C#矩阵类
using System;
using System.IO;
using System.Diagnostics;
namespace Adjust
{
/// <summary>
/// Matrix 的摘要说明。
/// 实现矩阵的基本运算
/// </summary>
public class Matrix
{
//构造方阵
public Matrix(int row)
{
m_data = new double[row,row];
}
public Matrix(int row,int col)
{
m_data = new double[row,col];
}
//复制构造函数
public Matrix(Matrix m)
{
int row = m.Row;
int col = m.Col;
m_data = new double[row,col];
for(int i=0;i<row;i++)
for(int j=0;j<col;j++)
m_data[i,j] = m[i,j];
}
/*
//分配方阵的大小
//对于已含有内存的矩阵，将清空数据
public void SetSize(int row)
{
m_data = new double[row,row];
}
//分配矩阵的大小
//对于已含有内存的矩阵，将清空数据
public void SetSize(int row,int col)
{
m_data = new double[row,col];
}
*/
//unit matrix:设为单位阵
public void SetUnit()
{
for(int i=0;i<m_data.GetLength(0);i++)
for(int j=0;j<m_data.GetLength(1);j++)
m_data[i,j] = ((i==j)?1:0);
}
//设置元素值
public void SetValue(double d)
{
for(int i=0;i<m_data.GetLength(0);i++)
for(int j=0;j<m_data.GetLength(1);j++)
m_data[i,j] = d;
}
// Value extraction：返中行数
public int Row
{
get
{
return m_data.GetLength(0);
}
}
//返回列数
public int Col
{
get
{
return m_data.GetLength(1);
}
}
//重载索引
//存取数据成员
public double this[int row,int col]
{
get
{
return m_data[row,col];
}
set
{
m_data[row,col] = value;
}
}
//primary change
// 初等变换 对调两行：ri<-->rj
public Matrix Exchange(int i,int j)
{
double temp;
for(int k=0;k<Col;k++)
{
temp = m_data[i,k];
m_data[i,k] = m_data[j,k];
m_data[j,k] = temp;
}
return this;
}
//初等变换 第index 行乘以mul
Matrix Multiple(int index,double mul)
{
for(int j=0;j<Col;j++)
{
m_data[index,j] *= mul;
}
return this;
}
//初等变换 第src行乘以mul加到第index行
Matrix MultipleAdd(int index,int src,double mul)
{
for(int j=0;j<Col;j++)
{
m_data[index,j] += m_data[src,j]*mul;
}
return this;
}
//transpose 转置
public Matrix Transpose()
{
Matrix ret = new Matrix(Col,Row);
for(int i=0;i<Row;i++)
for(int j=0;j<Col;j++)
{
ret[j,i] = m_data[i,j];
}
return ret;
}
//binary addition 矩阵加
public static Matrix operator+ (Matrix lhs,Matrix rhs)
{
if(lhs.Row != rhs.Row) //异常
{
System.Exception e = new Exception("相加的两个矩阵的行数不等");
throw e;
}
if(lhs.Col != rhs.Col) //异常
{
System.Exception e = new Exception("相加的两个矩阵的列数不等");
throw e;
}
int row = lhs.Row;
int col = lhs.Col;
Matrix ret=new Matrix(row,col);
for(int i=0;i<row;i++)
for(int j=0;j<col;j++)
{
double d = lhs[i,j] + rhs[i,j];
ret[i,j] = d;
}
return ret;
}
//binary subtraction 矩阵减
public static Matrix operator- (Matrix lhs,Matrix rhs)
{
if(lhs.Row != rhs.Row) //异常
{
System.Exception e = new Exception("相减的两个矩阵的行数不等");
throw e;
}
if(lhs.Col != rhs.Col) //异常
{
System.Exception e = new Exception("相减的两个矩阵的列数不等");
throw e;
}
int row = lhs.Row;
int col = lhs.Col;
Matrix ret=new Matrix(row,col);
for(int i=0;i<row;i++)
for(int j=0;j<col;j++)
{
double d = lhs[i,j] - rhs[i,j];
ret[i,j] = d;
}
return ret;
}
//binary multiple 矩阵乘
public static Matrix operator* (Matrix lhs,Matrix rhs)
{
if(lhs.Col != rhs.Row) //异常
{
System.Exception e = new Exception("相乘的两个矩阵的行列数不匹配");
throw e;
}
Matrix ret = new Matrix (lhs.Row,rhs.Col);
double temp;
for(int i=0;i<lhs.Row;i++)
{
for(int j=0;j<rhs.Col;j++)
{
temp = 0;
for(int k=0;k<lhs.Col;k++)
{
temp += lhs[i,k] * rhs[k,j];
}
ret[i,j] = temp;
}
}
return ret;
}
//binary division 矩阵除
public static Matrix operator/ (Matrix lhs,Matrix rhs)
{
return lhs * rhs.Inverse();
}
//unary addition单目加
public static Matrix operator+ (Matrix m)
{
Matrix ret = new Matrix(m);
return ret;
}
//unary subtraction 单目减
public static Matrix operator- (Matrix m)
{
Matrix ret = new Matrix(m);
for(int i=0;i<ret.Row;i++)
for(int j= 0;j<ret.Col;j++)
{
ret[i,j] = -ret[i,j];
}
return ret;
}
//number multiple 数乘
public static Matrix operator* (double d,Matrix m)
{
Matrix ret = new Matrix(m);
for(int i=0;i<ret.Row;i++)
for(int j=0;j<ret.Col;j++)
ret[i,j] *= d;
return ret;
}
//number division 数除
public static Matrix operator/ (double d,Matrix m)
{
return d*m.Inverse();
}
//功能：返回列主元素的行号
//参数：row为开始查找的行号
//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
int Pivot(int row)
{
int index=row;
for(int i=row+1;i<Row;i++)
{
if(m_data[i,row] > m_data[index,row])
index=i;
}
return index;
}
//inversion 逆阵：使用矩阵的初等变换，列主元素消去法
public Matrix Inverse()
{
if(Row != Col) //异常,非方阵
{
System.Exception e = new Exception("求逆的矩阵不是方阵");
throw e;
}
StreamWriter sw = new StreamWriter("..\\annex\\close_matrix.txt");
Matrix tmp = new Matrix(this);
Matrix ret =new Matrix(Row); //单位阵
ret.SetUnit();
int maxIndex;
double dMul;
for(int i=0;i<Row;i++)
{
maxIndex = tmp.Pivot(i);
if(tmp.m_data[maxIndex,i]==0)
{
System.Exception e = new Exception("求逆的矩阵的行列式的值等于0,");
throw e;
}
if(maxIndex != i) //下三角阵中此列的最大值不在当前行，交换
{
tmp.Exchange(i,maxIndex);
ret.Exchange(i,maxIndex);
}
ret.Multiple(i,1/tmp[i,i]);
tmp.Multiple(i,1/tmp[i,i]);
for(int j=i+1;j<Row;j++)
{
dMul = -tmp[j,i]/tmp[i,i];
tmp.MultipleAdd(j,i,dMul);
}
sw.WriteLine("tmp=\r\n"+tmp);
sw.WriteLine("ret=\r\n"+ret);
}//end for
sw.WriteLine("**=\r\n"+ this*ret);
for(int i=Row-1;i>0;i--)
{
for(int j=i-1;j>=0;j--)
{
dMul = -tmp[j,i]/tmp[i,i];
tmp.MultipleAdd(j,i,dMul);
ret.MultipleAdd(j,i,dMul);
}
}//end for
sw.WriteLine("tmp=\r\n"+tmp);
sw.WriteLine("ret=\r\n"+ret);
sw.WriteLine("***=\r\n"+ this*ret);
sw.Close();
return ret;
}//end Inverse
#region
/*
//inversion 逆阵：使用矩阵的初等变换，列主元素消去法
public Matrix Inverse()
{
if(Row != Col) //异常,非方阵
{
System.Exception e = new Exception("求逆的矩阵不是方阵");
throw e;
}
///////////////
StreamWriter sw = new StreamWriter("..\\annex\\matrix_mul.txt");
////////////////////
///
Matrix tmp = new Matrix(this);
Matrix ret =new Matrix(Row); //单位阵
ret.SetUnit();
int maxIndex;
double dMul;
for(int i=0;i<Row;i++)
{
maxIndex = tmp.Pivot(i);
if(tmp.m_data[maxIndex,i]==0)
{
System.Exception e = new Exception("求逆的矩阵的行列式的值等于0,");
throw e;
}
if(maxIndex != i) //下三角阵中此列的最大值不在当前行，交换
{
tmp.Exchange(i,maxIndex);
ret.Exchange(i,maxIndex);
}
ret.Multiple(i,1/tmp[i,i]);
/////////////////////////
//sw.WriteLine("nul \t"+tmp[i,i]+"\t"+ret[i,i]);
////////////////
tmp.Multiple(i,1/tmp[i,i]);
//sw.WriteLine("mmm \t"+tmp[i,i]+"\t"+ret[i,i]);
sw.WriteLine("111111111 tmp=\r\n"+tmp);
for(int j=i+1;j<Row;j++)
{
dMul = -tmp[j,i];
tmp.MultipleAdd(j,i,dMul);
ret.MultipleAdd(j,i,dMul);
}
sw.WriteLine("222222222222=\r\n"+tmp);
}//end for
for(int i=Row-1;i>0;i--)
{
for(int j=i-1;j>=0;j--)
{
dMul = -tmp[j,i];
tmp.MultipleAdd(j,i,dMul);
ret.MultipleAdd(j,i,dMul);
}
}//end for
//////////////////////////
sw.WriteLine("tmp = \r\n" + tmp.ToString());
sw.Close();
///////////////////////////////////////
///
return ret;
}//end Inverse
*/
#endregion
//determine if the matrix is square:方阵
public bool IsSquare()
{
return Row==Col;
}
//determine if the matrix is symmetric对称阵
public bool IsSymmetric()
{
if(Row != Col)
return false;
for(int i=0;i<Row;i++)
for(int j=i+1;j<Col;j++)
if( m_data[i,j] != m_data[j,i])
return false;
return true;
}
//一阶矩阵->实数
public double ToDouble()
{
Trace.Assert(Row==1 && Col==1);
return m_data[0,0];
}
//conert to string
public override string ToString()
{
string s="";
for(int i=0;i<Row;i++)
{
for(int j=0;j<Col;j++)
s += string.Format("{0} ",m_data[i,j]);
s += "\r\n";
}
return s;
}
//私有数据成员
private double[,] m_data;
}//end class Matrix
}