Matlab 线性拟合 非线性拟合

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使用Matlab进行拟合是图像处理中线条变换的一个重点内容，本文将详解Matlab中的直线拟合和曲线拟合用法。

关键函数：

fittype

Fit type for curve and surface fitting

Syntax

ffun = fittype(libname)

ffun = fittype(expr)

ffun = fittype({expr1,...,exprn})

ffun = fittype(expr, Name, Value,...)

ffun= fittype({expr1,...,exprn}, Name, Value,...)

/***********************************线性拟合***********************************/

线性拟合公式：

coeff1 * term1 + coeff2 * term2 + coeff3 * term3 + ...

其中，coefficient是系数，term都是x的一次项。

线性拟合Example：

Example1: y=kx+b;

法1：

x=[1,1.5,2,2.5,3];y=[0.9,1.7,2.2,2.6,3];p=polyfit(x,y,1);x1=linspace(min(x),max(x));y1=polyval(p,x1);plot(x,y,'*',x1,y1);

结果：p =    1.0200    0.0400

即y=1.0200 *x+ 0.0400

法2：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];p=fittype('poly1')f=fit(x,y,p)plot(f,x,y);

运行结果：

 x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];p=fittype('poly1')f=fit(x,y,p)plot(f,x,y);p =      Linear model Poly1:     p(p1,p2,x) = p1*x + p2f =      Linear model Poly1:     f(x) = p1*x + p2     Coefficients (with 95% confidence bounds):       p1 =        1.02  (0.7192, 1.321)       p2 =        0.04  (-0.5981, 0.6781)

Example2:y=a*x + b*sin(x) + c

法1：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];EXPR = {'x','sin(x)','1'};p=fittype(EXPR)f=fit(x,y,p)plot(f,x,y);

运行结果：

 x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];EXPR = {'x','sin(x)','1'};p=fittype(EXPR)f=fit(x,y,p)plot(f,x,y);p =      Linear model:     p(a,b,c,x) = a*x + b*sin(x) + cf =      Linear model:     f(x) = a*x + b*sin(x) + c     Coefficients (with 95% confidence bounds):       a =       1.249  (0.9856, 1.512)       b =      0.6357  (0.03185, 1.24)       c =     -0.8611  (-1.773, 0.05094)

法2：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x')f=fit(x,y,p)plot(f,x,y);

运行结果：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x')f=fit(x,y,p)plot(f,x,y);p =      General model:     p(a,b,c,x) = a*x+b*sin(x)+cWarning: Start point not provided, choosing random startpoint. > In fit>iCreateWarningFunction/nThrowWarning at 738  In fit>iFit at 320  In fit at 109 f =      General model:     f(x) = a*x+b*sin(x)+c     Coefficients (with 95% confidence bounds):       a =       1.249  (0.9856, 1.512)       b =      0.6357  (0.03185, 1.24)       c =     -0.8611  (-1.773, 0.05094)

/***********************************非线性拟合***********************************/

Example：y=a*x^2+b*x+c

法1：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x.^2+b*x+c','independent','x')f=fit(x,y,p)plot(f,x,y);

运行结果：

p =      General model:     p(a,b,c,x) = a*x.^2+b*x+cWarning: Start point not provided, choosing random startpoint. > In fit>iCreateWarningFunction/nThrowWarning at 738  In fit>iFit at 320  In fit at 109 f =      General model:     f(x) = a*x.^2+b*x+c     Coefficients (with 95% confidence bounds):       a =     -0.2571  (-0.5681, 0.05386)       b =       2.049  (0.791, 3.306)       c =       -0.86  (-2.016, 0.2964)

法2：

x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];%use c=0;c=0;p1=fittype(@(a,b,x) a*x.^2+b*x+c)f1=fit(x,y,p1)%use c=1;c=1;p2=fittype(@(a,b,x) a*x.^2+b*x+c)f2=fit(x,y,p2)%predict cp3=fittype(@(a,b,c,x) a*x.^2+b*x+c)f3=fit(x,y,p3)%show resultsscatter(x,y);%scatter pointc1=plot(f1,'b:*');%bluehold onplot(f2,'g:+');%greenhold onplot(f3,'m:*');%purplehold off

           

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