c++实现矩阵类矩阵行列式，伴随矩阵，逆矩阵

1 //Matrix ver1.0
  2 //只支持矩阵内部（方阵）的运算
  3 #include<iostream>
  4 #include<math.h>
  5 using namespace std;
  6 class matrix
  7 {
  8     double**num;
  9     int **e;//单位矩阵
 10     int r;
 11     int c;
 12     unsigned int *array;//为全排序原矩阵列标提供初始顺序模板
 13     unsigned int*arr;//为全排序伴随矩阵列标提供初始顺序模板
 14     int**b;//存放原矩阵列标
 15     int j;//计数变量，原矩阵的全排列
 16     int po;//计数变量，伴随矩阵的全排列
 17 
 18     double **comp;//伴随矩阵
 19     double**s;//存放每一个num的余子式
 20     int**sb;//存放每一个余子式的列标
 21 
 22 public:
 23     double caculate();
 24     matrix(int n, int m);//nrow
 25     void setmat();
 26     bool checkcomp() { if (po)return true; return false; }
 27     void showm();
 28     void showinver(double k);
 29     void swap(unsigned int* array, int i, int j);
 30     void FullArray(int n, int index);
 31     int func(int n) { if (n == 0)return 1; else return n*func(n - 1); }
 32     int ni(int a[], int n);
 33     void sets(int a, int b);
 34     double cacu(int a, int b);
 35     void setcomp();
 36     void showcomp();
 37     void fullArray(int n, int index = 0);
 38     void shows();
 39     void showsb();
 40 
 41 };
 42 void matrix::shows()//r
 43 {
 44     for (int i = 0; i < r - 1; i++)
 45     {
 46         for (int j = 0; j < c - 1; j++)
 47             cout << s[i][j] << " ";
 48         cout << endl;
 49     }
 50 }
 51 void matrix::showcomp()
 52 {
 53     for (int i = 0; i < r; i++)
 54     {
 55         for (int j = 0; j < c; j++)
 56             cout << comp[i][j] << " ";
 57         cout << endl;
 58     }
 59 }
 60 void matrix::setcomp()
 61 {
 62     for (int i = 0; i < r; i++)
 63         for (int j = 0; j < c; j++)
 64             comp[i][j] = pow(-1, j + i)*cacu(i, j);
 65 
 66 }
 67 double matrix::cacu(int a, int b)//计算每一位的代数余子式
 68 {
 69     sets(a, b);
 70     double sum = 0;
 71     double *p = new double[c - 1];
 72     for (int i = 0; i < func(c - 1); i++)
 73     {
 74         p[i] = 1;
 75         for (int j = 0; j < c - 1; j++)
 76             p[i] *= s[j][sb[i][j]];
 77         p[i] = p[i] * pow(-1, ni(sb[i], c - 1));
 78         sum += p[i];
 79     }
 80     return sum;
 81 }
 82 void  matrix::sets(int a, int b)//把(a,b)的余子式存入**s
 83 {
 84     int t = 0;
 85     int *cun = new int[(c - 1)*(r - 1)];
 86     for (int i = 0; i < r; i++)
 87         for (int j = 0; j < c; j++)
 88         {
 89             if (i != a&&j != b)
 90             {
 91                 cun[t] = num[i][j];
 92                 t++;
 93             }
 94         }
 95     for (int i = 0; i < r - 1; i++)
 96         for (int j = 0; j < c - 1; j++)
 97             s[i][j] = cun[i*(r - 1) + j];
 98 }
 99 void  matrix::showm()//r
100 {
101     for (int i = 0; i < r; i++)
102     {
103         for (int j = 0; j < c; j++)
104             cout << num[i][j] << " ";
105         cout << endl;
106     }
107 }
108 int matrix::ni(int a[], int n)//逆序数
109 {
110     int s = 0;
111     for (int j = n - 1; j >= 0; j--)
112         for (int i = 0; i < j; i++)
113         {
114             if (a[j] < a[i])
115                 s++;
116         }
117     return s;
118 }
119 void matrix::swap(unsigned int*array, int i, int j)//r
120 {
121     int t = array[i];
122     array[i] = array[j];
123     array[j] = t;
124 }
125 void  matrix::showsb()
126 {
127     for (int i = 0; i < func(r - 1); i++)
128     {
129         for (int j = 0; j < c - 1; j++)
130             cout << sb[i][j];
131         cout << endl;
132     }
133 }
134 void  matrix::fullArray(int n, int index)//对于伴随矩阵全排列
135 {
136     if (index >= n)
137     {
138         for (int i = 0; i <n; ++i)
139         {
140             sb[po][i] = arr[i];
141         }
142         po++;
143         //return;
144     }
145 
146     for (int i = index; i < n; ++i)
147     {
148         swap(arr, index, i);
149         fullArray(n, index + 1);
150         swap(arr, index, i);
151     }
152 }
153 void  matrix::FullArray(int n, int index)//r
154 {
155     if (index >= n)
156     {
157         for (int i = 0; i <n; ++i)
158         {
159             b[j][i] = array[i];//把全排列存入b[][]中
160         }
161         j++;
162     }
163 
164     for (int i = index; i < n; ++i)
165     {
166         swap(array, index, i);
167         FullArray(n, index + 1);
168         swap(array, index, i);
169     }
170 }
171 
172 void matrix::showinver(double k)
173 {
174     for (int i = 0; i < r; i++)
175     {
176         for (int j = 0; j < c; j++)
177             cout << comp[i][j] / k << " ";
178         cout << endl;
179     }
180 }
181 matrix::matrix(int n, int m) :r(n), c(m)//r
182 {
183     j = 0;
184     array = new unsigned int[c];
185     for (int i = 0; i < c; i++)
186         array[i] = i;
187     arr = new unsigned int[c - 1];
188     for (int i = 0; i < c - 1; i++)
189         arr[i] = i;
190     num = new double*[n];
191     b = new int*[func(c)];
192     for (int i = 0; i < r; i++)
193         num[i] = new double[c];
194     for (int i = 0; i < func(c); i++)
195         b[i] = new int[c];
196     e = 0;
197 
198     sb = 0;
199     s = 0;
200     po = 0;
201     if (r == c)
202     {
203         sb = new int*[func(c - 1)];
204         for (int i = 0; i < func(c - 1); i++)
205             sb[i] = new int[c - 1];
206         s = new double*[r - 1];
207         for (int i = 0; i < r; i++)
208             s[i] = new double[c - 1];
209         comp = new double*[r];
210 
211         for (int i = 0; i < r; i++)
212             comp[i] = new double[c];
213 
214 
215         e = new int*[r];
216         for (int i = 0; i < r; i++)
217             e[i] = new int[c];
218         for (int i = 0; i < r; i++)
219             for (int j = 0; j < c; j++)
220             {
221                 if (i == j)
222                     e[i][j] = 1;
223                 else
224                     e[i][j] = 0;
225             }
226     }
227 }
228 void matrix::setmat()
229 {
230     cout << "请按行输入你的矩阵：" << endl;
231     for (int i = 0; i < r; i++)
232         for (int j = 0; j < c; j++)
233             cin >> num[i][j];
234     //num[i][j] = i*r + j;
235 }
236 double matrix::caculate()//计算原矩阵行列式
237 {
238     FullArray(c, 0);
239     double sum = 0;
240     double *p = new double[c];
241     for (int i = 0; i < func(r); i++)
242     {
243         p[i] = 1;
244         for (int j = 0; j < c; j++)
245             p[i] *= num[j][b[i][j]];
246         p[i] = p[i] * pow(-1, ni(b[i], c));
247         sum += p[i];
248     }
249     return sum;
250 }
251 void main()
252 {
253     int C, R;
254     int choice = 100;
255     matrix *p = 0;
256     double k;//储存行列式的值
257     while (choice)
258     {
259         cout << "1:创建一个矩阵对象\n2:输出矩阵行列式的值\n3：输出伴随矩阵\n4：输出逆矩阵\n5:结束" << endl;
260         cout << "请输入你的选择" << endl;
261         cin >> choice;
262         switch (choice)
263         {
264         case 1:
265             cout << "请输入矩阵的行与列：" << endl;
266             cin >> C >> R;
267             p = new matrix(C, R);
268             p->setmat();
269             break;
270         case 2:
271             if (C == R)
272             {
273                 k = p->caculate();
274                 cout << "矩阵行列式的值：" << k << endl;
275             }
276             else
277                 cout << "非方阵，无法计算" << endl;
278             break;
279         case 3:
280             if (C == R)
281             {
282                 p->fullArray(C - 1, 0);//先给下标全排序好，存入相应数组
283                 p->setcomp();
284                 p->showcomp();
285             }
286             else
287                 cout << "非方阵，无法计算" << endl;
288             break;
289         case 4:
290             if (C == R)
291                     if (p->checkcomp())
292                         p->showinver(k);
293                     else
294                         cout << "请先计算伴随矩阵。" << endl;
295             else
296                 cout << "非方阵，无法计算" << endl;
297             break;
298         case 5:
299             choice = 0;
300             break;
301         }
302     }
303 }

=====================6.18update&BUG已改===========================
原文链接: https://www.cnblogs.com/yuelien/p/5373823.html

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