nag_det_complex_gen (f03bnc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_det_complex_gen (f03bnc)

+ Contents

    1  Purpose
    7  Accuracy

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:     orderNag_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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     nIntegerInput
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:     pdaIntegerInput
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:     dComplex *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:     failNagError *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 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.
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  Further Comments

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

9  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 .

9.1  Program Text

Program Text (f03bnce.c)

9.2  Program Data

Program Data (f03bnce.d)

9.3  Program Results

Program Results (f03bnce.r)


nag_det_complex_gen (f03bnc) (PDF version)
f03 Chapter Contents
f03 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012