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Thread: Help with Fast Matrix Exponentiation

  1. #1
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    Default Help with Fast Matrix Exponentiation

    hey everyone,

    I feel like I am close to the answer, but I'm just missing something little. What I'm supposed to do, basically, is come up with a program that allows me to increase matrices exponentially. My problem lies when I want to do anything higher than a power of two. For example, when I raise it to the power of 3, it does it by 4 instead. If I do it by 4, it does it by 6. Can anyone help me? I feel like it's something small that I am overlooking, but I am not able to figure it out.

    	import java.io.*;
    	import java.util.Scanner;
    	public class Matrix {
    	  static int[][] mult(int[][] X, int[][] Y) {
    	  int Z[][] = new int[2][2];
    	  Z[0][0] = X[0][0]*Y[0][0] + X[0][1]*Y[1][0];
    	  Z[0][1] = X[0][0]*Y[0][1] + X[0][1]*Y[1][1];
    	  Z[1][0] = X[1][0]*Y[0][0] + X[1][1]*Y[0][1];
    	  Z[1][1] = X[1][0]*Y[1][0] + X[1][1]*Y[1][1];
    	  return Z;
    	  }
    	  public static void main(String argv[]) {
    	    // create a scanner for interactive input
    	    Scanner scin = new Scanner(System.in);
    	    int matrix[][] = new int[2][2];
    	    int B[][] = new int[2][2];
    	    int A[][] = new int[2][2];
    	    int k,n;
    	    // Ask for the matrix
    	    System.out.print("[ M[0][0] M[0][1] ] =  ");
    	    matrix[0][0] = scin.nextInt(); matrix[0][1] = scin.nextInt();
    	    System.out.print("[ M[1][0] M[1][1] ] =  ");
    	    matrix[1][0] = scin.nextInt(); matrix[1][1] = scin.nextInt();
    	    System.out.print("n =  ");
    	    n = scin.nextInt();
    	    k = n; B = matrix;
    	    if ((k==1)) 
    	    {
    	    	A = matrix;
    	    }
    	    	else 
    	    {
    	    		int m=1;
    	    		int C[][]=matrix;
    	    		C[0][0]=1;C[0][1]=2;
    	    		C[1][0]=3;C[1][1]=4;
    	      while(m<n)
    	      {
    	    	  if(m==n)  
    	    	  {
    	    		  break;
    	    	  }
    	    	  m++;
     
    	    	  A[0][0] = (C[0][0]*matrix[0][0])+(C[1][0]*matrix[0][1]); A[0][1] = (C[0][0]*matrix[0][1])+(C[0][1]*matrix[1][1]);
    	    	  A[1][0] = (C[1][0]*matrix[0][0])+(C[1][1]*matrix[1][0]); A[1][1] = (C[1][0]*matrix[0][1])+(C[1][1]*matrix[1][1]);
     
    	    	  C[0][0]=A[0][0];C[0][1]=A[0][1];
    	    	  C[1][0]=A[1][0];C[1][1]=A[1][1];
     
     
     
    	      }
    	    }
    	    while(k > 0) 
    	    {
    	      B= mult(B,B);
    	      if ((k%1) == 1) A = mult(A,B);
    	      k = k/2;
    	}
    	System.out.println( A[0][0] + "  " + A[0][1]);
    	  System.out.println( A[1][0] + "  " + A[1][1]);
    	}
    	}


  2. #2
    Super Moderator Norm's Avatar
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    Default Re: Help with Fast Matrix Exponentiation

    Can you post the program's output, explain what is wrong with it and show what the output should be?

    Also please post pseudo code (or a detailed description) for the algorithm that the code is supposed to be following.

    NOTE: This code has a poor coding style: putting multiple statements on the same line.
    Last edited by Norm; September 18th, 2012 at 01:06 PM.
    If you don't understand my answer, don't ignore it, ask a question.

  3. #3
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    Default Re: Help with Fast Matrix Exponentiation

    Ignore this, I found out what had happened from someone in my class about two hours later. Sorry for prematurely posting.

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