C# 矩陣計算

private void button3_Click(object sender, EventArgs e)
        {
            double[] arrDataA = new double[2] {    3, 4 };
            double[,] arrDataB = new double[2,2]{ {1,2},
                                                  {2,3}
                                                };
            
            Matrix a = new Matrix(arrDataA);
            Matrix b = new Matrix(arrDataA);
            Matrix c;
            c = a + b;
            Console.WriteLine("A + B  ：" + c.ToString());            
            c = a - b;
            Console.WriteLine("A - B  ：" + c.ToString());
            Console.WriteLine("A == B  ：" + (a == b).ToString());
            b = new Matrix(arrDataB);
            Console.WriteLine("A == B  ：" + (a == b).ToString());
            c = a * b;
            Console.WriteLine("A * B  ：" + c.ToString());
        }

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ProgressTest
{
    /// <summary>
    /// 矩陣類
    /// </summary>
    /// <remarks>
    /// 孫繼磊，2010-10-18
    /// [e-mail]
    /// </remarks>
    public sealed class Matrix
    {
        int row, column;            //矩陣的行列數
        double[,] data;            //矩陣的數據

        #region 構造函數
        public Matrix(int rowNum, int columnNum)
        {
            row = rowNum;
            column = columnNum;
            data = new double[row, column];
        }
        public Matrix(double[,] members)
        {
            row = members.GetUpperBound(0) + 1;
            column = members.GetUpperBound(1) + 1;
            data = new double[row, column];
            Array.Copy(members, data, row * column);
        }
        public Matrix(double[] vector)
        {
            row = 1;
            column = vector.GetUpperBound(0) + 1;
            data = new double[1, column];
            for (int i = 0; i < vector.Length; i++)
            {
                data[0, i] = vector[i];
            }
        }
        #endregion


        #region 屬性和索引器
        public int rowNum { get { return row; } }
        public int columnNum { get { return column; } }

        public double this[int r, int c]
        {
            get { return data[r, c]; }
            set { data[r, c] = value; }
        }
        #endregion


        public override string ToString()
        {
            string strRet = "";
            for(int i=0;i<row;i++)
                for (int j = 0; j < column; j++)
                {
                    strRet +=  data[i,j] + " , ";
                }
            return strRet;
        }
        #region 轉置
        /// <summary>
        /// 將矩陣轉置，得到一個新矩陣（此操作不影響原矩陣）
        /// </summary>
        /// <param name="input">要轉置的矩陣</param>
        /// <returns>原矩陣經過轉置得到的新矩陣</returns>
        public static Matrix transpose(Matrix input)
        {
            double[,] inverseMatrix = new double[input.column, input.row];
            for (int r = 0; r < input.row; r++)
                for (int c = 0; c < input.column; c++)
                    inverseMatrix[c, r] = input[r, c];
            return new Matrix(inverseMatrix);
        }
        #endregion

        #region 得到行向量或者列向量
        public Matrix getRow(int r)
        {
            if (r > row || r <= 0) throw new Exception("沒有這一行。");
            double[] a = new double[column];
            Array.Copy(data, column * (row - 1), a, 0, column);
            Matrix m = new Matrix(a);
            return m;
        }
        public Matrix getColumn(int c)
        {
            if (c > column || c < 0) throw new Exception("沒有這一列。");
            double[,] a = new double[row, 1];
            for (int i = 0; i < row; i++)
                a[i, 0] = data[i, c];
            return new Matrix(a);
        }
        #endregion

        #region 操作符重載  + - * / == !=
        public static Matrix operator +(Matrix a, Matrix b)
        {
            if (a.row != b.row || a.column != b.column)
                throw new Exception("矩陣維數不匹配。");
            Matrix result = new Matrix(a.row, a.column);
            for (int i = 0; i < a.row; i++)
                for (int j = 0; j < a.column; j++)
                    result[i, j] = a[i, j] + b[i, j];
            return result;
        }

        
        public static Matrix operator -(Matrix a, Matrix b)
        {
            return a + b * (-1);
        }

        public static Matrix operator *(Matrix matrix, double factor)
        {
            Matrix result = new Matrix(matrix.row, matrix.column);
            for (int i = 0; i < matrix.row; i++)
                for (int j = 0; j < matrix.column; j++)
                    matrix[i, j] = matrix[i, j] * factor;
            return matrix;
        }
        public static Matrix operator *(double factor, Matrix matrix)
        {
            return matrix * factor;
        }

        //a 行元素 * b 列元素
        //a 列數 == b行數
        public static Matrix operator *(Matrix a, Matrix b)
        {
            if (a.column != b.row)
                throw new Exception("矩陣維數不匹配。");
            Matrix result = new Matrix(a.row, b.column);
            for (int i = 0; i < a.row; i++)
                for (int j = 0; j < b.column; j++)
                    for (int k = 0; k < a.column; k++)
                        result[i, j] += a[i, k] * b[k, j];

            return result;
        }
        public static bool operator ==(Matrix a, Matrix b)
        {
            if (object.Equals(a, b)) return true;
            if (object.Equals(null, b))
                return a.Equals(b);
            return b.Equals(a);
        }
        public static bool operator !=(Matrix a, Matrix b)
        {
            return !(a == b);
        }
        public override bool Equals(object obj)
        {
            if (obj == null) return false;
            if (!(obj is Matrix)) return false;
            Matrix t = obj as Matrix;
            if (row != t.row || column != t.column) return false;
            return this.Equals(t, 10);
        }
        /// <summary>
        /// 按照給定的精度比較兩個矩陣是否相等
        /// </summary>
        /// <param name="matrix">要比較的另外一個矩陣</param>
        /// <param name="precision">比較精度（小數位）</param>
        /// <returns>是否相等</returns>
        public bool Equals(Matrix matrix, int precision)
        {
            if (precision < 0) throw new Exception("小數位不能是負數");
            double test = Math.Pow(10.0, -precision);
            if (test < double.Epsilon)
                throw new Exception("所要求的精度太高，不被支持。");
            for (int r = 0; r < this.row; r++)
                for (int c = 0; c < this.column; c++)
                    if (Math.Abs(this[r, c] - matrix[r, c]) >= test)
                        return false;

            return true;
        }
        #endregion
    }
}