NAG C Library Function Document

nag_det_complex_gen (f03bnc)

1
Purpose

nag_det_complex_gen (f03bnc) computes the determinant of a complex n by n matrix A. nag_zgetrf (f07arc) must be called first to supply the matrix A in factorized form.

2
Specification

#include <nag.h>
#include <nagf03.h>
void  nag_det_complex_gen (Nag_OrderType order, Integer n, const Complex a[], Integer pda, const Integer ipiv[], Complex *d, Integer id[], NagError *fail)

3
Description

nag_det_complex_gen (f03bnc) computes the determinant of a complex n by n matrix A that has been factorized by a call to nag_zgetrf (f07arc). The determinant of A is the product of the diagonal elements of U with the correct sign determined by the row interchanges.

4
References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

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 order=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: order=Nag_RowMajor or Nag_ColMajor.
2:     n IntegerInput
On entry: n, the order of the matrix A.
Constraint: n>0.
3:     a[dim] const ComplexInput
Note: the dimension, dim, of the array a must be at least pda×n.
The i,jth element of the factorized form of the matrix A is stored in
  • a[j-1×pda+i-1] when order=Nag_ColMajor;
  • a[i-1×pda+j-1] when order=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: pdan.
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=dr,di, is returned as dr=Dr×2j and di=Di×2k, where d=Dr,Di 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 3.7 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 value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n1.
NE_INT_2
On entry, pda=value and n=value.
Constraint: pdan.
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

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

nag_det_complex_gen (f03bnc) is not threaded in any implementation.

9
Further Comments

The time taken by nag_det_complex_gen (f03bnc) is approximately proportional to n.

10
Example

This example calculates the determinant of the complex matrix
1 1+2i 2+10i 1+i 3i -5+14i 1+i 5i -8+20i .  

10.1
Program Text

Program Text (f03bnce.c)

10.2
Program Data

Program Data (f03bnce.d)

10.3
Program Results

Program Results (f03bnce.r)