数学：《线性代数》矩阵初等行变换及其应用（线性方程求解）

背景

高斯小朋友确实聪明，发明了高斯消元法，进而引入了线性代数，本文给出矩阵的初等行变换代码实现及其应用（线性方程求解）。

实现

代码

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

namespace DataStuctureStudy.Matrixes
{
    class MatrixTest
    {
        public static void Test()
        {
            var matrix =
                new Matrix(3, 4)
                .SetRowData(0, 1, 2, 3, 2)
                .SetRowData(1, 1, 2, 7, 5)
                .SetRowData(2, 4, 9, 2, 6);

            matrix.Dispaly();

            matrix.Simplify().Dispaly();
        }
        class Matrix
        {
            private readonly int _m;
            private readonly int _n;
            private readonly double[][] _data;

            public Matrix(int m, int n)
            {
                _m = m;
                _n = n;
                _data = new double[m][];
                for (var i = 0; i < m; i++)
                {
                    _data[i] = new double[n];
                }
            }

            public Matrix SetRowData(int row, params double[] values)
            {
                Array.Copy(values, _data[row], _n);

                return this;
            }

            public Matrix SwapRow(int rowX, int rowY)
            {
                var temp = _data[rowX];
                _data[rowX] = _data[rowY];
                _data[rowY] = temp;

                return this;
            }

            public Matrix MultiplyRow(int row, double operand)
            {
                for (var i = 0; i < _n; i++)
                {
                    _data[row][i] *= operand;
                }

                return this;
            }

            public Matrix AddSourceRowToTargetRow(int sourceRow, double operand, int targetRow)
            {
                for (var i = 0; i < _n; i++)
                {
                    _data[targetRow][i] += _data[sourceRow][i] * operand;
                }

                return this;
            }

            public Matrix Simplify()
            {
                for (var col = 0; col < _n; col++)
                {
                    if (col >= _m)
                    {
                        break;
                    }

                    if (_data[col][col] == 0)
                    {
                        var nonZeroRowIndex = this.FindNonZeroRowIndex(col, col + 1);
                        if (nonZeroRowIndex == -1)
                        {
                            break;
                        }
                        this.SwapRow(col, nonZeroRowIndex);
                    }

                    this.MultiplyRow(col, 1 / _data[col][col]);

                    for (var row = 0; row < _m; row++)
                    {
                        if (row == col)
                        {
                            continue;
                        }
                        this.AddSourceRowToTargetRow(col, -1 * _data[row][col], row);
                    }
                }

                return this;
            }

            public int FindNonZeroRowIndex(int col, int startRow)
            {
                if (startRow >= _m)
                {
                    return -1;
                }

                for (var i = startRow; i < _m; i++)
                {
                    if (_data[i][col] != 0)
                    {
                        return i;
                    }
                }

                return -1;
            }

            public void Dispaly()
            {
                Console.WriteLine();
                foreach (var row in _data)
                {
                    Console.WriteLine("[ " + String.Join(" , ", row) + " ]");
                }
                Console.WriteLine();
            }
        }
    }
}

输出结果