递归模板函数导致初始化中的负数组大小

时间：2013-08-30 18:24:38

标签： c++ arrays templates recursion negative-number

我正在开发一个支持矩阵上各种数学运算的矩阵类。 Matrix类有三个模板参数：

template<typename T, int rows, int columns>
class Matrix
{
   ...
};

这很好用。然而，由于许多操作（例如反转矩阵并采用其行列式）仅适用于方形矩阵（其中行==列），我选择使这些函数不是成员函数来控制模板参数并且仅允许这些操作在正方形上矩阵：

template<typename T, int rc>
const Matrix<T, rc, rc> inverse (const Matrix<T, rc, rc>& src)
{
    ...
}

我有几个以这种方式运作的功能。

现在，我得到的错误消息非常复杂，因为模板的使用已经将运行时堆栈跟踪转换为编译时堆栈跟踪。以下是我的想法：

  • 我的矩阵类以三种方式存储其数据：2d指针数组，1d行数组和1d列数组（行和列是在矩阵内声明的内部类，函数和函数作为包装器对于1d指针数组）。所有这些指针都指向Matrix数据。这允许在整个行和列上进行操作。

  • 我得到的错误是这些数组的声明，以及用于初始化行和列的构造函数中的一些其他临时数组。错误消息是：

    [错误]数组的大小为负数。

  • 堆栈跟踪很大，但它多次通过函数subMatrix。其中许多函数以递归的形式相互调用。

  • subMatrix获取包含m行和n列的矩阵，并返回包含m-1行和n-1列的新矩阵（一行）并删除一列以创建子矩阵）。

  • 我已经确保在我的代码中从不在小于2 x 2的矩阵上调用此函数，但我怀疑编译器没有检测到它。

  • 另一个函数determinant计算方阵的行列式。对于大于2 x 2的矩阵，此函数是递归的。在此函数的递归部分期间，它调用subMatrix，创建一个较小的矩阵，直到矩阵达到2 x 2的大小。

  • 我怀疑我的问题是由于编译器在determinant中看到递归并推断subMatrix在逐渐变小的矩阵上被调用并且保持外推直到它达到-1的大小，这导致我的问题声明new =，较小矩阵的行和列时出错（即使此代码永远不会被执行）。

我完全不知道如何解决这个问题，假设我已准确分析了情况。

以下是我的代码的相关部分：

//matrix.h
template <typename T, int rows, int columns>

class Matrix
{
public:
    class Column;

    class Row;

private:

    T* m_data[rows][columns];  //errors on these lines.
    Row m_rows[rows];
    Column m_columns[columns];

//    ... much more in class

}

//matrix.cpp

template<typename T, int rows, int columns>
const Matrix<T, rows - 1, columns - 1> Matrix<T, rows, columns>::subMatrix(int row, int column) const
{
    Matrix<T, rows - 1, columns - 1> result;

    if (row > rows || column > columns)
    {
        std::cout << "death: bad bounds\n";
        return result;
    }

    for (int m = 1, mr = 1; m <= rows; m ++)
    {
        if (m == row)
        {
            continue;
        }

        for (int n = 1, nr = 1; n <= columns; n ++)
        {
            if (n == column)
            {
                continue;
            }

            result.at(mr, nr) = *(m_data[m - 1][n - 1]);

            nr ++;
        }

        mr ++;
    }

    return result;
}



template<typename T, int rc>
T minor(const Matrix<T, rc, rc>& src, int m, int n)
{
    return determinant(src.subMatrix(m, n));
}


template<typename T, int rc>
T cofactor(const Matrix<T, rc, rc>& src, int m, int n)
{
    return pow(-1, m + n) * minor(src, m, n);
}



template<typename T, int rc>
T determinant(const Matrix<T, rc, rc>& src)
{
    T det;

    if (rc == 2)
    {
        det = (src.get(1, 1) * src.get(2, 2)) - (src.get(1, 2) * src.get(2, 1));
        return det;
    }

    T temp;

    for (int n = 1; n <= rc; n ++)
    {
        temp = src.get(1, n) * cofactor(src, 1, n);
    }

    return det;
}

一切都从这里开始：

int main(void)
{
    auto m1 = Matrix<int, 3, 3>().map(

     //lambda to fill the matrix with increasing values
     [](int,int,int) { static int n = 0; return ++n; }
    ); 

    int m2 = determinant(m1); //trace leads back to here

    std::cout << m1 << '\n' << m2;

    return 0;
}

这是完整的“堆栈跟踪”。我怀疑它会有所帮助。

C:\Users\noah dove\Documents\Devcpp\matrix.h: In instantiation of 'class Matrix<int, -1, -1>':
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   [ skipping 2 instantiation contexts ]

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here
C:\Users\noah dove\Documents\Devcpp\matrix.h:21:25: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.h:21:25: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.h:22:17: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.h: In instantiation of 'class Matrix<int, -1, -1>::Row':
C:\Users\noah dove\Documents\Devcpp\matrix.h:22:17:   required from 'class Matrix<int, -1, -1>'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   [ skipping 3 instantiation contexts ]
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here

C:\Users\noah dove\Documents\Devcpp\matrix.h:105:20: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.h: In instantiation of 'class Matrix<int, -1, -1>':
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   [ skipping 2 instantiation contexts ]
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here
C:\Users\noah dove\Documents\Devcpp\matrix.h:23:26: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.h: In instantiation of 'class Matrix<int, -1, -1>::Column':
C:\Users\noah dove\Documents\Devcpp\matrix.h:23:26:   required from 'class Matrix<int, -1, -1>'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   [ skipping 3 instantiation contexts ]

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here
C:\Users\noah dove\Documents\Devcpp\matrix.h:134:17: error: size of array is negative
In file included from C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:1:0:
C:\Users\noah dove\Documents\Devcpp\matrix.cpp: In instantiation of 'Matrix<T, rows, columns>::Matrix(T) [with T = int; int rows = -1; int columns = -1]':
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:365:35:   required from 'const Matrix<T, (rows - 1), (columns - 1)> Matrix<T, rows, columns>::subMatrix(int, int) const [with T = int; int rows = 0; int columns = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'

C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   [ skipping 3 instantiation contexts ]
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:11:25: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:12:28: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.cpp: In instantiation of 'Matrix<T, rows, columns>::Matrix(const Matrix<T, rows, columns>&) [with T = int; int rows = -1; int columns = -1; Matrix<T, rows, columns> = Matrix<int, -1, -1>]':
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:370:10:   required from 'const Matrix<T, (rows - 1), (columns - 1)> Matrix<T, rows, columns>::subMatrix(int, int) const [with T = int; int rows = 0; int columns = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 0]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 1]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   [ skipping 3 instantiation contexts ]
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 2]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:411:40:   required from 'T minor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:419:41:   required from 'T cofactor(const Matrix<T, rc, rc>&, int, int) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:439:3:   required from 'T determinant(const Matrix<T, rc, rc>&) [with T = int; int rc = 3]'
C:\Users\noah dove\Documents\Devcpp\matrix_driver.cpp:9:26:   required from here
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:38:25: error: size of array is negative
C:\Users\noah dove\Documents\Devcpp\matrix.cpp:39:28: error: size of array is negative

如果有人可以就此事提供任何帮助，我将非常感激。

1 个答案:

答案 0 :(得分：2)

rc == 2的特殊情况不应该是代码中的运行时检查 - 它应该是部分特化，它将在编译时终止递归。这些方面的东西：

template <typename T, int rc>
struct DeterminantHelper {
  static T calculate(const Matrix<T, rc, rc>& src) {
    T det;
    for (int n = 1; n <= rc; n ++)
    {
        det = src.get(1, n) * cofactor(src, 1, n);
    }

    return det;
  }
};

template <typename T>
struct DeterminantHelper<T, 2> {
  static T calculate(const Matrix<T, 2, 2>& src) {
    return (src.get(1, 1) * src.get(2, 2)) - (src.get(1, 2) * src.get(2, 1));
  }
};

template<typename T, int rc>
T determinant(const Matrix<T, rc, rc>& src) {
  return DeterminantHelper<T, rc>::calculate(src);
}
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