164 lines
5.5 KiB
Java
164 lines
5.5 KiB
Java
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/*
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This is a Java Program to Implement Strassen Matrix Multiplication Algorithm.
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This is a program to compute product of two matrices using Strassen Multiplication algorithm. Here the dimensions of matrices must be a power of 2.
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*/
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/**
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** Java Program to Implement Strassen Algorithm
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**/
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import java.util.Scanner;
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/** Class Strassen **/
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public class Strassen
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{
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/** Function to multiply matrices **/
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public int[][] multiply(int[][] A, int[][] B)
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{
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int n = A.length;
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int[][] R = new int[n][n];
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/** base case **/
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if (n == 1)
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R[0][0] = A[0][0] * B[0][0];
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else
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{
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int[][] A11 = new int[n/2][n/2];
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int[][] A12 = new int[n/2][n/2];
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int[][] A21 = new int[n/2][n/2];
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int[][] A22 = new int[n/2][n/2];
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int[][] B11 = new int[n/2][n/2];
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int[][] B12 = new int[n/2][n/2];
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int[][] B21 = new int[n/2][n/2];
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int[][] B22 = new int[n/2][n/2];
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/** Dividing matrix A into 4 halves **/
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split(A, A11, 0, 0);
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split(A, A12, 0, n/2);
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split(A, A21, n/2, 0);
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split(A, A22, n/2, n/2);
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/** Dividing matrix B into 4 halves **/
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split(B, B11, 0, 0);
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split(B, B12, 0, n/2);
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split(B, B21, n/2, 0);
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split(B, B22, n/2, n/2);
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/*
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M1 = (A11 + A22)(B11 + B22)
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M2 = (A21 + A22) B11
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M3 = A11 (B12 - B22)
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M4 = A22 (B21 - B11)
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M5 = (A11 + A12) B22
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M6 = (A21 - A11) (B11 + B12)
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M7 = (A12 - A22) (B21 + B22)
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*/
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int [][] M1 = multiply(add(A11, A22), add(B11, B22));
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int [][] M2 = multiply(add(A21, A22), B11);
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int [][] M3 = multiply(A11, sub(B12, B22));
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int [][] M4 = multiply(A22, sub(B21, B11));
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int [][] M5 = multiply(add(A11, A12), B22);
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int [][] M6 = multiply(sub(A21, A11), add(B11, B12));
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int [][] M7 = multiply(sub(A12, A22), add(B21, B22));
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/*
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C11 = M1 + M4 - M5 + M7
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C12 = M3 + M5
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C21 = M2 + M4
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C22 = M1 - M2 + M3 + M6
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*/
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int [][] C11 = add(sub(add(M1, M4), M5), M7);
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int [][] C12 = add(M3, M5);
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int [][] C21 = add(M2, M4);
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int [][] C22 = add(sub(add(M1, M3), M2), M6);
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/** join 4 halves into one result matrix **/
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join(C11, R, 0, 0);
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join(C12, R, 0, n/2);
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join(C21, R, n/2, 0);
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join(C22, R, n/2, n/2);
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}
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/** return result **/
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return R;
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}
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/** Funtion to sub two matrices **/
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public int[][] sub(int[][] A, int[][] B)
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{
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int n = A.length;
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int[][] C = new int[n][n];
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++)
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C[i][j] = A[i][j] - B[i][j];
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return C;
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}
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/** Funtion to add two matrices **/
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public int[][] add(int[][] A, int[][] B)
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{
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int n = A.length;
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int[][] C = new int[n][n];
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++)
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C[i][j] = A[i][j] + B[i][j];
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return C;
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}
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/** Funtion to split parent matrix into child matrices **/
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public void split(int[][] P, int[][] C, int iB, int jB)
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{
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for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
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for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
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C[i1][j1] = P[i2][j2];
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}
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/** Funtion to join child matrices intp parent matrix **/
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public void join(int[][] C, int[][] P, int iB, int jB)
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{
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for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
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for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
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P[i2][j2] = C[i1][j1];
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}
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/** Main function **/
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public static void main (String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Strassen Multiplication Algorithm Test\n");
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/** Make an object of Strassen class **/
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Strassen s = new Strassen();
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System.out.println("Enter order n :");
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int N = scan.nextInt();
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/** Accept two 2d matrices **/
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System.out.println("Enter N order matrix 1\n");
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int[][] A = new int[N][N];
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for (int i = 0; i < N; i++)
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for (int j = 0; j < N; j++)
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A[i][j] = scan.nextInt();
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System.out.println("Enter N order matrix 2\n");
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int[][] B = new int[N][N];
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for (int i = 0; i < N; i++)
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for (int j = 0; j < N; j++)
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B[i][j] = scan.nextInt();
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int[][] C = s.multiply(A, B);
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System.out.println("\nProduct of matrices A and B : ");
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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System.out.print(C[i][j] +" ");
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System.out.println();
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}
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}
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}
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/*
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Enter order n :
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4
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Enter N order matrix 1
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2 3 1 6
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4 0 0 2
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4 2 0 1
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0 3 5 2
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Enter N order matrix 2
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3 0 4 3
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1 2 0 2
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0 3 1 4
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5 1 3 2
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Product of matrices A and B :
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39 15 27 28
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22 2 22 16
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19 5 19 18
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13 23 11 30
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