INNOVATION: Algorithm For Solving Determinant Using Echelon Form

Algorithm Of solving Determinant using Echelon Form

As we there is general method available for solving determinant of given matrix but that is not efficient. But if we solve that through Echelon form method that it is quite easier to get determinant.
Because if your able to get Echelon form of given matrix that just multiply diagonal element of that echelon form matrix and that is answer of given matrix determinant.

As we can see in graph that if you take general algorithm for solving determinant than it take too much time for higher dimension matrix at that time it is efficient to use EF algorithm for solving determinant computerized.

import java.util.Scanner;

class Matrix
{
 private int Row;
 private int Column;
 private float [][]Elements;
        private float Determinat;
 
 public Matrix(int No_Row,int No_Column)
 {
  Row=No_Row;
  Column=No_Column;
  Elements = new float[No_Row][No_Column];
                Determinat=0; 
 }
 
 public void SetElements()
 {
  Scanner x=new Scanner(System.in);
  
  for(int i=0;i<Row;i++)
  {
   for(int j=0;j<Column;j++)
   {
    System.out.print("\nENTER ["+i+"]["+j+"] ELEMENT OF MATRIX :- ");
    Elements[i][j]=x.nextFloat();
   }
  }
 }
 
 
 private void Algorithms_of_EF()
 {
   int R=0;
  for(int i=0;i<Column;i++)
  {
   if(R<Row)
   {  
    if(Elements[R][i]!=0)
    {
     
     for(int k=R+1;k<Row;k++)
     {
      float []Array=new float[Column];

for(int l=0;l<Column;l++)
      {
       Array[l]=Elements[k][l] - ((Elements[R][l]*Elements[k][i])/Elements[R][i]);
      }
      for(int l=0;l<Column;l++)
      {
       Elements[k][l]=Array[l];
      }
     }
     R++; 
    }
    else
    {

int Temp=-1;
     for(int j=(Row-1);j>R;j--)
     {
      if(Elements[j][i]!=0)
      {
       Temp=j;
       break;
      }
     }

if(Temp!=-1)
     {
      for(int f=0;f<Column;f++)
      {
       float Temp1= Elements[Temp][f];
       Elements[Temp][f]=Elements[R][f];
       Elements[R][f]=Temp1;
      }
      
     
      for(int k=R+1;k<Row;k++)
      {
       float []Array=new float[Column];
      
      
       for(int l=0;l<Column;l++)
       {
        Array[l]=Elements[k][l] - ((Elements[R][l]*Elements[k][i])/Elements[R][i]);
       }
       for(int l=0;l<Column;l++)
       {
        Elements[k][l]=Array[l];
       }
      }
      R++;
     }
    }
   }
  }

}
 
    public float GET_DETERMINAT_OF_MATRIX()
    {
        if(Row==Column)
        {
            Algorithms_of_EF();
            if(Row==Column)
            {
                Determinat=1;
                for(int i=0;i<Row;i++)
                {
                    Determinat=Determinat*Elements[i][i];
                }
            }
            return Determinat;
        }
        else
        {
            System.out.println("\nDETERMINAT OF THIS MATRIX MIGHT NOT POSSIBLE.\n");
            return -1;
        }
    }
 
 
 public void Display()
 {
  System.out.println("\n\n");
  for(int i=0;i<Row;i++)
  {
   for(int j=0;j<Column;j++)
   {
    if(Elements[i][j]==(-0.0)){Elements[i][j]=0;}
    System.out.print(Elements[i][j]+"  ");
   }
   System.out.println();
  }
 }
}

INNOVATION

Saturday, 8 August 2015

Algorithm For Solving Determinant Using Echelon Form

Algorithm Of solving Determinant using Echelon Form

Main Class

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