Evaluation of Determinant using partial pivoting

//

//  main.cpp

//  2015 New Start

//

//  Created by zr9558 on 13/2/15.

//  Copyright (c) 2015 zr9558. All rights reserved.

//

#include <iostream>

using namespace std;

#include<math.h>

// Algorithm 5.1 (Evaluation of determinant using partial pivoting), Algorithm Det_Partial_Pivoting.

const double eps=1e-10;

int max1( double b[],int k,int n) // return the index of maximum value from b[k] to b[n-1]

{

    double max=fabs(b[k]);int index=k;

    for( int i=k; i!=n; ++i)

    {

        if(fabs(b[i])>max) { index=i; max=b[i];}

    }

    return index;

}

int main()

{

    double a[100][100], b[100];// Calculate the determinant of the matrix a;

    int sign=1, n;

    cout<<"Enter the size of the matrix"<<endl;

    cin>>n;

    cout<<"Enter the Matrix"<<endl;// input the matrix;

    for( int i=0; i!=n; ++i)

        for( int j=0; j!=n; ++j)

            cin>>a[i][j];

 

    for(int k=0; k!=n; ++k)

    {

        for( int i=k; i!=n; ++i) b[i]=a[i][k];

        

        int j=max1(b,k,n);

        

        if( fabs(a[j][k])<eps)exit(0);

        

        if( j!=k) // if j!=k, then interchange the kth and jth rows and set sign=-sign; else exit the loop;

        {

            sign*=-1;// sign indicates the sign of the determinant when interchanges two rows;

            for( int i=k; i!=n; ++i)

            {

                double temp=a[j][i]; a[j][i]=a[k][i]; a[k][i]=temp;

            }

        }

        

        for(int j=k+1; j!=n; ++j)// Subtract a[j][k]/a[k][k] times the kth row from the jth row for j=k+1, k+2,..., n-1. This step makes a[k+1][k], a[k+2][k],..., a[n-1][k] zero.

        {

            double t1=a[j][k]/a[k][k];

            for( int i=0; i!=n; ++i)

                a[j][i]-=t1*a[k][i];

        }

    }

    

    double Value=sign;

    

    for( int i=0; i!=n; ++i)

        Value*=a[i][i];

    

    cout<<"The Determinant is "<<Value<<endl;

    

    return 0;

}