矩阵基本操作的实现(C# 源代码)
第一次搬进自己的blog,打算放点东东到里面。在工程软件开发过程中,会碰到很多有关矩阵的运算。这是一年前的源代码
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using System;
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using System.IO;
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using System.Diagnostics;
4![](/Images/OutliningIndicators/None.gif)
5![](/Images/OutliningIndicators/None.gif)
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namespace Adjust
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{
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/// <summary>
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/// Matrix 的摘要说明。
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/// 实现矩阵的基本运算
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/// </summary>
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public class Matrix
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{
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//构造方阵
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public Matrix(int row)
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{
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m_data = new double[row,row];
19![](/Images/OutliningIndicators/InBlock.gif)
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}
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public Matrix(int row,int col)
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{
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m_data = new double[row,col];
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}
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//复制构造函数
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public Matrix(Matrix m)
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{
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int row = m.Row;
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int col = m.Col;
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m_data = new double[row,col];
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for(int i=0;i<row;i++)
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for(int j=0;j<col;j++)
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m_data[i,j] = m[i,j];
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}
37![](/Images/OutliningIndicators/InBlock.gif)
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/*
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//分配方阵的大小
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//对于已含有内存的矩阵,将清空数据
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public void SetSize(int row)
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{
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m_data = new double[row,row];
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}
45![](/Images/OutliningIndicators/InBlock.gif)
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//分配矩阵的大小
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//对于已含有内存的矩阵,将清空数据
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public void SetSize(int row,int col)
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{
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m_data = new double[row,col];
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}
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*/
54![](/Images/OutliningIndicators/InBlock.gif)
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//unit matrix:设为单位阵
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public void SetUnit()
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{
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for(int i=0;i<m_data.GetLength(0);i++)
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for(int j=0;j<m_data.GetLength(1);j++)
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m_data[i,j] = ((i==j)?1:0);
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}
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//设置元素值
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public void SetValue(double d)
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{
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for(int i=0;i<m_data.GetLength(0);i++)
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for(int j=0;j<m_data.GetLength(1);j++)
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m_data[i,j] = d;
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}
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// Value extraction:返中行数
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public int Row
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{
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get
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{
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return m_data.GetLength(0);
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}
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}
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//返回列数
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public int Col
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{
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get
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{
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return m_data.GetLength(1);
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}
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}
89![](/Images/OutliningIndicators/InBlock.gif)
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//重载索引
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//存取数据成员
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public double this[int row,int col]
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{
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get
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{
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return m_data[row,col];
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}
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set
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{
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m_data[row,col] = value;
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}
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}
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//primary change
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// 初等变换 对调两行:ri<-->rj
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public Matrix Exchange(int i,int j)
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{
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double temp;
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for(int k=0;k<Col;k++)
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{
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temp = m_data[i,k];
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m_data[i,k] = m_data[j,k];
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m_data[j,k] = temp;
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}
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return this;
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}
118![](/Images/OutliningIndicators/InBlock.gif)
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//初等变换 第index 行乘以mul
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Matrix Multiple(int index,double mul)
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{
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for(int j=0;j<Col;j++)
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{
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m_data[index,j] *= mul;
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}
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return this;
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}
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130![](/Images/OutliningIndicators/InBlock.gif)
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//初等变换 第src行乘以mul加到第index行
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Matrix MultipleAdd(int index,int src,double mul)
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{
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for(int j=0;j<Col;j++)
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{
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m_data[index,j] += m_data[src,j]*mul;
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}
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return this;
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}
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//transpose 转置
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public Matrix Transpose()
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{
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Matrix ret = new Matrix(Col,Row);
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for(int i=0;i<Row;i++)
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for(int j=0;j<Col;j++)
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{
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ret[j,i] = m_data[i,j];
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}
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return ret;
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}
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//binary addition 矩阵加
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public static Matrix operator+ (Matrix lhs,Matrix rhs)
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{
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if(lhs.Row != rhs.Row) //异常
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{
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System.Exception e = new Exception("相加的两个矩阵的行数不等");
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throw e;
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}
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if(lhs.Col != rhs.Col) //异常
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{
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System.Exception e = new Exception("相加的两个矩阵的列数不等");
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throw e;
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}
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int row = lhs.Row;
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int col = lhs.Col;
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Matrix ret=new Matrix(row,col);
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for(int i=0;i<row;i++)
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for(int j=0;j<col;j++)
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{
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double d = lhs[i,j] + rhs[i,j];
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ret[i,j] = d;
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}
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return ret;
180![](/Images/OutliningIndicators/InBlock.gif)
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}
182![](/Images/OutliningIndicators/InBlock.gif)
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//binary subtraction 矩阵减
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public static Matrix operator- (Matrix lhs,Matrix rhs)
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{
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if(lhs.Row != rhs.Row) //异常
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{
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System.Exception e = new Exception("相减的两个矩阵的行数不等");
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throw e;
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}
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if(lhs.Col != rhs.Col) //异常
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{
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System.Exception e = new Exception("相减的两个矩阵的列数不等");
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throw e;
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}
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int row = lhs.Row;
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int col = lhs.Col;
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Matrix ret=new Matrix(row,col);
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for(int i=0;i<row;i++)
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for(int j=0;j<col;j++)
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{
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double d = lhs[i,j] - rhs[i,j];
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ret[i,j] = d;
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}
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return ret;
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}
209![](/Images/OutliningIndicators/InBlock.gif)
210![](/Images/OutliningIndicators/InBlock.gif)
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//binary multiple 矩阵乘
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public static Matrix operator* (Matrix lhs,Matrix rhs)
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{
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if(lhs.Col != rhs.Row) //异常
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{
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System.Exception e = new Exception("相乘的两个矩阵的行列数不匹配");
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throw e;
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}
219![](/Images/OutliningIndicators/InBlock.gif)
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Matrix ret = new Matrix (lhs.Row,rhs.Col);
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double temp;
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for(int i=0;i<lhs.Row;i++)
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{
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for(int j=0;j<rhs.Col;j++)
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{
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temp = 0;
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for(int k=0;k<lhs.Col;k++)
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{
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temp += lhs[i,k] * rhs[k,j];
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}
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ret[i,j] = temp;
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}
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}
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return ret;
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}
237![](/Images/OutliningIndicators/InBlock.gif)
238![](/Images/OutliningIndicators/InBlock.gif)
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//binary division 矩阵除
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public static Matrix operator/ (Matrix lhs,Matrix rhs)
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{
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return lhs * rhs.Inverse();
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}
244![](/Images/OutliningIndicators/InBlock.gif)
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//unary addition单目加
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public static Matrix operator+ (Matrix m)
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{
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Matrix ret = new Matrix(m);
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return ret;
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}
251![](/Images/OutliningIndicators/InBlock.gif)
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//unary subtraction 单目减
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public static Matrix operator- (Matrix m)
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{
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Matrix ret = new Matrix(m);
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for(int i=0;i<ret.Row;i++)
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for(int j= 0;j<ret.Col;j++)
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{
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ret[i,j] = -ret[i,j];
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}
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return ret;
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}
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//number multiple 数乘
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public static Matrix operator* (double d,Matrix m)
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{
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Matrix ret = new Matrix(m);
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for(int i=0;i<ret.Row;i++)
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for(int j=0;j<ret.Col;j++)
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ret[i,j] *= d;
272![](/Images/OutliningIndicators/InBlock.gif)
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return ret;
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}
275![](/Images/OutliningIndicators/InBlock.gif)
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//number division 数除
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public static Matrix operator/ (double d,Matrix m)
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{
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return d*m.Inverse();
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}
281![](/Images/OutliningIndicators/InBlock.gif)
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//功能:返回列主元素的行号
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//参数:row为开始查找的行号
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//说明:在行号[row,Col)范围内查找第row列中绝对值最大的元素,返回所在行号
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int Pivot(int row)
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{
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int index=row;
288![](/Images/OutliningIndicators/InBlock.gif)
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for(int i=row+1;i<Row;i++)
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{
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if(m_data[i,row] > m_data[index,row])
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index=i;
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}
294![](/Images/OutliningIndicators/InBlock.gif)
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return index;
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}
297![](/Images/OutliningIndicators/InBlock.gif)
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//inversion 逆阵:使用矩阵的初等变换,列主元素消去法
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public Matrix Inverse()
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{
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if(Row != Col) //异常,非方阵
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{
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System.Exception e = new Exception("求逆的矩阵不是方阵");
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throw e;
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}
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StreamWriter sw = new StreamWriter("..\\annex\\close_matrix.txt");
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Matrix tmp = new Matrix(this);
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Matrix ret =new Matrix(Row); //单位阵
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ret.SetUnit();
310![](/Images/OutliningIndicators/InBlock.gif)
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int maxIndex;
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double dMul;
313![](/Images/OutliningIndicators/InBlock.gif)
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for(int i=0;i<Row;i++)
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{
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maxIndex = tmp.Pivot(i);
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if(tmp.m_data[maxIndex,i]==0)
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{
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System.Exception e = new Exception("求逆的矩阵的行列式的值等于0,");
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throw e;
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}
323![](/Images/OutliningIndicators/InBlock.gif)
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if(maxIndex != i) //下三角阵中此列的最大值不在当前行,交换
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{
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tmp.Exchange(i,maxIndex);
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ret.Exchange(i,maxIndex);
328![](/Images/OutliningIndicators/InBlock.gif)
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}
330![](/Images/OutliningIndicators/InBlock.gif)
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ret.Multiple(i,1/tmp[i,i]);
332![](/Images/OutliningIndicators/InBlock.gif)
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tmp.Multiple(i,1/tmp[i,i]);
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for(int j=i+1;j<Row;j++)
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{
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dMul = -tmp[j,i]/tmp[i,i];
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tmp.MultipleAdd(j,i,dMul);
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ret.MultipleAdd(j,i,dMul);
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}
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sw.WriteLine("tmp=\r\n"+tmp);
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sw.WriteLine("ret=\r\n"+ret);
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}//end for
345![](/Images/OutliningIndicators/InBlock.gif)
346![](/Images/OutliningIndicators/InBlock.gif)
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sw.WriteLine("**=\r\n"+ this*ret);
348![](/Images/OutliningIndicators/InBlock.gif)
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for(int i=Row-1;i>0;i--)
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{
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for(int j=i-1;j>=0;j--)
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{
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dMul = -tmp[j,i]/tmp[i,i];
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tmp.MultipleAdd(j,i,dMul);
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ret.MultipleAdd(j,i,dMul);
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}
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}//end for
358![](/Images/OutliningIndicators/InBlock.gif)
359![](/Images/OutliningIndicators/InBlock.gif)
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sw.WriteLine("tmp=\r\n"+tmp);
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sw.WriteLine("ret=\r\n"+ret);
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sw.WriteLine("***=\r\n"+ this*ret);
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sw.Close();
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return ret;
366![](/Images/OutliningIndicators/InBlock.gif)
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}//end Inverse
368![](/Images/OutliningIndicators/InBlock.gif)
369
#region
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/*
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//inversion 逆阵:使用矩阵的初等变换,列主元素消去法
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public Matrix Inverse()
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{
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if(Row != Col) //异常,非方阵
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{
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System.Exception e = new Exception("求逆的矩阵不是方阵");
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throw e;
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}
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///////////////
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StreamWriter sw = new StreamWriter("..\\annex\\matrix_mul.txt");
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////////////////////
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///
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Matrix tmp = new Matrix(this);
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Matrix ret =new Matrix(Row); //单位阵
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ret.SetUnit();
386![](/Images/OutliningIndicators/InBlock.gif)
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int maxIndex;
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double dMul;
389![](/Images/OutliningIndicators/InBlock.gif)
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for(int i=0;i<Row;i++)
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{
392![](/Images/OutliningIndicators/InBlock.gif)
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maxIndex = tmp.Pivot(i);
394
395
if(tmp.m_data[maxIndex,i]==0)
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{
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System.Exception e = new Exception("求逆的矩阵的行列式的值等于0,");
398
throw e;
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}
400![](/Images/OutliningIndicators/InBlock.gif)
401
if(maxIndex != i) //下三角阵中此列的最大值不在当前行,交换
402
{
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tmp.Exchange(i,maxIndex);
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ret.Exchange(i,maxIndex);
405![](/Images/OutliningIndicators/InBlock.gif)
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}
407![](/Images/OutliningIndicators/InBlock.gif)
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ret.Multiple(i,1/tmp[i,i]);
409![](/Images/OutliningIndicators/InBlock.gif)
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/////////////////////////
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//sw.WriteLine("nul \t"+tmp[i,i]+"\t"+ret[i,i]);
412
////////////////
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tmp.Multiple(i,1/tmp[i,i]);
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//sw.WriteLine("mmm \t"+tmp[i,i]+"\t"+ret[i,i]);
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sw.WriteLine("111111111 tmp=\r\n"+tmp);
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for(int j=i+1;j<Row;j++)
417
{
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dMul = -tmp[j,i];
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tmp.MultipleAdd(j,i,dMul);
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ret.MultipleAdd(j,i,dMul);
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422
}
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sw.WriteLine("222222222222=\r\n"+tmp);
424![](/Images/OutliningIndicators/InBlock.gif)
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}//end for
426![](/Images/OutliningIndicators/InBlock.gif)
427![](/Images/OutliningIndicators/InBlock.gif)
428![](/Images/OutliningIndicators/InBlock.gif)
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for(int i=Row-1;i>0;i--)
430
{
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for(int j=i-1;j>=0;j--)
432
{
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dMul = -tmp[j,i];
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tmp.MultipleAdd(j,i,dMul);
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ret.MultipleAdd(j,i,dMul);
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}
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}//end for
438
439
//////////////////////////
440![](/Images/OutliningIndicators/InBlock.gif)
441![](/Images/OutliningIndicators/InBlock.gif)
442
sw.WriteLine("tmp = \r\n" + tmp.ToString());
443![](/Images/OutliningIndicators/InBlock.gif)
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sw.Close();
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///////////////////////////////////////
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///
447
return ret;
448![](/Images/OutliningIndicators/InBlock.gif)
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}//end Inverse
450![](/Images/OutliningIndicators/InBlock.gif)
451
*/
452![](/Images/OutliningIndicators/InBlock.gif)
453
#endregion
454![](/Images/OutliningIndicators/InBlock.gif)
455
//determine if the matrix is square:方阵
456
public bool IsSquare()
457
{
458
return Row==Col;
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}
460![](/Images/OutliningIndicators/InBlock.gif)
461
//determine if the matrix is symmetric对称阵
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public bool IsSymmetric()
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{
464![](/Images/OutliningIndicators/InBlock.gif)
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if(Row != Col)
466
return false;
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468
for(int i=0;i<Row;i++)
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for(int j=i+1;j<Col;j++)
470
if( m_data[i,j] != m_data[j,i])
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return false;
472![](/Images/OutliningIndicators/InBlock.gif)
473
return true;
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}
475![](/Images/OutliningIndicators/InBlock.gif)
476
//一阶矩阵->实数
477
public double ToDouble()
478
{
479
Trace.Assert(Row==1 && Col==1);
480![](/Images/OutliningIndicators/InBlock.gif)
481
return m_data[0,0];
482
}
483![](/Images/OutliningIndicators/InBlock.gif)
484
//conert to string
485
public override string ToString()
486
{
487
488
string s="";
489
for(int i=0;i<Row;i++)
490
{
491
for(int j=0;j<Col;j++)
492
s += string.Format("{0} ",m_data[i,j]);
493![](/Images/OutliningIndicators/InBlock.gif)
494
s += "\r\n";
495
}
496
return s;
497![](/Images/OutliningIndicators/InBlock.gif)
498
}
499![](/Images/OutliningIndicators/InBlock.gif)
500![](/Images/OutliningIndicators/InBlock.gif)
501
//私有数据成员
502
private double[,] m_data;
503
504
}//end class Matrix
505
}
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![](/Images/OutliningIndicators/InBlock.gif)
465
![](/Images/OutliningIndicators/InBlock.gif)
466
![](/Images/OutliningIndicators/InBlock.gif)
467
![](/Images/OutliningIndicators/InBlock.gif)
468
![](/Images/OutliningIndicators/InBlock.gif)
469
![](/Images/OutliningIndicators/InBlock.gif)
470
![](/Images/OutliningIndicators/InBlock.gif)
471
![](/Images/OutliningIndicators/InBlock.gif)
472
![](/Images/OutliningIndicators/InBlock.gif)
473
![](/Images/OutliningIndicators/InBlock.gif)
474
![](/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
475
![](/Images/OutliningIndicators/InBlock.gif)
476
![](/Images/OutliningIndicators/InBlock.gif)
477
![](/Images/OutliningIndicators/InBlock.gif)
478
![](/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
479
![](/Images/OutliningIndicators/InBlock.gif)
480
![](/Images/OutliningIndicators/InBlock.gif)
481
![](/Images/OutliningIndicators/InBlock.gif)
482
![](/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
483
![](/Images/OutliningIndicators/InBlock.gif)
484
![](/Images/OutliningIndicators/InBlock.gif)
485
![](/Images/OutliningIndicators/InBlock.gif)
486
![](/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
487
![](/Images/OutliningIndicators/InBlock.gif)
488
![](/Images/OutliningIndicators/InBlock.gif)
489
![](/Images/OutliningIndicators/InBlock.gif)
490
![](/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
491
![](/Images/OutliningIndicators/InBlock.gif)
492
![](/Images/OutliningIndicators/InBlock.gif)
493
![](/Images/OutliningIndicators/InBlock.gif)
494
![](/Images/OutliningIndicators/InBlock.gif)
495
![](/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
496
![](/Images/OutliningIndicators/InBlock.gif)
497
![](/Images/OutliningIndicators/InBlock.gif)
498
![](/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
499
![](/Images/OutliningIndicators/InBlock.gif)
500
![](/Images/OutliningIndicators/InBlock.gif)
501
![](/Images/OutliningIndicators/InBlock.gif)
502
![](/Images/OutliningIndicators/InBlock.gif)
503
![](/Images/OutliningIndicators/InBlock.gif)
504
![](/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
505
![](/Images/OutliningIndicators/ExpandedBlockEnd.gif)
例子:
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](/Images/OutliningIndicators/InBlock.gif)
![](/Images/OutliningIndicators/InBlock.gif)
![](/Images/OutliningIndicators/InBlock.gif)
![](/Images/OutliningIndicators/ExpandedBlockEnd.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)
![](/Images/OutliningIndicators/None.gif)