我正试着写一个程序来求一个N × N矩阵的行列式，在这个过程中，我第一次了解了std::array和templates。
我提出了这个实现，基于辅因子和次因子的方法。

#include <array>
#include <iostream>

template <int N>
using Matrix = std::array<std::array<double, N>, N>;

template <int N>
Matrix<N - 1> subMatrix(Matrix<N> matrix, size_t focusRow, size_t focusColumn) {
    Matrix<N - 1> returnMatrix;

    int subMatrixRow = 0, subMatrixColumn = 0;
    static const int matrixSize = matrix.size();

    for (size_t matrixRow = 0; matrixRow < matrixSize; matrixRow++) {
        for (size_t matrixColumn = 0; matrixColumn < matrixSize; matrixColumn++) {
            if (matrixRow != focusRow && matrixColumn != focusColumn) {
                returnMatrix[subMatrixRow][subMatrixColumn++] = matrix[matrixRow][matrixColumn];

                if (subMatrixColumn == matrixSize - 1) {
                    subMatrixColumn = 0;
                    subMatrixRow++;
                }
            }
        }
    }

    return returnMatrix;
}

template <int N>
double getDeterminant(Matrix<N> matrix) {
    static const int matrixSize = matrix.size();
    double determinant = 0;

    if (matrixSize == 1) {
        determinant = matrix[0][0];
    }

    else if (matrixSize == 2) {
        determinant = (matrix[0][0] * matrix[1][1]) - (matrix[0][1] * matrix[1][0]);
    }

    else if (matrixSize > 0) {
        int sign = 1;

        for (size_t dimension = 0; dimension < N; dimension++) {
            determinant += sign * matrix[0][dimension] * getDeterminant(subMatrix(matrix, 0, dimension));
            sign = -sign;
        }
    }

    else {
        throw std::invalid_argument("expected square matrix");
    }

    return determinant;
}

int main(int argc, char const* argv[]) {
    static const int length = 3;

    Matrix<length> matrix = {{{1, 2, 3},
                              {4, 5, 6},
                              {7, 8, 9}}};

    printf("determinant = %.2f\n", getDeterminant(matrix));
}

然而，当我运行make时，我得到了一个我无法解决的错误。

vscode ➜ /workspaces/c-cpp-mirror/11032023-arrays $ make determinant
g++     determinant.cpp   -o determinant
determinant.cpp: In function ‘int main(int, const char**)’:
determinant.cpp:68:57: error: no matching function for call to ‘getDeterminant(Matrix<3>&)’
   68 |     printf("determinant = %.2f\n", getDeterminant(matrix));
      |                                                         ^
determinant.cpp:31:8: note: candidate: ‘template<int N> double getDeterminant(Matrix<N>)’
   31 | double getDeterminant(Matrix<N> matrix) {
      |        ^~~~~~~~~~~~~~
determinant.cpp:31:8: note:   template argument deduction/substitution failed:
determinant.cpp:68:57: note:   mismatched types ‘int’ and ‘long unsigned int’
   68 |     printf("determinant = %.2f\n", getDeterminant(matrix));
      |                                                         ^
make: *** [<builtin>: determinant] Error 1

下面是一个较小的程序，它仍然表现出相同的行为：

#include <array>
#include <iostream>

template <int N>
using Matrix = std::array<std::array<double, N>, N>;

template <int N>
void printMatrix(Matrix<N> matrix) {}

int main(int argc, char const* argv[]) {
    static const int length = 4;

    Matrix<length> matrix = {{{7, -2, 2, 1},
                              {3, 1, -5, 2},
                              {2, 2, -5, 3},
                              {3, 2, 5, 1}}};

    printMatrix(matrix);
}