MyMathLib系列(向量及矩阵--准备工作)

来源：互联网发布：大数据政府治理编辑：程序博客网时间：2024/05/16 21:22

因为向量和矩阵的计算工作量比较大，为了更好的书写代码，这里增加了几个定义类，这些定义或者扩展方法将在以后的代码中应用到：
1、公共枚举类型

/*   文件:PublicEnums.cs * 目的：定义公共枚举类型. */using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace MyMathLib{    /// <summary>    /// 初等变换类型(课本上是加，这里是减，仅仅是个系数符号的区别.    /// </summary>    public enum BasicTransMethod    {        /// <summary>        /// 交换i< == >j        /// </summary>        Swap,        /// <summary>        /// 乘以非零数:i=i*M        /// </summary>        Multipler,        /// <summary>        /// 第i行减去第j行乘以一个系数:i=i-j*M        /// </summary>        CoPlus1,        /// <summary>        /// 第i行乘以系数减去第j行乘以一个系数:i=i*M1 - j*M2        /// </summary>        CoPlus2    }    /// <summary>    /// 行变换还是列变换.    /// </summary>    public enum TransRowOrCol    {        /// <summary>        /// 行        /// </summary>        Row,        /// <summary>        /// 列        /// </summary>        Col    }    public static class ConstDef    {        public const int Decimals = 15;    }    public enum SolutionType    {        /// <summary>        /// 无解        /// </summary>        None,        /// <summary>        /// 只有零解        /// </summary>        OnlyZero,        //仅有一个非零解        OnlyOne,        /// <summary>        /// 有很多解.        /// </summary>        Many    }}

2、方程求解结果

/* * SolutionOfEquation.cs * Added by Hawksoft. */using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace MyMathLib{    /// <summary>    /// 方程解结果,用于方程组求解后的结果存放.    /// </summary>    public class SolutionOfEquation    {        /// <summary>        /// 解类型        /// </summary>        public SolutionType SolutionType{ get; set; }        /// <summary>        /// 解向量        /// </summary>        public List<double[]> SolutionVectors { get; set; }        /// <summary>        /// 基本未知量        /// </summary>        public List<int> PrimaryUnknownVariations { get; set; }        /// <summary>        /// 自由未知量.        /// </summary>        public List<int> FreeUnknownVariations { get; set; }        public SolutionOfEquation()        {            SolutionVectors = new List<double[]>();            PrimaryUnknownVariations = new List<int>();            FreeUnknownVariations = new List<int>();        }    }}

3、初等变换记录项

using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace MyMathLib{    /// <summary>    /// 初等变换记录项,用于矩阵初等变换的过程演示和矩阵求逆.    /// </summary>    public class TransformItem    {        public BasicTransMethod TransMethod { get; set; }        public int i { get; set; }        public int j { get; set; }        public double M1 { get; set; }        public double M2 { get; set; }        public TransRowOrCol RowOrCol { get; set; }        public static TransformItem CreateEleTransRow1(int i, int j)        {            return new TransformItem()            {                i = i,                j = j,                M1 = 1,                TransMethod = BasicTransMethod.Swap,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransRow2(int i,double Multipler)        {            return new TransformItem()            {                i = i,                j = i,                M1 = Multipler,                M2 = Multipler,                TransMethod = BasicTransMethod.Multipler,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransRow3(int i, int j,double Multipler)        {            return new TransformItem()            {                i = i,                j = j,                M1 = Multipler,                M2 = Multipler,                TransMethod = BasicTransMethod.CoPlus1,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransRow4(int i, int j, double M1,double M2)        {            return new TransformItem()            {                i = i,                j = j,                M1 = M1,                M2 = M2,                TransMethod = BasicTransMethod.CoPlus2,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransCol1(int i, int j)        {            return new TransformItem()            {                i = i,                j = j,                M1 = 1,                M2 = 1,                TransMethod = BasicTransMethod.Swap,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransCol2(int i, double Multipler)        {            return new TransformItem()            {                i = i,                j = i,                M1 = Multipler,                M2 = Multipler,                TransMethod = BasicTransMethod.Multipler,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransCol3(int i, int j, double Multipler)        {            return new TransformItem()            {                i = i,                j = j,                M1 = 1,                M2 = Multipler,                TransMethod = BasicTransMethod.CoPlus1,                RowOrCol = TransRowOrCol.Row            };        }        public static TransformItem CreateEleTransCol4(int i, int j, double M1,double M2)        {            return new TransformItem()            {                i = i,                j = j,                M1 = M1,                M2 = M2,                TransMethod = BasicTransMethod.CoPlus2,                RowOrCol = TransRowOrCol.Row            };        }    }

另外说明一下：原来一直用decimal来计算，但在矩阵计算测试中发现，decimal很容易爆仓，所以改用double类型，其实decimal的位数比double多很多，但由于其特殊性，其表达的范围要比double小，所以后面改成了double.

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