矩阵的逆

矩阵的逆

原理：
连接：
https://baike.baidu.com/item/%E9%80%86%E7%9F%A9%E9%98%B5




代码：

QT c++版：

//求逆矩阵
QVector> Matrix_inverse(QVector> &A)
{

    int cols = A[0].size();
    int rows = A.size();
    QVector col(cols,0);
    QVector> res(rows,col);
    int i,j,k;
    double temp,temp2;



    //初始单位阵
    for (i = 0; i < rows; i++)
    {
        for (j = 0; j < rows; j++)
        {
            res[i][j] = (i == j) ? 1 : 0;
        }
    }

    // 求左下

     for (i = 0; i <= rows - 1; i++)
     {
         //提取该行的主对角线元素
         temp2 = A[i][i];   //可能为0
         if (temp2 == 0)  //为0 时，在下方搜索一行不为0的行并交换
         {
             for (i = 0; i < rows; i++)
             {
                 k = i;
                 for (j = i + 1; j < rows; j++)
                 {
                     if (A[j][i] != 0) //不为0的元素
                     {
                         k = j;
                         break;
                     }
                 }

                 if (k != i) //如果没有发生交换： 情况1 下方元素也全是0
                 {
                     for (j = 0; j < rows; j++)
                     {
                         //行交换
                         temp = A[i][j];
                         A[i][j] = A[k][j];
                         A[k][j] = temp;
                         //伴随交换
                         temp = res[i][j];
                         res[i][j] = res[k][j];
                         res[k][j] = temp;
                     }
                 }
                 else {
                     //满足条件1
                     cout<<"不可逆矩阵ERROR"<= 0; i--)
    {
        for (k = i - 1; k >= 0; k--)
        {
            temp2 = A[k][i];
            for (j = 0; j < rows; j++)
            {
                A[k][j] = A[k][j] - temp2 * A[i][j];
                res[k][j] = res[k][j] - temp2 * res[i][j];
            }
        }
    }


    return res;
}

vs c++版：

#include 
  #include 
  using namespace std;
  double ffabs(double p)        //计算实数的绝对值
  {
	  double q;
	  q = fabs(p);
	  return(q);
  }
  double ff(double p)         //计算1.0/p
  {
	  double q;
	  q = 1.0/p;
	  return(q);
  }
  //a   原矩阵。返回逆矩阵。
//n   矩阵阶数
  template         //模板声明T为类型参数
  int inv(T a[], int n)       //若矩阵奇异，则返回标志值0，否则返回标志值非0。
  { 
	  int *is,*js,i,j,k,l,u,v;
	  double d, q;
      T p;
      is=new int[n];
      js=new int[n];
      for (k=0; k<=n-1; k++)
      { 
		  d=0.0;
          for (i=k; i<=n-1; i++)      //选主元
          for (j=k; j<=n-1; j++)
          { 
			  l=i*n+j; 
			  q = ffabs(a[l]);        //计算元素绝对值（模）
              if (q>d) { d=q; is[k]=i; js[k]=j;}
          }
          if (d+1.0==1.0)            //矩阵奇异
          { 
			  delete[] is; delete[] js; 
			  cout <<"矩阵奇异！" <=0; k--)      //恢复行列交换
      { 
		  if (js[k]!=k)
            for (j=0; j<=n-1; j++)
            { 
				u=k*n+j; v=js[k]*n+j;
				p=a[u]; a[u]=a[v]; a[v]=p;
            }
          if (is[k]!=k)
            for (i=0; i<=n-1; i++)
            {
				u=i*n+k; v=i*n+is[k];
                p=a[u]; a[u]=a[v]; a[v]=p;
            }
      }
      delete[] is; delete[] js;
      return(1);
  }

test 测试：

#include 
#include 
  using namespace std;
  int main()
  { 
	  int i,j;
      double a[4][4]={ {0.2368,0.2471,0.2568,1.2671},
                            {1.1161,0.1254,0.1397,0.1490},
                            {0.1582,1.1675,0.1768,0.1871},
                            {0.1968,0.2071,1.2168,0.2271}};
      double b[4][4];
      for (i=0; i<=3; i++)
      for (j=0; j<=3; j++)  b[i][j]=a[i][j];
      i=inv(&b[0][0],4);
      if (i!=0)
      { 
		  cout <<"实矩阵 A:" <