NAG CL Interface
f03bnc (complex_​gen)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

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

2: $\mathbf{n}$ – Integer Input

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

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

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

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 f07arc.

4: $\mathbf{pda}$ – Integer Input

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 Integer Input

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

6: $\mathbf{d}$ – Complex * Output

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

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

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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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

10.2 Program Data

10.3 Program Results