代码实现：
/**
* 矩阵乘法求解
* @author Administrator
*
*/
public class Strassen {
public static final int NUMBER = 4;
private static int[][] A;
private static int[][] B; public Strassen() {
A = new int[NUMBER][NUMBER];
B = new int[NUMBER][NUMBER];
} public int[][] starssen(int[][] A, int[][] B) {
int divide_length = A.length / 2;
// 定义一些中间变量
int[][] result = new int[A.length][A.length]; int[][] M1 = new int[divide_length][divide_length];
int[][] M2 = new int[divide_length][divide_length];
int[][] M3 = new int[divide_length][divide_length];
int[][] M4 = new int[divide_length][divide_length];
int[][] M5 = new int[divide_length][divide_length];
int[][] M6 = new int[divide_length][divide_length];
int[][] M7 = new int[divide_length][divide_length]; int[][] C11 = new int[divide_length][divide_length];
int[][] C12 = new int[divide_length][divide_length];
int[][] C21 = new int[divide_length][divide_length];
int[][] C22 = new int[divide_length][divide_length]; int[][] A11 = new int[divide_length][divide_length];
int[][] A12 = new int[divide_length][divide_length];
int[][] A21 = new int[divide_length][divide_length];
int[][] A22 = new int[divide_length][divide_length]; int[][] B11 = new int[divide_length][divide_length];
int[][] B12 = new int[divide_length][divide_length];
int[][] B21 = new int[divide_length][divide_length];
int[][] B22 = new int[divide_length][divide_length]; if (A.length == 2) {
result = multi(A, B, A.length);
} else {
// 首先将矩阵A,B分为4块
for (int i = 0; i < divide_length; ++i) {
for (int j = 0; j < divide_length; ++j) {
A11[i][j] = A[i][j];
A12[i][j] = A[i][j + divide_length];
A21[i][j] = A[i + divide_length][j];
A22[i][j] = A[i + divide_length][j + divide_length]; B11[i][j] = B[i][j];
B12[i][j] = B[i][j + divide_length];
B21[i][j] = B[i + divide_length][j];
B22[i][j] = B[i + divide_length][j + divide_length];
}
} // 计算M1
M1 = starssen(A11, sub(B12, B22, divide_length));
// 计算M2
M2 = starssen(add(A11, A12, divide_length), B22);
// 计算M3
M3 = starssen(add(A21, A22, divide_length), B11);
// 计算M4
M4 = starssen(A22, sub(B21, B11, divide_length));
// 计算M5
M5 = starssen(add(A11, A22, divide_length), add(B11, B22, divide_length));
// 计算M6
M6 = starssen(sub(A12, A22, divide_length), add(B21, B22, divide_length));
// 计算M7
M7 = starssen(sub(A11, A21, divide_length), add(B11, B12, divide_length)); // 计算C11,C12,C21,C22
C11 = add(sub(add(M5, M4, divide_length), M2, divide_length), M6, divide_length);
C12 = add(M1, M2, divide_length);
C21 = add(M3, M4, divide_length);
C22 = sub(sub(add(M5, M1, divide_length), M3, divide_length), M7, divide_length); // 合并C11,C12,C21,C22到C
for (int i = 0; i < divide_length; ++i) {
for (int j = 0; j < divide_length; ++j) {
result[i][j] = C11[i][j];
result[i][j + divide_length] = C12[i][j];
result[i + divide_length][j] = C21[i][j];
result[i + divide_length][j + divide_length] = C22[i][j];
}
}
}
return result;
} public static int[][] initial() {
int [][] result = new int[NUMBER][NUMBER];
for (int i = 0; i < NUMBER; ++i) {
for (int j = 0; j < NUMBER; ++j) {
// 采用Math生成1~10之间的随机数
result[i][j] = (int)(Math.random()*10);
}
}
return result;
} public void output(int[][] result) {
for (int b[] :result) {
for (int temp : b) {
System.out.print(temp + " ");
}
System.out.println();
}
} /**
* 蛮力求解矩阵乘法
* @param a：矩阵a n*n
* @param b：矩阵b n*n
* @param n： 矩阵大小
*/
public int[][] multi(int a[][], int b[][], int n) {
int result[][] = new int[n][n];
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
result[i][j] = 0;
for (int k = 0; k < n; ++k) {
result[i][j] += a[i][k] * b[k][j];
}
}
}
return result;
} /**
* 矩阵加法
* @param a
* @param b
* @param n
* @return
*/
public int[][] add(int a[][], int b[][], int n) {
int result[][] = new int[n][n];
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
result[i][j] = a[i][j] + b[i][j];
}
}
return result;
} /**
* 矩阵减法
* @param a
* @param b
* @param n
* @return
*/
public int[][] sub(int a[][], int b[][], int n) {
int result[][] = new int[n][n];
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
result[i][j] = a[i][j] - b[i][j];
}
}
return result;
} public static void main(String[] args) {
Strassen s = new Strassen();
A = initial();
B = initial();
s.output(A);
System.out.println("----------------------");
s.output(B);
System.out.println("----------------------"); s.output(s.multi(A, B, NUMBER));
System.out.println("----------------------"); int K[][] = new int[2][2];
K = s.starssen(A, B);
s.output(K);
}
}