ArrayIndex OutOfBoundsException?

[Ellen Zhao]

Here is a class that solves linear equation system with LU-decomposition algorithmus. I got the error message when ran it:
Please enter an integer as the size of the matrix:
5
java.lang.ArrayIndex OutOfBoundsException: 5
at NB2A71.main(NB2A71.java:31)
Press any key to continue...
The source code is as following:

 import java.io.*;
import java.util.*;
class NB2A71{

public static void main(String[] args){
int  size;
int[] p;
double[][] a;
double[] b, result;                  
double sum = 0;
double h;

System.out.println("Please enter an integer as the size of the matrix: ");
        InputStreamReader ir = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ir);

try {
      String input;
      StringTokenizer stn;
      input = br.readLine();
      
      size = Integer.parseInt(input);
      a = new double[size][size];
      b = new double[size];
      p = new int[size];
      result = new double[size];
            
      for ( int i = 1; i <= size; i ++ ){
      for (  int j = 1; j <= size; j ++ ){
      a[i][j] = 1 / ( i + j - 1 );
      sum += j / ( i + j - 1 );
      }
      b[i] = sum;
      }
      
      for( int k = 1; k < size; k ++ )
      {
      double max = 0;
      p[k] = 0;
      for( int i = k; i <= size; i ++ )
      {
      double s = 0;
      for ( int j = k; j <= size; j ++ )
      {
      s += Math.abs( a[i][j] );
      }
      if ( s == 0 ) System.out.println( "STOP" );
      double q = Math.abs( a[i][k] / s );
      if ( q > max )
      {
      max = q;
      p[k] = i;
      }
      }
      if ( max == 0 ) System.out.println( "STOP" );
      if ( p[k] != k )
      {
      for ( int j = 1; j <= size; j ++ )
      {
      h = a[k][j];
      a[k][j] = a[p[k]][j];
      a[p[k]][j] = h;
      }
      for ( int i = k + 1; i <= size; i ++ )
      {
      a[i][k] /= a[k][k];
      for ( int j = k + 1; j <= size; j ++ )
      {
      a[i][j] -= a[i][k] * a[k][j];
      }
      }
      }
      }
      if ( a[size][size] == 0 ) System.out.println("STOP");
      
      result[size] = b[size]/a[size][size];
      System.out.println("x" + (size) + " = " + result[size]);
      
      
      
      for(int i = size; i > 0; i --){
      double sum1 = 0;
      for (int j = i + 1; j <= size; j ++ ){
      sum1 += a[i][j]*result[j];
      }
      result[i] = ( b[i] - sum1 ) / a[i][i];
      System.out.println("x" + i + " = " + result[i]);
      }
      
      for ( int i = 0; i < size; i ++ ){
      for ( int j = 0; j < size; j ++ ){
      System.out.print(a[i][j]);
      System.out.print(" ");
      }
      System.out.print("  ");
      System.out.print(b[i]);
      System.out.print("  ");
      System.out.print(result[i]);
        System.out.println();
    }
      
}
  catch(Exception e) {
             e.printStackTrace();
          }
        }
    } 

In this program, the initial values of a[i][j] and b[i] are specified here:

      for ( int i = 1; i <= size; i ++ ){
      for (  int j = 1; j <= size; j ++ ){
      a[i][j] = 1 / ( i + j - 1 );
      sum += j / ( i + j - 1 );
      }
      b[i] = sum;
      }  

How should I modify the code so that it can run? Thank you very much in advance!

[Michael Ernest]

Arrays start at zero, so that valid index range of your arrays will be 0 through 4. Modify the loop so that 5 cannot be a counter value.