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

order = 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:

order = Nag_RowMajor

Nag_ColMajor

2: $n$ – Integer Input

On entry:

n

, the order of the matrix

A

Constraint:

n > 0

3: $a [\dim]$ – const Complex Input

Note: the dimension, dim, of the array a must be at least

pda \times n

the

(i, j)

th element of the factorized form of the matrix

A

is stored in

$a [(j - 1) \times pda + i - 1]$ when $order = Nag_ColMajor$ ;
$a [(i - 1) \times pda + j - 1]$ when $order = Nag_RowMajor$ .

On entry: the

n \times n

matrix

A

in factorized form as returned by f07arc.

4: $pda$ – Integer Input

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

Constraint:

pda \geq n

5: $ipiv [n]$ – const Integer Input

On entry: the row interchanges used to factorize matrix

A

as returned by f07arc.

6: $d$ – Complex * Output

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

7: $id [2]$ – Integer Output

On exit: the exponents for the real and imaginary parts of the determinant. The determinant,

d = (d_{r}, d_{i})

, is returned as

d_{r} = D_{r} \times 2^{j}

and

d_{i} = D_{i} \times 2^{k}

, where

d = (D_{r}, D_{i})

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 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 $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .
NE_INT_2: On entry, $pda = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $pda \geq n$ .
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

The accuracy of the determinant depends on the conditioning of the original matrix. For a detailed error analysis, see page 107 of Wilkinson and Reinsch (1971).

8 Parallelism and Performance

f03bnc is not threaded in any implementation.

9 Further Comments

The time taken by f03bnc is approximately proportional to

n

10 Example

This example calculates the determinant of the complex matrix

(\begin{array}{lr} 1 & 1 + 2 i & 2 + 10 i \\ 1 + i & 3 i & −5 + 14 i \\ 1 + i & 5 i & −8 + 20 i \end{array}) .

f03bn: FL CL CPP AD

NAG CL Interfacef03bnc (complex_​gen)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
f03bnc (complex_gen)