如何使用递归函数计算 C 中矩阵的行列式

Question

你好，我正在尝试编写一个 C 程序来计算给定矩阵的行列式。我稍微完成了它，但是当我试图创建一个函数来查找给定矩阵和组件的子矩阵时，我被卡住了。我在每个部分都尽可能清楚地评论了，但我认为该程序的主要问题是最后一种方法 subMatrix.If 您可以帮助我修复它或提出替代解决方案，我将非常感激。
PS :我知道部分代码或注释可能不清楚，所以请随时在注释中问我。

#define MAX 10000
    //here I was trying to make a "matrix" type to be able to return values in the function "subMatrix"
    struct Matrix
    {
        double a[MAX][MAX];
    };


    struct Matrix subMatrix(int n, double m[n][n], int I, int J);
    double determinant(int n, double M[n][n]);


    int main()
    {
        int n, k = 0;
        printf("how many rows does the matrix have"); 
        scanf("%d", &n);
        double Matrix[n][n];
        double temp[n * n];
        printf("enter the numbers in order with an enter after each one");
        //gathering all the data from the user
        for (int i = 0; i < n * n; i++)
        {
            scanf("%d", temp[i]);
        }
        //sorting the data into a matrix
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                Matrix[i][j] = temp[k];
                k++;
            }
        }
        //prints the determinant
        printf("%d",determinant(n,Matrix));

        return 0;
    }
    //this recursive function calculates the determinant 
    double determinant(int n, double M[n][n])
    {
        double det = 0;
        //the functions continues to call its self until n=2
        if (n == 2)
        {
            det = M[0][0] *M[1][1]-M[0][1]*M[1][0];
        }
        else
        {
            for (int i = 0; i < n; i++)
            {
                det += M[0][i] * determinant(n - 1, subMatrix(n, M, 0, i));
            }
        }



        return det;
    }
    //here I tried to make the subMatrix of a given matrix and one of its components
    //by sub matrix I mean the matrix that doesn't include the row and columns that are in line with one of the matrix componants
    struct Matrix subMatrix(int n, double m[n][n], int I, int J)
    {
        int i, a = 0, b = 0;
        int j;
        struct Matrix M[n - 1][n - 1];
        for (i = 0; i < n; i++)
        {
            if (i != I)
            {
                for (j = 0; j < n; j++)
                {
                    if (J != j)
                    {
                        M[a][b] = m[i][j];
                        b++;
                    }
                }
                a++;
            }
        }
        return M;
    }

Answer 1

您的代码存在多个问题，

subMatrix 正在返回 struct Matrix 的指针，但预计只是 struct Matrix
在 subMatrix 中，b 的值递增并且不会在新行上重置。
determinant 的参数期望 double M[n][n] 但在递归调用中传递 struct Matrix
局部变量的冗余使用 temp[n * n]
输入错误 n=1

从subMatrix获取二维数组的简单解决方案是传递二维数组的引用并在函数中填充所需的值。

我试着把混乱简单化如下，

void subMatrix(int n, double m[n][n], int I, int J,double M[n-1][n-1])
{
    int i, a = 0, b = 0;
    int j;
    for (i = 0; i < n; i++)
    {
        if (i == I)
        {
            continue;
        }

        b = 0;//in-order to start fresh for new row
        for (j = 0; j < n; j++)
        {
            if (J == j)
            {
                continue;
            }
            M[a][b] = m[i][j];
            b++;
        }
        a++;
    }
}

//this recursive function calculates the determinant 
double  determinant(int n, double M[n][n])
{
    double det = 0;
    //the functions continues to call its self until n=2
    if(n==1)
    {
        return M[0][0];
    }
    if (n == 2)
    {
        det = M[0][0] *M[1][1]-M[0][1]*M[1][0];
    }
    else
    {
        double subArray[n-1][n-1];
        for (int i = 0; i < n; i++)
        {
            //subMatrix is filling the subArray
            subMatrix(n,M,0,i,subArray);
            det += M[0][i] * ((i&1)?-1:1)*determinant(n - 1,subArray);
        }
    }
    return det;
}

int main()
{
    int n, k = 0;

    printf("how many rows does the matrix have"); 
    scanf("%d", &n);

    double Matrix[n][n];
    printf("enter the numbers in order with an enter after each one");

   //Taking user input for 2D array
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            scanf("%lf", &Matrix[i][j]);
        }
    }

    printf("%f",determinant(n,Matrix));
    return 0;
}

Answer 2

这是我自己的解决方案，我没有早点 post 因为我找不到错误，但多亏了@Truthseeker，我发现我没有让 b=0 并且我明白了这个程序可以计算行列式，但求真者的答案在数学上是有缺陷的，因为他在行列式方法中忘记了 pow (-1, i)

    #include <stdio.h>
    #include <math.h>


    void subMatrix(int n,double M[n-1][n-1], double m[n][n], int I, int J)
    {
        int i, a = 0, b = 0;
        int j;
        for (i = 0; i < n; i++)
        {
            if (i != I)
            {
                for (j = 0; j < n; j++)
                {
                    if (J != j)
                    {
                        M[a][b] = m[i][j];

                        b++;

                    }
                }

                a++;
                b=0;
            }
        }

    }

    //this recursive function calculates the determinant
    double determinant (int n, double m[n][n])
    {

      double det = 0;
      //the functions continues to call its self until n=2
      if (n == 1)
        {
          return m[0][0];
        }
      if (n == 2)
        {
          det = m[0][0] * m[1][1] - m[0][1] * m[1][0];
        }
      else
        {
          double M[n - 1][n - 1];
          for (int i = 0; i < n; i++)
        {
          subMatrix (n, M, m, 0, i);
          det += m[0][i] * pow (-1, i) * determinant (n - 1, M);
        }
        }

      return det;
    }

    int
    main ()
    {
      int n, k = 0;


      printf ("how many rows does the matrix have");
      scanf ("%d", &n);
      double Matrix[n][n];
      printf ("enter the numbers in order with an enter after each one");
      //Taking user input for 2D array
      for (int i = 0; i < n; i++)
        {
          for (int j = 0; j < n; j++)
        {
          scanf ("%lf", &Matrix[i][j]);
        }
        }

      //prints the determinant
      printf ("the determinant is %lf\n", determinant (n, Matrix));

      return 0;
    }

如何使用递归函数计算 C 中矩阵的行列式

how to compute the determinant of a Matrix in C using recursive functions

c

recursion

matrix

determinants