d_i=D_i\times 2^k$, where $\mathbf{d}=\left(D_r,D_i\right)$ and $j$ and $k$ are stored in the first and second elements respectively of the array id on successful exit.

8:    $\mathbf{fail}$ – 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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

NE_INT_2

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \mathbf{n}$.

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_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.

NE_SINGULAR

The matrix $A$ is approximately singular.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f03bnce.c)

10.2

Program Data

Program Data (f03bnce.d)

10.3

Program Results

Program Results (f03bnce.r)