c - 段错误 - 施特拉森矩阵乘法

Question

我是新手，我尝试实现 Strassen 算法来将两个 NxN 矩阵相乘。我目前正在研究偶数维度。对于 N 大于 4 的值，我遇到了段错误。

调试后我发现段错误是在第一次调用乘法函数之前和显示两个矩阵之后立即遇到的。

感谢任何帮助。

非常感谢!

#define N 8
typedef struct matrix
{
    int rs;
    int re;
    int cs;
    int ce;
    int a[N][N];
}matrix;

void display(matrix);
matrix multiply(matrix, matrix);
matrix add(matrix, matrix);
matrix sub(matrix, matrix);

int main(int argc, char *argv[])
{
    matrix m1;
    matrix m2;
    matrix result;

    printf("Enter the values for matrix one: ");
    for (int i=0; i<N; i++ )
    {
        for (int j=0; j<N ; j++)
            scanf(" %d", &m1.a[i][j]);
    }

    printf("Enter the values for matrix two: ");    
    for (int i=0; i<N; i++ )
    {
        for (int j=0; j<N ; j++)
            scanf(" %d", &m2.a[i][j]);
    }

    m1.rs = m2.rs = m1.cs = m2.cs = 0;
    m1.re = m2.re = m1.ce = m2.ce = N-1;

    display(m1);
    display(m2);
    **I believe the first call to multiply is not executed and there's a segmentation fault here.**
    result = multiply(m1, m2);

    display(result);

}

void display(matrix mat)
{
    for(int i=0;i<=mat.re;i++)
    {
        for(int j=0;j<=mat.ce;j++)
            printf("%d ", mat.a[i][j]);
        printf("\n");
    }
    printf("\n");
}
matrix multiply(matrix m1, matrix m2)
{

    int dimension = m1.re - m1.rs + 1;

    matrix result;
    result.rs = result.cs = 0;
    result.re = result.ce = dimension -1;

    if (dimension <=2)
    {
        matrix m3 = m1;

        int a, b, c, d, e, f, g, h;

        a = m1.a[m1.rs][m1.cs];
        b = m1.a[m1.rs][m1.cs + 1];
        c = m1.a[m1.rs + 1][m1.cs];
        d = m1.a[m1.rs + 1][m1.cs + 1];

        e = m2.a[m2.rs][m2.cs];
        f = m2.a[m2.rs][m2.cs + 1];
        g = m2.a[m2.rs + 1][m2.cs];
        h = m2.a[m2.rs + 1][m2.cs + 1];

        m3.a[m3.rs][m3.cs] = a*e + b*g;
        m3.a[m3.rs][m3.cs+1] = a*f + b*h;
        m3.a[m3.rs+1][m3.cs] = c*e + d*g;
        m3.a[m3.rs+1][m3.cs+1] = c*f + d*h;

        return m3;
    }
    else
    {
        matrix A, B, C, D, E, F, G, H;
        matrix P1, P2, P3, P4, P5, P6, P7;
        matrix R1, R2, R3, R4;

        A = B = C = D = m1;
        E = F = G = H = m2;

        A.rs = m1.rs;
        A.re = m1.re/2;
        A.cs = m1.cs;
        A.ce = m1.ce/2;

        B.rs = m1.rs;
        B.re = m1.re/2;
        B.cs = (m1.ce/2)+1;
        B.ce = m1.ce;

        C.rs = (m1.re/2)+1;
        C.re = m1.re;
        C.cs = m1.cs;
        C.ce = m1.ce/2;

        D.rs = (m1.re/2)+1;
        D.re = m1.re;
        D.cs = (m1.ce/2)+1;
        D.ce = m1.ce;

        E.rs = m2.rs;
        E.re = m2.re/2;
        E.cs = m2.cs;
        E.ce = m2.ce/2;

        F.rs = m2.rs;
        F.re = m2.re/2;
        F.cs = (m2.ce/2)+1;
        F.ce = m2.ce;

        G.rs = (m2.re/2)+1;
        G.re = m2.re;
        G.cs = m2.cs;
        G.ce = m2.ce/2;

        H.rs = (m2.re/2)+1;
        H.re = m2.re;
        H.cs = (m2.ce/2)+1;
        H.ce = m2.ce;

        P1 = multiply(A, sub(F, H));    
        P2 = multiply(add(A, B), H);    
        P3 = multiply(add(C, D), E);
        P4 = multiply(D, sub(G, E));
        P5 = multiply(add(A, D), add(E, H));
        P6 = multiply(sub(B, D), add(G, H));
        P7 = multiply(sub(A,C), add(E, F));


        R1 = add(add(P5, P6), sub(P4,P2));
        R2 = add(P1, P2);
        R3 = add(P3, P4);
        R4 = sub(sub(add(P1,P5), P3), P7);

        int m1_i, m1_j;
        int i,j;

        for(m1_i=R1.rs, i=0; m1_i<=R1.re; m1_i++, i++)
        {
            for(m1_j=R1.cs, j=0; m1_j<=R1.ce; m1_j++, j++)
                result.a[i][j] = R1.a[m1_i][m1_j];
        }

        for(m1_i=R2.rs, i=0; m1_i<=R2.re; m1_i++, i++)
        {
            for(m1_j=R2.cs, j=dimension/2; m1_j<=R2.ce; m1_j++, j++)
                result.a[i][j] = R2.a[m1_i][m1_j];
        }

        for(m1_i=R3.rs, i=dimension/2; m1_i<=R3.re; m1_i++, i++)
        {
            for(m1_j=R3.cs, j=0; m1_j<=R3.ce; m1_j++, j++)
                result.a[i][j] = R3.a[m1_i][m1_j];
        }

        for(m1_i=R4.rs, i=dimension/2; m1_i<=R4.re; m1_i++, i++)
        {
            for(m1_j=R4.cs, j=dimension/2; m1_j<=R4.ce; m1_j++, j++)
                result.a[i][j] = R4.a[m1_i][m1_j];
        }

        return result;
    }
}

matrix add(matrix m1, matrix m2)
{
    matrix result;
    int m1_i, m1_j, m2_i, m2_j, i, j;

    result.rs = result.cs = 0;
    result.re = result.ce = m1.re - m1.rs;

    for(m1_i = m1.rs, m2_i = m2.rs, i=0; m1_i<=m1.re;  m1_i++, m2_i++, i++)
    {
        for(m1_j=m1.cs, m2_j = m2.cs, j=0; m1_j<=m1.ce; m1_j++, m2_j++, j++)
            result.a[i][j] = m1.a[m1_i][m1_j] + m2.a[m2_i][m2_j];
    }

    return result;
}

matrix sub(matrix m1, matrix m2)
{
    matrix result;
    int m1_i, m1_j, m2_i, m2_j, i, j;

    result.rs = result.cs = 0;
    result.re = result.ce = m1.re - m1.rs;

    for(m1_i = m1.rs, m2_i = m2.rs, i=0; m1_i<=m1.re;  m1_i++, m2_i++, i++)
    {
        for(m1_j=m1.cs, m2_j = m2.cs, j=0; m1_j<=m1.ce; m1_j++, m2_j++, j++)
            result.a[i][j] = m1.a[m1_i][m1_j] - m2.a[m2_i][m2_j];
    }

    return result;
}

Answer 1

您的程序正在 multiply() 中进入无限递归，gdb 显示如下堆栈跟踪:

#0  0x0000000000400899 in multiply (m1=..., m2=...) at b.c:60
#1  0x0000000000400fc7 in multiply (m1=..., m2=...) at b.c:140
#2  0x0000000000401584 in multiply (m1=..., m2=...) at b.c:142
#3  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#4  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#5  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#6  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#7  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#8  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#9  0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#10 0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
(...)
#421 0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#422 0x0000000000401859 in multiply (m1=..., m2=...) at b.c:143
#423 0x000000000040067c in main (argc=<optimized out>, argv=<optimized out>) at b.c:43

这可能会导致堆栈溢出，从而导致您观察到的崩溃。这是第 143 行附近的代码:

   140          P1 = multiply(A, sub(F, H));    
   141          P2 = multiply(add(A, B), H);    
   142          P3 = multiply(add(C, D), E);
   143          P4 = multiply(D, sub(G, E));
   144          P5 = multiply(add(A, D), add(E, H));
   145          P6 = multiply(sub(B, D), add(G, H));
   146          P7 = multiply(sub(A,C), add(E, F));

我怀疑您用来计算子数组大小的逻辑有问题。进一步挖掘表明 m2 在递归调用中有 负 维度，您应该做一些进一步的调试以找出到底出了什么问题。

我的编译器警告的另一个问题是:

b.c: In function 'multiply':
b.c:166:28: warning: array subscript is above array bounds [-Warray-bounds]
                 result.a[i][j] = R2.a[m1_i][m1_j];
                            ^
b.c:178:28: warning: array subscript is above array bounds [-Warray-bounds]
                 result.a[i][j] = R4.a[m1_i][m1_j];

这是相应的源代码行:

   163          for(m1_i=R2.rs, i=0; m1_i<=R2.re; m1_i++, i++)
   164          {
   165              for(m1_j=R2.cs, j=dimension/2; m1_j<=R2.ce; m1_j++, j++)
   166                  result.a[i][j] = R2.a[m1_i][m1_j];
   167          }
...
   175          for(m1_i=R4.rs, i=dimension/2; m1_i<=R4.re; m1_i++, i++)
   176          {
   177              for(m1_j=R4.cs, j=dimension/2; m1_j<=R4.ce; m1_j++, j++)
   178                  result.a[i][j] = R4.a[m1_i][m1_j];
   179          }