矩阵计算器

线代必备工具

#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];
        }
    }
    //起始行列
    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;
        }
        //交换两行;
        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;
            }
        }
        //化第一行首个为1
        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();
    }
}