NAG Library Function Document

nag_det_complex_gen (f03bnc)

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:     n – IntegerInput

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

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

3:     a[$\mathit{dim}$] – 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:     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:     ipiv[n] – const IntegerInput

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

6:     d – Complex *Output

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

7:     id[$2$] – 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:     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, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
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.

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)