VC中实现最小二乘法 直线拟合 Y=a0+a1X 以及 Y=aX
2007-07-06 20:00
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用最小二乘法做直线拟合真的是非常简单,我随便写了一下并经过测试,需要使用的朋友随便改几个地方(例如变量名等)就可以用在自己的应用程序中了。在这里给出拟合直线Y=a0+a1X 以及Y=aX的例子。
我写了一个曲线拟合的类,这个其实就是其中的一部分。目前这个类可以拟合如下几种曲线:Y=aX,Y=aX+b,Y=aX^2+bX,Y=X^a+bX,Y=alnX+b,Y=aX^b,Y=aX^2+bX+c。
首先是关于最小二乘法的数学基础,就不多说了,无非就是求偏导之类的。
在VC中的具体代码如下(先是拟合直线Y=a0+a1X的):
函数声明:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void linearReg_Y_a0_a1X(double &a_0, double &a_1, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg);
函数定义:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void CYourDlg::linearReg_Y_a0_a1X(double &a0, double &a1, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
double sumXiYi(0.0), sumXi(0.0), sumYi(0.0), sumXi_2(0.0), X_Average(0.0), Y_Average(0.0);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
INT_PTR n = X_Con_Lin_Reg.GetSize();
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
for (int i=0; i<n; i++)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXiYi += X_Con_Lin_Reg[i]*Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi += X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumYi += Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi_2 += X_Con_Lin_Reg[i]*X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockEnd.gif)
}
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
/**//*求平均值*/
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
X_Average = sumXi/n;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
Y_Average = sumYi/n;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
/**//*y=a0+a1x*/
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a1 = (sumXiYi-n*X_Average*Y_Average)/(sumXi_2-n*X_Average*X_Average);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a0 = Y_Average - a1*X_Average;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockEnd.gif)
}
使用说明:
假设你想把求得的a0存在变量double a0中,a1存在double a1中,原始数据X值存在CArray<double,double> X中,原始数据Y值存在CArray<double,double> Y中,则调用函数的方法如下:
linearReg_Y_a0_a1X(a0, a1, X, Y);
这样调用之后,a0和a1中求得的就是你要求的值了。
将CYourDlg换成你的类名(你在哪个类中使用,就换成那个类的名字,然后把函数声明放在那个类的头文件中),最后求得的a0和a1将作为引用被传递回去,想必各位一看就明白了。至于CArray,它是MFC中的动态数组,具体可以去查MSDN,使用上真的是非常简单的。
求Y=aX的代码更简单,具体说明就不多说了,可以参考上面Y=a0+a1X的说明。
函数声明:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void linearReg_Y_aX(double &a, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg);
函数定义:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void CYourDlg::linearReg_Y_aX(double &a, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
double sumXiYi(0.0), sumXi_2(0.0);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
INT_PTR n = X_Con_Lin_Reg.GetSize();
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
for (int i=0; i<n; i++)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXiYi += X_Con_Lin_Reg[i]*Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi_2 += X_Con_Lin_Reg[i]*X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockEnd.gif)
}
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a= sumXiYi/sumXi_2;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockEnd.gif)
}
我写了一个曲线拟合的类,这个其实就是其中的一部分。目前这个类可以拟合如下几种曲线:Y=aX,Y=aX+b,Y=aX^2+bX,Y=X^a+bX,Y=alnX+b,Y=aX^b,Y=aX^2+bX+c。
首先是关于最小二乘法的数学基础,就不多说了,无非就是求偏导之类的。
在VC中的具体代码如下(先是拟合直线Y=a0+a1X的):
函数声明:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void linearReg_Y_a0_a1X(double &a_0, double &a_1, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg);
函数定义:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void CYourDlg::linearReg_Y_a0_a1X(double &a0, double &a1, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
double sumXiYi(0.0), sumXi(0.0), sumYi(0.0), sumXi_2(0.0), X_Average(0.0), Y_Average(0.0);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
INT_PTR n = X_Con_Lin_Reg.GetSize();
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
for (int i=0; i<n; i++)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXiYi += X_Con_Lin_Reg[i]*Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi += X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumYi += Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi_2 += X_Con_Lin_Reg[i]*X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockEnd.gif)
}
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
/**//*求平均值*/
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
X_Average = sumXi/n;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
Y_Average = sumYi/n;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
/**//*y=a0+a1x*/
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a1 = (sumXiYi-n*X_Average*Y_Average)/(sumXi_2-n*X_Average*X_Average);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a0 = Y_Average - a1*X_Average;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockEnd.gif)
}
使用说明:
假设你想把求得的a0存在变量double a0中,a1存在double a1中,原始数据X值存在CArray<double,double> X中,原始数据Y值存在CArray<double,double> Y中,则调用函数的方法如下:
linearReg_Y_a0_a1X(a0, a1, X, Y);
这样调用之后,a0和a1中求得的就是你要求的值了。
将CYourDlg换成你的类名(你在哪个类中使用,就换成那个类的名字,然后把函数声明放在那个类的头文件中),最后求得的a0和a1将作为引用被传递回去,想必各位一看就明白了。至于CArray,它是MFC中的动态数组,具体可以去查MSDN,使用上真的是非常简单的。
求Y=aX的代码更简单,具体说明就不多说了,可以参考上面Y=a0+a1X的说明。
函数声明:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void linearReg_Y_aX(double &a, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg);
函数定义:
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/None.gif)
void CYourDlg::linearReg_Y_aX(double &a, const CArray<double,double> & X_Con_Lin_Reg, const CArray<double,double> & Y_Volts_Lin_Reg)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
double sumXiYi(0.0), sumXi_2(0.0);
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
INT_PTR n = X_Con_Lin_Reg.GetSize();
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
for (int i=0; i<n; i++)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockStart.gif)
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ContractedSubBlock.gif)
...{
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXiYi += X_Con_Lin_Reg[i]*Y_Volts_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
sumXi_2 += X_Con_Lin_Reg[i]*X_Con_Lin_Reg[i];
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedSubBlockEnd.gif)
}
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/InBlock.gif)
a= sumXiYi/sumXi_2;
![](http://images.csdn.net/syntaxhighlighting/OutliningIndicators/ExpandedBlockEnd.gif)
}
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