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| #include<cstdio> #include<cstdlib> #include<time.h> #include<graphics.h> #include<conio.h> #include<fstream> #include<string> #include<iostream> double** 生成矩阵(double** a, int* r, int* c); double 计算行列式(double** a, int n); void 打开菜单(); int 执行程序(); void 写入文件(double** a, int r1, int c1, double** d, int r2, int c2, std::string name); void 写入逆矩阵(double** a, double** d, int r, std::string name); void 写入行列式(double** a, int r, double ss); void 写入秩(double** a, int r1, int c1, int 秩); void 写入加减法(double** a, int r1, int c1, double** b, double** d, int r, int c, int sign); void 写入乘法(double** a, int r1, int c1, double** b, int r2, int c2, double** d); void 读取文件(); void 矩阵转置(double** a, int r, int c); void 矩阵加减法(double** a, double** b, int r1, int c1, int r2, int c2, int sign); void 矩阵数乘(double** a, int r, int c); void 矩阵乘法(double** a, double** b, int r1, int c1, int r2, int c2); int 矩阵化简(double** a, int r, int c, int sign); void 矩阵求逆(double** a, int r); void 打印d数组(double** d, int r, int c); void 打印d数组(double** d, int r); void 内存释放(double** d, int r); int main() { int 开始; do { 打开菜单(); 开始 = 执行程序(); } while (开始 == 0); } void 矩阵转置(double** a, int r, int c) { double** d = NULL; d = new double* [c]; for (int i = 0; i < c; i++) { d[i] = new double[r]; } for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { d[j][i] = a[i][j]; } } 打印d数组(d, c, r); 写入文件(a, r, c, d, c, r, "的转置为:"); 内存释放(d, c); } void 矩阵加减法(double** a, double** b, int r1, int c1, int r2, int c2, int sign) { if (r1 == r2 && c1 == c1) { double** d = NULL; d = new double* [r1]; for (int i = 0; i < r1; i++) { d[i] = new double[c1]; } for (int i = 0; i < r1; i++) { for (int j = 0; j < c1; j++) { d[i][j] = a[i][j] + b[i][j] * sign; } } 打印d数组(d, r1, c1); 写入加减法(a, r1, c1, b, d, r1, c1, sign); 内存释放(d, r1); } else printf("这两个矩阵不可以这样运算!"); } void 矩阵数乘(double** a, int r, int c) { double** d = NULL; d = new double* [r]; for (int i = 0; i < r; i++) { d[i] = new double[c]; } int k; printf("请输入数值:"); scanf_s("%d", &k); for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { d[i][j] = k * a[i][j]; } } 打印d数组(d, r, c); std::to_string(k); std::string name = "数乘" + std::to_string(k) + "的结果为:"; 写入文件(a, r, c, d, r, c, name); 内存释放(d, r); } void 矩阵乘法(double** a, double** b, int r1, int c1, int r2, int c2) { if (r2 == c1) { double** d = NULL, sum; d = new double* [r1]; for (int i = 0; i < r1; i++) { d[i] = new double[c2]; } for (int i = 0; i < r1; i++) { for (int j = 0; j < c2; j++) { sum = 0; for (int k = 0; k < c1; k++) { sum += a[i][k] * b[k][j]; } d[i][j] = sum; } } 打印d数组(d, r1, c2); 写入乘法(a, r1, c1, b, r2, c2, d); 内存释放(d, r1); } else printf("这两个矩阵不能相乘!"); } int 矩阵化简(double** a, int r, int c, int sign) { double** d; d = new double* [r]; for (int i = 0; i < r; i++) { d[i] = new double[c]; } for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { d[i][j] = a[i][j]; } } int cnt = 0; int cct = 0; int flag; double t; while (cnt <= r && cct <= c) { flag = -1; for (int i = cnt; i < r; i++) { if (d[i][cct] != 0) { flag = i; break; } } if (flag == -1) { cct++; continue; } if (flag != cnt) { double tmp = 0; for (int j = cct; j < c; j++) { tmp = d[flag][j]; d[flag][j] = d[cnt][j]; d[cnt][j] = tmp; } } t = d[cnt][cct]; for (int j = cct; j < c; j++) { d[cnt][j] /= t; } for (int i = cnt + 1; i < r; i++) { if (d[i][cct] != 0) { t = d[i][cct]; for (int j = cct; j < c; j++) { d[i][j] = d[i][j] - d[cnt][j] * t; } } } cnt++; cct++; } for (int i = r - 1; i > 0; i--) { flag = -1; for (int j = 0; j < c; j++) { if (d[i][j] != 0) { flag = j; break; } } if (flag != -1) { for (int k = i - 1; k >= 0; k--) { t = d[k][flag]; for (int j = 0; j < c; j++) { d[k][j] = d[k][j] - t * d[i][j]; } } } } int number = 0; for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { if (d[i][j] != 0) { number++; break; } } } if (sign == 0) {
打印d数组(d, r, c); 写入文件(a, r, c, d, r, c, "的化简结果为:"); } else { 打印d数组(d, r); 写入逆矩阵(a, d,r, "的逆矩阵为: "); } 内存释放(d, r); return number; } void 矩阵求逆(double** a, int r) { if (计算行列式(a, r) != 0) { double** d; d = new double* [r]; for (int i = 0; i < r; i++) { d[i] = new double[2 * r]; } for (int i = 0; i < r; i++) { for (int j = 0; j < r; j++) { d[i][j] = a[i][j]; } for (int j = r; j < 2 * r; j++) { if (i == j - r) d[i][j] = 1; else d[i][j] = 0; } } 矩阵化简(d, r, 2 * r, 1); 内存释放(d, r); } else printf("这个矩阵不可逆!");
} void 打印d数组(double** d, int r, int c) { printf("结果如下:\n"); for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { if ((int)(d[i][j] * 100) % 100 == 0) printf("%d\t", (int)d[i][j]); else printf("%.2lf\t", d[i][j]); } printf("\n"); } } void 打印d数组(double** d, int r) { printf("结果如下:\n"); for (int i = 0; i < r; i++) { for (int j = r; j < 2 * r; j++) { if ((int)(d[i][j] * 100) % 100 == 0) printf("%d\t", (int)d[i][j]); else printf("%.2lf\t", d[i][j]); } printf("\n"); } } double 计算行列式(double** a, int n) { double** d; d = new double* [n]; for (int i = 0; i < n; i++) { d[i] = new double[n]; } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { d[j][i] = a[i][j]; } } int flag = -1; for (int i = 0; i < n; i++) { if (d[i][0] != 0) { flag = i; break; } } if (flag != 0) { double tmp = 0; for (int j = 0; j < n; j++) { tmp = d[flag][j]; d[flag][j] = d[0][j]; d[0][j] = tmp; } } double tmp; for (int k = 1; k < n; k++) { for (int i = k; i < n; i++) { tmp = d[i][k - 1] / d[k - 1][k - 1]; for (int j = k - 1; j < n; j++) { d[i][j] = d[i][j] - tmp * d[k - 1][j]; } } } double ss = 1; for (int i = 0; i < n; i++) { ss *= d[i][i]; } 写入行列式(a, n, ss); 内存释放(d, n); return ss; } double** 生成矩阵(double** a, int* r, int* c) { printf("请输入矩阵的行数,列数:"); scanf_s("%d%d", r, c); printf("请输入矩阵:\n"); a = new double* [*r]; for (int i = 0; i < *r; i++) { a[i] = new double[*c]; } for (int i = 0; i < *r; i++) { for (int j = 0; j < *c; j++) { scanf_s("%lf", &a[i][j]); } } return a; } void 打开菜单() { printf("=======================================================================\n"); printf("| ----------1|我要求矩阵的加法 ----------- |\n"); printf("| ----------2|我要求矩阵的减法 ----------- |\n"); printf("| ----------3|我要求矩阵的转置 ----------- |\n"); printf("| ----------4|我要求矩阵的逆矩阵----------- |\n"); printf("| ----------5|我要求最简行矩阵 ----------- |\n"); printf("| ----------6|我要求矩阵的数乘 ----------- |\n"); printf("| ----------7|我要求矩阵的乘法 ----------- |\n"); printf("| ----------8|我要求矩阵的秩 ----------- |\n"); printf("| ----------9|我要计算行列式的值----------- |\n"); printf("| ----------0|读取计算结果文件 ----------- |\n"); printf("| ----------QAQ|输入字母可以退出----------- |\n"); printf("=======================================================================\n"); } int 执行程序() { double** a = NULL, ** b = NULL; int r1, c1, r2, c2; char ch; switch (ch = getchar()) { case'1': { a = 生成矩阵(a, &r1, &c1); b = 生成矩阵(b, &r2, &c2); 矩阵加减法(a, b, r1, c1, r2, c2, 1); 内存释放(a, r1); 内存释放(b, r2); break; } case'2': { a = 生成矩阵(a, &r1, &c1); b = 生成矩阵(b, &r2, &c2); 矩阵加减法(a, b, r1, c1, r2, c2, -1); 内存释放(a, r1); 内存释放(b, r2); break; } case'3': { a = 生成矩阵(a, &r1, &c1); 矩阵转置(a, r1, c1); 内存释放(a, r1); break; } case'4': { a = 生成矩阵(a, &r1, &c1); 矩阵求逆(a, r1); 内存释放(a, r1); break; } case'5': { a = 生成矩阵(a, &r1, &c1); 矩阵化简(a, r1, c1, 0); 内存释放(a, r1); break; } case'6': { a = 生成矩阵(a, &r1, &c1); 矩阵数乘(a, r1, c1); 内存释放(a, r1); break; } case'7': { a = 生成矩阵(a, &r1, &c1); b = 生成矩阵(b, &r2, &c2); 矩阵乘法(a, b, r1, c1, r2, c2); 内存释放(a, r1); 内存释放(b, r2); break; } case'8': { a = 生成矩阵(a, &r1, &c1); int 秩; 秩 = 矩阵化简(a, r1, c1, 0); printf("矩阵的秩为:%d\n", 秩); 内存释放(a, r1); break; } case'9': { a = 生成矩阵(a, &r1, &c1); double ss = 计算行列式(a, r1); if ((int)(ss * 100) % 100 == 0) printf("%d\t", (int)ss); else printf("%.2lf\t", ss); 内存释放(a, r1); break; } case '0': { 读取文件(); break; } default: { return -1; } } getchar(); return 0; } void 内存释放(double** d, int r) { for (int i = 0; i < r; i++) { delete[]d[i]; } delete[]d; } void 写入文件(double** a, int r1, int c1, double** d, int r2, int c2,std::string name) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(),ios_base::out|ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r1; i++) { for (int j = 0; j < c1; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } fout << name << endl; for (int i = 0; i < r2; i++) { for (int j = 0; j < c2; j++) { if ((int)(d[i][j] * 100) % 100 == 0) fout << (int)d[i][j] << "\t"; else fout << d[i][j] << "\t"; } fout << endl; }
} void 写入逆矩阵(double** a, double** d,int r, std::string name) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(), ios_base::out | ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r; i++) { for (int j = 0; j < r; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } fout << name << endl; for (int i = 0; i < r; i++) { for (int j = r; j < 2*r; j++) { if ((int)(d[i][j] * 100) % 100 == 0) fout << (int)d[i][j] << "\t"; else { fout << d[i][j] << "\t"; } } fout << endl; }
} void 写入行列式(double** a, int r,double ss) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(), ios_base::out | ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r; i++) { for (int j = 0; j < r; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } fout << "的行列式的值为:" << ss << endl; } void 写入秩(double** a, int r1, int c1, int 秩) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(), ios_base::out | ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r1; i++) { for (int j = 0; j < 1; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } fout << "的秩为:" << 秩 << endl; } void 写入加减法(double** a, int r1, int c1, double** b,double**d,int r,int c, int sign) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(), ios_base::out | ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r1; i++) { for (int j = 0; j < c1; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } if (sign == 1) { fout << "加矩阵:" << endl; } else { fout << "减矩阵:" << endl; } for (int i = 0; i < r1; i++) { for (int j = 0; j < c1; j++) { if ((int)(b[i][j] * 100) % 100 == 0) fout << (int)b[i][j] << "\t"; else fout << b[i][j] << "\t"; } fout << endl; } fout << "的结果为:" << endl; for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { if ((int)(d[i][j] * 100) % 100 == 0) fout << (int)d[i][j] << "\t"; else fout << d[i][j] << "\t"; } fout << endl; } } void 写入乘法(double**a,int r1,int c1,double**b,int r2,int c2,double**d) { using namespace std; string 文件名; 文件名 = "计算结果.txt"; ofstream fout(文件名.c_str(), ios_base::out | ios_base::app); fout << "矩阵:" << endl; for (int i = 0; i < r1; i++) { for (int j = 0; j < c1; j++) { if ((int)(a[i][j] * 100) % 100 == 0) fout << (int)a[i][j] << "\t"; else { fout << a[i][j] << "\t"; } } fout << endl; } fout << "乘矩阵:" << endl; for (int i = 0; i < r2; i++) { for (int j = 0; j < c2; j++) { if ((int)(b[i][j] * 100) % 100 == 0) fout << (int)b[i][j] << "\t"; else fout << b[i][j] << "\t"; } fout << endl; } fout << "的结果为:" << endl; for (int i = 0; i < r1; i++) { for (int j = 0; j < c2; j++) { if ((int)(d[i][j] * 100) % 100 == 0) fout << (int)d[i][j] << "\t"; else fout << d[i][j] << "\t"; } fout << endl; } } void 读取文件() { using namespace std; char ch; string 文件名; 文件名 = "计算结果.txt"; ifstream fin(文件名); if (fin.is_open()) { while (fin.get(ch)) { cout << ch; } fin.close(); } }
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