C# 简单的矩阵运算

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代码文件Matrix.cs

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace Matrix
{
    public partial class Matrix : Form
    {
        public Matrix()
        {
            InitializeComponent();
        }

        //成员变量、、、、、、、、、、、、、、、

        int row = 0;
        int column = 0;
        int row_b = 0;
        int column_b = 0;
        string str;

        double[] cov; //协方差矩阵
        bool cov_flag = false;
        double[] padjoint; //伴随矩阵 的返回数组
        double[] pinverse; //逆矩阵 的返回数组

        double[] matrix_A;
        double[] matrix_B;

        double[] pab; //A*B



        private void textBox1_TextChanged(object sender, EventArgs e)
        {

        }
        private void textBox2_TextChanged(object sender, EventArgs e)
        {

        }

        private void save_A(object sender, EventArgs e)
        {          
            if (text_in.Text.Equals(""))
            {
                MessageBox.Show(" Please input matrix_A ! ");
                return;
            }
            List<double> temp_list = new List<double>();  //临时list 存数据
            row = 0;
            column = 0;
            int cmax = 0;

            str = text_in.Text.Replace("\r\n", " # ");
           // MessageBox.Show(str);
            str = str.TrimEnd("# ".ToCharArray());  //   
            //MessageBox.Show(str);
            bool row1 = true;
            int index = str.IndexOf(" ");
            string[] Array = str.Split(new Char[] { '#' }, StringSplitOptions.RemoveEmptyEntries);
            foreach (string ii in Array)
            {
                string ss = ii.ToString();
                row++;
                //MessageBox.Show( string.Format("row={0}, ", ss));
                string[] subArray = ss.Split(new Char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
                foreach (string i in subArray)
                {
                    cmax++;
                    try
                    {
                        temp_list.Add(Convert.ToDouble(i.ToString()));
                    }
                    catch
                    {
                        MessageBox.Show(string.Format("第{0}行{1}列有非数字字符 ",row ,cmax));
                        return;
                    }
                }
                if (row1 == true)
                {
                    column = cmax;
                    row1 = false;
                }
                if (cmax != column)
                {
                    MessageBox.Show("每行元素数量不相等，\r\n修改后再读取!");
                    return;
                }                  
                cmax = 0; 
            }

            ///开始存储
            matrix_A = new double[row * column]; /* 把list的数据存到数组 matrix_A[]   */
            text_out.Text = string.Format("row={0}   column={1} \r\n\r\n", row.ToString(), column.ToString());
            for (int i = 0; i < row ; i++)
            {
                for (int j = 0; j <  column; j++)
                {
                    matrix_A[i * column + j] = temp_list[i * column + j];
                    text_out.Text += string.Format("{0} ", matrix_A[i * column + j]);
                }
                text_out.Text += "\r\n";
            }
        }

        private void clear_out(object sender, EventArgs e)
        {

            text_out.Text = "";

        }

        private void save_B(object sender, EventArgs e)
        {
            if (text_in.Text.Equals(""))
            {
                MessageBox.Show(" Please input matrix_B ! ");
                return;
            }
            row_b = 0;
            column_b = 0;
            int cmax = 0 ;
            List<double> temp_list = new List<double>();  //临时list 存数据


            str = text_in.Text.Replace("\r\n", " # ");
            // MessageBox.Show(str);
            str = str.TrimEnd("# ".ToCharArray());  //   
            //MessageBox.Show(str);
            bool row1 = true;
            int index = str.IndexOf(" ");
            string[] Array = str.Split(new Char[] { '#' }, StringSplitOptions.RemoveEmptyEntries);
            foreach (string ii in Array)
            {
                string ss = ii.ToString();
                row_b++;
                //MessageBox.Show( string.Format("row={0}, ", ss));
                string[] subArray = ss.Split(new Char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
                foreach (string i in subArray)
                {
                    cmax++;
                    try
                    {
                        temp_list.Add(Convert.ToDouble(i.ToString()));
                    }
                    catch
                    {
                        MessageBox.Show(string.Format("第{0}行{1}列有非数字字符 ", row_b, cmax));
                        return;
                    }
                }
                if (row1 == true)
                {
                    column_b = cmax;
                    row1 = false;
                }
                if (cmax != column_b)
                {
                    MessageBox.Show("每行元素数量不相等，\r\n修改后再读取!");
                    return;
                }
                cmax = 0;
            }

            text_out.Text = string.Format("row_b={0}   column_b={1} \r\n\r\n", row_b.ToString(), column_b.ToString());
            matrix_B = new double[row_b * column_b]; /* n 是一个带有 10 个整数的数组 */

            for (int i = 0; i < row_b; i++)
            {
                for (int j = 0; j < column_b; j++)
                {
                    matrix_B[i * column_b + j] = temp_list[i * column_b + j];
                    text_out.Text += string.Format("{0} ", matrix_B[i * column_b + j]);
                }
                text_out.Text += "\r\n";
            }
        }

        private void cov_A(object sender, EventArgs e)
        {
            //row 样本数，column 变量数
            if (column == 0)
            {
                MessageBox.Show("先检查数据");
                return;
            }
            double[] mean = new double[column];
            cov = new double[column * column];
            cov_flag = true;  //表示已经创建协方差矩阵

            for (int j = 0; j < column; j++) //init
            {
                mean[j] = 0.0;
            }
            for (int j = 0; j < column * column; j++) //init
            {
                cov[j] = 0.0;
            }
            for (int j = 0; j < column; j++) //mean
            {
                for (int i = 0; i < row; i++)
                {
                    mean[j] += matrix_A[i * column + j];
                }
                mean[j] /= row;
            }

            for (int i = 0; i < column; i++) //第一个变量
            {
                for (int j = i; j < column; j++) //第二个变量
                {
                    for (int k = 0; k < row; k++) //计算
                    {
                        cov[i * column + j] += (matrix_A[k * column + i] - mean[i]) * (matrix_A[k * column + j] - mean[j]);

                    }
                    cov[i * column + j] /= (row);
                    /*temp.Format("cov=%f,column=%d mean(%d)=%f,mean(%d)=%f",cov[i*column+j],row,i,mean[i],j,mean[j]);
                    MessageBox(temp);*/
                }
            }
            for (int i = 0; i < column; i++) //补全对应面
            {
                for (int j = 0; j < i; j++)
                {
                    cov[i * column + j] = cov[j * column + i];
                }
            }
            text_out.Text = "均值向量：\r\n";
            for (int j = 0; j < column; j++) //mean
            {
                // temp.Format("%f   ", mean[j]);
                text_out.Text += string.Format("{0}    ", (float)mean[j]);
            }


            text_out.Text += "\r\n协方差阵S：\r\n";
            for (int i = 0; i < column; i++) //print
            {
                for (int j = 0; j < column; j++)
                {

                    text_out.Text += string.Format("{0}    ", (float)cov[i * column + j]);
                }

                text_out.Text += "\r\n";
            }

        }

        private void cov_S_A(object sender, EventArgs e)
        {
            //row 样本数，column 变量数
            if (column == 0)
            {
                MessageBox.Show("先检查数据");
                return;
            }

            double[] mean = new double[column];
            cov = new double[column * column];
            for (int j = 0; j < column; j++) //init
            {
                mean[j] = 0.0;
            }
            for (int j = 0; j < column * column; j++) //init
            {
                cov[j] = 0.0;
            }
            for (int j = 0; j < column; j++) //mean
            {
                for (int i = 0; i < row; i++)
                {
                    mean[j] += matrix_A[i * column + j];
                }
                mean[j] /= row;
            }

            for (int i = 0; i < column; i++) //第一个变量
            {
                for (int j = i; j < column; j++) //第二个变量
                {
                    for (int k = 0; k < row; k++) //计算
                    {
                        cov[i * column + j] += (matrix_A[k * column + i] - mean[i]) * (matrix_A[k * column + j] - mean[j]);

                    }
                    cov[i * column + j] /= (row - 1);
                }
            }
            for (int i = 0; i < column; i++) //补全对应面
            {
                for (int j = 0; j < i; j++)
                {
                    cov[i * column + j] = cov[j * column + i];
                }
            }
            text_out.Text = "均值向量：\r\n";
            for (int j = 0; j < column; j++) //mean
            {
                // temp.Format("%f   ", mean[j]);
                text_out.Text += string.Format("{0}    ", (float)mean[j]);
            }


            text_out.Text += "\r\n样本方差阵S：\r\n";
            for (int i = 0; i < column; i++) //print
            {
                for (int j = 0; j < column; j++)
                {

                    text_out.Text += string.Format("{0}    ", (float)cov[i * column + j]);
                }

                text_out.Text += "\r\n";
            }
        }

        double det(int n, double[] ab)
        {
            double[] aa = new double[n * n];
            for (int i = 0; i < n * n; i++) /*赋值*/
                aa[i] = ab[i];
            double[] bb = new double[(n - 1) * (n - 1)];//创建n-1阶的代数余子式阵bb   
            int p = 0,//判断行是否移动
                q = 0;//代数余子式
            if (n == 1)
            {
                return aa[0];
            }
            double sum = 0.0;//sum为行列式的值
            for (int ai = 0; ai < n; ai++) // a的行数把矩阵a(nn)赋值到b(n-1)
            {
                for (int bi = 0; bi < n - 1; bi++)//把元素aa[ai][0]代数余子式存到bb[][]
                {
                    if (ai > bi)    //ai行的代数余子式是：小于ai的行，aa与bb阵，同行赋值
                        p = 0;
                    else
                        p = 1;     //大于等于ai的行，取aa阵的ai+1行赋值给阵bb的bi行
                    for (int j = 0; j < n - 1; j++)  //从aa的第二列赋值到第n列
                    {
                        bb[bi * (n - 1) + j] = aa[(bi + p) * n + j + 1];
                    }
                }
                if (ai % 2 == 0) q = 1;//因为列数为0，所以行数是偶数时候，代数余子式为-1.
                else q = (-1);
                sum += q * aa[ai * n] * det(n - 1, bb);
            }
            return sum;
        }
        private void det_A(object sender, EventArgs e)
        {
            if (column == row)
            {

                text_out.Text =string.Format("|A|={0}", (float)det(row, matrix_A));
            }
            else
            {
                MessageBox.Show("行列不相等无法计算");
            }

        }

        private void det_S(object sender, EventArgs e)
        {
            if (cov_flag == false)
            {
                MessageBox.Show("先计算协方差，在计算协方差的行列式");
                return;
            }
            else
            {
                text_out.Text = string.Format("|S|={0}", (float)det(column, cov));

            }
        }

        void adjoint(int n, double[] aa)
        {
            //调动之前，检查时候方阵，这里默认为aa为方阵
            //确定本函数是否修改传入的数据 ：no
            padjoint = new double[n * n];
            double[] bb = new double[(n - 1) * (n - 1)];//创建n-1阶的代数余子式阵bb 

            int pi, pj, q;
            for (int ai = 0; ai < n; ai++) // a的行数把矩阵a(nn)赋值到b(n-1)
            {
                for (int aj = 0; aj < n; aj++)
                {
                    for (int bi = 0; bi < n - 1; bi++)//把元素aa[ai][0]余子式存到bb[][]
                    {
                        for (int bj = 0; bj < n - 1; bj++)//把元素aa[ai][0]代数余子式存到bb[][]
                        {
                            if (ai > bi)    //ai行的代数余子式是：小于ai的行，aa与bb阵，同行赋值
                                pi = 0;
                            else
                                pi = 1;     //大于等于ai的行，取aa阵的ai+1行赋值给阵bb的bi行
                            if (aj > bj)    //ai行的代数余子式是：小于ai的行，aa与bb阵，同行赋值
                                pj = 0;
                            else
                                pj = 1;     //大于等于ai的行，取aa阵的ai+1行赋值给阵bb的bi行
                            bb[bi * (n - 1) + bj] = aa[(bi + pi) * n + bj + pj];
                        }
                    }
                    if ((ai + aj) % 2 == 0) q = 1;//因为列数为0，所以行数是偶数时候，代数余子式为-1.
                    else q = (-1);
                    padjoint[ai * n + aj] = q * det(n - 1, bb);  //加符号变为代数余子式
                }
            }

        }
        private void Adjoint(object sender, EventArgs e)
        {
            if (column != row)
            {
                MessageBox.Show("行列不相等,无法计算");
                return;
            }
            if (column ==0|| row==0)
            {
                MessageBox.Show("先输入数据");
                return;
            }
            adjoint(row, matrix_A);  ////计算

            text_out.Text += "\r\n伴随阵: \r\n";
            for (int ai = 0; ai < row; ai++)
            {
                for (int aj = 0; aj < row; aj++)
                {

                    text_out.Text += string.Format("{0}    ", padjoint[ai * row + aj]);
                }
                text_out.Text += "\r\n";
            }
        }

        void inverse(int n, double[] aa)
        {
            //调动之前，检查时候方阵，这里默认为aa为方阵
            //确定本函数是否修改传入的数据 ：no
            //调用函数内删除内存delete []pinverse;

            double det_aa = det(n, aa);
            if (det_aa == 0)
            {
                MessageBox.Show("行列式为0 ，不能计算逆矩阵。\n");
                return;
            }
            pinverse = new double[n * n]; //为成员变量分配内存

            adjoint(n, aa); //计算

            for (int i = 0; i < n; i++) //print
            {
                for (int j = 0; j < n; j++)
                {
                    pinverse[i * n + j] = padjoint[i * n + j] / det_aa;
                }
            }

        }
        private void Inverse(object sender, EventArgs e)
        {
            //计算A的逆
            if (column != row)
            {
                MessageBox.Show ("行列不相等,无法计算");
                return;
            }
            if (column == 0 || row == 0)
            {
                MessageBox.Show("先输入数据");
                return;
            }
            inverse(row, matrix_A);  //计算函数

            text_out.Text += "\r\n逆矩阵:\r\n";
            for (int i = 0; i < row; i++) //print
            {
                for (int j = 0; j < row; j++)
                {
                    text_out.Text += string.Format("{0}    ", pinverse[i * row + j]);
                }
                text_out.Text += "\r\n";
            }
        }

        private void R_A(object sender, EventArgs e)
        {
            //row 样本数，column 变量数
            if (column == 0)
            {
                MessageBox.Show ("先检查数据");
                return;
            }
            double[] mean = new double[column];
            cov = new double[column * column];
            double[] rr = new double[column * column];
            for (int j = 0; j < column; j++) //init
            {
                mean[j] = 0.0;
            }
            for (int j = 0; j < column * column; j++) //init
            {
                cov[j] = 0.0;
            }
            for (int j = 0; j < column; j++) //mean
            {
                for (int i = 0; i < row; i++)
                {
                    mean[j] += matrix_A[i*column+j];
                }
                mean[j] /= row;
            }

            for (int i = 0; i < column; i++) //第一个变量
            {
                for (int j = i; j < column; j++) //第二个变量
                {
                    for (int k = 0; k < row; k++) //计算
                    {
                        cov[i * column + j] += (matrix_A[k * column + i] - mean[i]) * (matrix_A[k*column+j] - mean[j]);
                    }
                    cov[i * column + j] /= (row);
                }
            }
            for (int i = 0; i < column; i++) //补全对应面
            {
                for (int j = 0; j < i; j++)
                {
                    cov[i * column + j] = cov[j * column + i];
                }
            }
            for (int i = 0; i < column; i++) //第一个变量
            {
                for (int j = 0; j < column; j++) //第二个变量
                {
                    rr[i * column + j] = cov[i * column + j] / Math.Sqrt(cov[i * column + i] * cov[j * column + j]);
                }
            }
            text_out.Text += "\r\n相关系数阵R：\r\n";
            for (int i = 0; i < column; i++) //print
            {
                for (int j = 0; j < column; j++)
                {
                    text_out.Text += string.Format("{0}  ", (float)rr[i * column + j]);
                }
                text_out.Text += "\r\n";
            }
        }

        void a_b(int ai, int aj, int bj, double[] aa, double[] bb)
        {
            //  调用函数内加上delete []pab;
            //  默认aj=bi
            if (ai == 0 || aj == 0 || bj == 0)
            {
                MessageBox.Show("先输入A、B");
                return;
            }
            pab = new double[ai * bj];
            for (int j = 0; j < ai * bj; j++) //init
            {
                pab[j] = 0.0;
            }
            for (int i = 0; i < ai; i++) //print
            {
                for (int j = 0; j < bj; j++)
                {
                    for (int k = 0; k < aj; k++)
                    {

                        pab[i * bj + j] += aa[i * aj + k] * bb[k * bj + j];
                        /*temp.Format("ab=%f  ,a=%f,b=%f  ",pab[i*bj+j],aa[i*aj+k] ,bb[k*bj+j]);
                        MessageBox(temp);*/
                    }
                }
            }
        }
        private void A_B(object sender, EventArgs e)
        {
            // TODO: 在此添加控件通知处理程序代码
            text_out.Text = "";
            if (column == 0 || row == 0 || column_b == 0 || row_b == 0)
            {
                MessageBox.Show("先输入A、B");
                return;
            }
            if (column != row_b)
            {
                MessageBox.Show("A的列与B的行不相等,无法计算");
                return;
            }
            a_b(row, column, column_b, matrix_A, matrix_B); ///计算

            text_out.Text += "A*B矩阵:   \r\n";
            for (int i = 0; i < row; i++) //print
            {
                for (int j = 0; j < column_b; j++)
                {

                    text_out.Text += string.Format("{0}  ", (float)pab[i * column_b+j]);
                }
                text_out.Text += "\r\n";
            }

        }

        private void Gramer(object sender, EventArgs e)
        {
            // TODO: 在此添加控件通知处理程序代码
            if (column == 0 || row == 0)
            {
                MessageBox.Show("先输入 A");
                return;
            }
            if (column != row + 1)
            {
                MessageBox.Show("解方程组A*x=b 需要column=row+1");
                return;
            }

            double[] Dx = new double[row * row];
            for (int i = 0; i < row; i++)
            {
                for (int j = 0; j < row; j++)
                {
                    Dx[i * row + j] = matrix_A[i * column + j];
                }
            }
            double D = det(row, Dx);
            if (D == 0)
            {
                MessageBox.Show("Cramer法则只能计算系数矩阵为满秩的矩阵");
                return;
            }


            text_out.Text = "\r\n x=";
            for (int k = 0; k < row; k++)
            {
                for (int i = 0; i < row; i++)
                {
                    for (int j = 0; j < row; j++)
                    {
                        Dx[i * row + j] = matrix_A[i * column + j];
                    }
                }
                for (int i = 0; i < row; i++)
                {
                    Dx[i * row + k] = matrix_A[(i + 1) * column - 1]; //A的最后一列赋值给第j列
                }
                text_out.Text += string.Format("{0}    ", (float )(det(row, Dx) / D));
            }

            //text_out.Text += "\r\n";
        }

        private void Jacobi(object sender, EventArgs e)
        {      
            /*
            8 -3 2 20
            4 11 -1 33
            2 1 4 12
            */
            if (column == 0 || row == 0)
            {
                MessageBox.Show ("先输入 A");
                return;
            }
            if (column != row + 1)
            {
                MessageBox.Show("解方程组A*x=b 需要column=row+1");
                return;
            }
            double[] A = new double[row * row];//系数矩阵
            double[] b = new double[row];    ///b
            double[] x = new double[row];    //x解向量
            double[] Bjx = new double[row];

            for (int i = 0; i < row; i++)
            {
                b[i] = matrix_A[(i + 1) * column - 1];  //b
                x[i] = 0.0;                     //初始化x  
                for (int j = 0; j < row; j++)
                {
                    A[i * row + j] = matrix_A[i * column + j]; //提取系数矩阵
                }
            }

            double aii;
            for (int i = 0; i < row; i++)
            {
                aii = A[i * row + i];   //处理i行对角线元素
                A[i * row + i] = 0;
                b[i] = b[i] / aii;     //b转化为f=D^-1*b,at same time assign x[i]
                for (int j = 0; j < row; j++)
                {
                    A[i * row + j] = -A[i * row + j] / aii; //A 转化为BJ
                }
            }

            text_out.Text = "Jacobi 迭代：\r\n";
            for (int it = 0; it < 20; it++) //it 
            {
                for (int i = 0; i < row; i++)
                {
                    Bjx[i] = 0.0;   //每个循环都要赋0
                }

                for (int i = 0; i < row; i++) //print
                {
                    for (int k = 0; k < row ; k++)
                    {
                        Bjx[i] += A[i * row + k] * x[k];   //A[i]=BJ*x
                    }

                }

                for (int i = 0; i < row; i++) //print
                {
                    x[i] = Bjx[i] + b[i];//b转化为f,
                }

                text_out.Text += string.Format("x{0}： ",it);
                for (int i = 0; i < row; i++) //print
                {
                    text_out.Text += string.Format("{0}  ", (float)x[i]);

                }
                text_out.Text += "\r\n";

            }
        }

        private void Gauss_seidel(object sender, EventArgs e)
        {
            if (column == 0 || row == 0)
            {
                MessageBox.Show ("先输入 A");
                return;
            }
            if (column != row + 1)
            {
                MessageBox.Show("解方程组A*x=b 需要column=row+1");
                return;
            }
            double[] A = new double[row * row];//系数矩阵
            double[] b = new double[row];    ///b 后来存放fg=（D-L）^-1*b
            double[] x = new double[row];    //x

            for (int i = 0; i < row; i++)
            {
                x[i] = 0.0;                     //初始化x  
                b[i] = matrix_A[(i + 1) * column - 1];  //b     
                for (int j = 0; j < row; j++)
                {
                    A[i * row + j] = matrix_A[i * column + j]; //提取系数矩阵
                }
            }
            ////////////BG,fg/////////////////////////
            for (int i = 0; i < row; i++)    //除以aii
            {
                double aii = A[i * row + i];
                A[i * row + i] = 0;
                b[i] = b[i] / aii;
                for (int j = 0; j < row; j++)
                {
                    A[i * row + j] = A[i * row + j] / aii;
                }
            }


            /*
        8 -3 2 20
        4 11 -1 33
        2 1 4 12
        10.000000  -2.000000  -1.000000  3.000000  
        -2.000000  10.000000  -1.000000  15.000000  
        -1.000000  -2.000000  5.000000  10.000000  
        1 2 3
        */
            text_out.Text = "Gauss_Seidel 迭代 ：";
            for (int it = 0; it < 20; it++)
            {
                for (int i = 0; i < row; i++)
                {
                    double xx = 0;
                    for (int j = 0; j < row; j++)
                    {
                        xx -= A[i * row + j] * x[j];
                        /*  temp.Format("%f    %f:  ",A[i*row+j ],x[i]);
                            MessageBox(temp );*/
                    }
                    x[i] = xx + b[i];
                }

                text_out.Text += string.Format("\r\nx{0}:  ", it);
                for (int i = 0; i < row; i++) //print
                {
                    text_out.Text += string.Format("{0}  ", (float)x[i]);
                }
            }
        }

        private void 关于ToolStripMenuItem1_Click(object sender, EventArgs e)
        {
            About form = new About();
            form.Show();
        }

        private void illustration(object sender, EventArgs e)
        {
            MessageBox.Show("在浅色文本框输入数据，\r\n每个数据以空格和换行分开,\r\n输入完成后点击save_A或save_B,\r\n然后在点击相应的计算。");
        }

        private void Example(object sender, EventArgs e)
        {
            text_in.Text = "8 -3 2\r\n4 11 -1\r\n2 1 4";
        }

        private void explain_Gramer(object sender, EventArgs e)
        {
            MessageBox.Show("Gramer法则用于计算系数矩阵满秩的齐次方程组");
        }

        private void example_data(object sender, EventArgs e)
        {
            text_in.Text = "8 -3 2 20 \r\n4 11 -1 33 \r\n2 1 4 12";
        }

        private void explain_RA(object sender, EventArgs e)
        {
            MessageBox.Show("矩阵A的相关系数阵主对角线元素为1，其它为Rij=cov（x,y）/sqrt(D(X)*D(Y))");
        }
    }
}