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我正在研究一个支持矩阵上各种数学运算的矩阵类。Matrix 类具有三个模板参数：

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

这工作正常。但是，由于许多操作（例如反转矩阵并取其行列式）仅适用于方阵（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，并且只允许在平方上进行这些操作矩阵：

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行的函数。

现在，我收到的错误消息非常复杂，因为模板的使用已经将原本是运行时堆栈跟踪的东西变成了编译时堆栈跟踪。这是我认为正在发生的事情：

  • 我的矩阵类以三种方式存储其数据：二维指针数组、一维行数组和一维列数组（行和列是在矩阵中声明的内部类函数和函数作为一维指针数组的包装器） . 所有这些指针都指向矩阵数据。这允许对整个行和列进行操作。

  • 我得到的错误来自这些数组的声明，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。错误信息是：

    [错误] 数组大小为负数。

  • 堆栈跟踪很大，但它会subMatrix多次通过函数。其中许多函数以迂回的递归形式相互调用。

  • subMatrix接受具有m行和列的矩阵并返回具有行和n列的新矩阵（删除一行和一列以创建子矩阵）。m-1n-1

  • 我已确保在我的代码中永远不会在小于 2 x 2 的矩阵上调用此函数，但我怀疑编译器没有检测到这一点。

  • 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，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看到递归determinant和外推subMatrix在逐渐更小的矩阵上调用并不断外推直到它达到 -1 的大小，这在声明新 = 时会导致错误，更小的矩阵的行和列（即使这段代码永远不会被执行）。

假设我已经准确地分析了情况，我完全不知道如何解决这个问题。

这是我的代码的相关位：

//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”。我怀疑它会不会有帮助。

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

如果有人能在这件事上提供任何帮助，我将不胜感激。

4

1 回答 1

2

的特殊情况rc == 2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);
}
于 2013-08-30T18:44:07.897 回答