nag_det_real_gen (f03bac) (PDF version)
f03 Chapter Contents
f03 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_det_real_gen (f03bac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_det_real_gen (f03bac) computes the determinant of a real n by n matrix A. nag_dgetrf (f07adc) must be called first to supply the matrix A in factorized form.

2  Specification

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

3  Description

nag_det_real_gen (f03bac) computes the determinant of a real n by n matrix A that has been factorized by a call to nag_dgetrf (f07adc). 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 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 doubleInput
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_dgetrf (f07adc).
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_dgetrf (f07adc).
6:     ddouble *Output
7:     idInteger *Output
On exit: the determinant of A is given by d×2.0id. It is given in this form to avoid overflow or underflow.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n1.
On entry, pda=value and n=value.
Constraint: pdan.
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.
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_real_gen (f03bac) is approximately proportional to n.

9  Example

This example computes the LU factorization with partial pivoting, and calculates the determinant, of the real matrix
33 16 72 -24 -10 -57 -8 -4 -17 .

9.1  Program Text

Program Text (f03bace.c)

9.2  Program Data

Program Data (f03bace.d)

9.3  Program Results

Program Results (f03bace.r)

nag_det_real_gen (f03bac) (PDF version)
f03 Chapter Contents
f03 Chapter Introduction
NAG C Library Manual

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