Matlab 线性拟合 & 非线性拟合

目录(?)[-]

1. fittype
   1. Syntax

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 + p2

 f =

      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) + c

 f =

      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)+c
 Warning: Start point not provided, choosing random start
 point.
 > 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+c
 Warning: Start point not provided, choosing random start
 point.
 > 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 c
 p3=fittype(@(a,b,c,x) a*x.^2+b*x+c)
 f3=fit(x,y,p3)

 %show results
 scatter(x,y);%scatter point
 c1=plot(f1,'b:*');%blue
 hold on
 plot(f2,'g:+');%green
 hold on
 plot(f3,'m:*');%purple
 hold off