在过去的几个小时里，我一直在尝试实现 Strassen 的矩阵乘法算法，并且在获得正确的产品时遇到了麻烦。我认为我的辅助函数之一（helpSub、createProd、helpProduct）可能是我的 strass2 函数的问题或格式（命令顺序等）。任何提示都会受到欢迎，因为我完全被难住了。我一直在使用两个 4 x 4 矩阵作为测试矩阵。我已经尝试了很多我在互联网上看到的 p1-p7 和 c1-c4 变体，但似乎都没有。下面是我创建的课程。
/* @author williamnewman
public class strassen2 {
//Main Strassen multiplication function
//BASE CASE:
int [][] strass2(int[][] x, int[][]y){
if(x.length == 1 && y.length == 1){
System.out.println("Donezo");
int [][] nu = new int[1][1];
nu[0][0] = x[0][0] * y[0][0];
return nu;
}
else{
int[][] a,b,c,d,e,f,g,h;
int dim = x.length/2;
//Dividing two matrices into 8 sub matrices
System.out.println("A<B<C");
a = helpSub(0,0,x);
C(a);
b = helpSub(0,dim,x);
C(b);
c = helpSub(dim,0,x);
C(c);
d = helpSub(dim,dim,x);
C(d);
e = helpSub(0,0,y);
C(e);
f = helpSub(0,dim,y);
C(f);
g = helpSub(dim,0,y);
C(g);
h = helpSub(dim,dim,y);
C(h);
int[][] p1,p2,p3,p4,p5,p6,p7;
//Creating p1-p7
/
p1 = strass2(a,subtract(f,h));
p2 = strass2(h, add(a,b));
p3 = strass2(e,add(c,d));
p4 = strass2(d,subtract(g,e));
p5 = strass2(add(a,d),add(e,h));
p6 = strass2(subtract(b,d),add(g,h));
p7 = strass2(subtract(a,c),add(e,f));
int [][] prod;
int [][] c1,c2,c3,c4;
//Creating c1-c4
c1 = subtract(add(p6,p5),subtract(p4,p2));
c2 = add(p1,p2);
c3 = add(p3,p4);
c4 = subtract(add(p1,p5),subtract(p3,p7));
C(c1);
System.out.println("C1::");
C(c2);
System.out.println("C2::");
C(c3);
System.out.println("C3::");
C(c4);
System.out.println("C4::");
//CREATES PRODUCT MATRIX
prod = createProd(c1,c2,c3,c4);
return prod;
}
}
//Creates product matrix from c1-c4
int[][] createProd(int[][] c1, int[][] c2, int[][] c3, int[][] c4){
int[][] product = new int[c1.length*2][c1.length*2];
int mid = c1.length;
int fin = c1.length * 2;
helpProduct(0,0,mid,mid,product,c1);
helpProduct(0,mid,mid,fin,product,c2);
helpProduct(mid,0,fin,mid,product,c3);
helpProduct(mid,mid,fin,fin,product,c4);
System.out.println();
System.out.println("PRODUCT::!:");
C(product);
return product;
}
//Helper function to create larger matrix from submatrices
void helpProduct(int x, int y, int z1, int z2,int[][] product, int[][] a1){
int indR = 0;
int indC = 0;
for(int i = x; i < z1; i++){
indC = 0;
for(int j = y; j < z2; j++){
product[i][j] = a1[indR][indC];
indC++;
}
indR++;
}
}
int[][] helpSub(int x, int y, int[][] mat){
int[][] sub = new int[mat.length/2][mat.length/2];
for(int i1 = 0, i2=x; i1 < (mat.length/2); i1++, i2++)
for(int j1 = 0, j2=y; j1<(mat.length/2); j1++, j2++)
{
sub[i1][j1] = mat[i2][j2];
// System.out.println(sub[i1][j1]);
}
return sub;
}
//Normal Matrix Multiplication Function
int[][] multiply(int[][]a,int[][]b){
MM nu = new MM(a,b);
return nu.product;
}
//Adds one matrix to the next
int[][] add(int[][]a, int[][]b){
int [][] nu = new int[a.length][a[0].length];
for(int i = 0; i < a.length; i++){
for(int j = 0; j < a[i].length;j++){
nu[i][j] = a[i][j] + b[i][j];
}
}
return nu;
}
//Subtracts second matrix from the first
int[][] subtract(int[][] a, int[][] b){
int [][] sub = new int[a.length][a.length];
//System.out.println("made it");
for(int i = 0; i < a.length; i++){
for(int j = 0; j < a[i].length;j++){
sub[i][j] = a[i][j] - b[i][j];
}
}
return sub;
}
//Prints the matrix
void C(int[][] product){
for(int i = 0; i <product.length; i++){
for(int j = 0; j < product[i].length; j++){
System.out.print(product[j][i] + " ");
}
System.out.println();
}
}
}
如果有任何令人困惑的地方，请告诉我，我会更新问题！
这是主要功能::
public static void main(String[] args) {
int [][]a = {{1,2,3,4},
{4,3,2,1},
{1,2,3,4},
{4,3,2,1}};
int [][]b = {{3,4,5,6},
{3,4,5,6},
{5,4,3,2},
{5,4,3,2}
};
MM a1 = new MM(a,b);
a1.C();
int[][] prod;
System.out.println("----");
strassen2 a2 = new strassen2();
prod = a2.strass2(a,b);
a2.C(prod);
}
}
以下是目前的结果（预期结果是显示的第一个 4x4 矩阵，实际结果是显示的最后一个 4x4 矩阵）：
EXPECTED:
44 40 36 32
36 40 44 48
44 40 36 32
36 40 44 48
----
ACTUAL::
70 78 50 42
86 86 34 34
30 38 30 38
38 54 38 54
我很确定我的 helpSub() 函数可以正常工作，因为它们产生了更正的啊。但是，我在 strass2 递归调用中使用的参数可能存在问题。很抱歉，如果它不够具体，我只是对此有点筋疲力尽，并且很好奇是否有人看到任何明显的问题。