Matlab系数拟合-fittype

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：
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1. x=[1,1.5,2,2.5,3];y=[0.9,1.7,2.2,2.6,3];
2. p=polyfit(x,y,1);   %
3. x1=linspace(min(x),max(x));
4. y1=polyval(p,x1);
5. plot(x,y, '*' ,x1,y1);
结果： p = 1.0200 0.0400
即y=1.0200 *x+ 0.0400

法2：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. p=fittype( 'poly1' )
3. f=fit(x,y,p)
4. plot(f,x,y);
运行结果：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. p=fittype( 'poly1' )
3. f=fit(x,y,p)
4. plot(f,x,y);
5.
6. p =
7.
8. Linear model Poly1:
9. p(p1,p2,x) = p1*x + p2
10.
11. f =
12.
13. Linear model Poly1:
14. f(x) = p1*x + p2
15. Coefficients (with 95% confidence bounds):
16. p1 = 1.02 (0.7192, 1.321)
17. p2 = 0.04 (-0.5981, 0.6781)

Example2:y=a*x + b*sin(x) + c
法1：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. EXPR = { 'x' , 'sin(x)' , '1' };
3. p=fittype(EXPR)
4. f=fit(x,y,p)
5. plot(f,x,y);
运行结果：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. EXPR = { 'x' , 'sin(x)' , '1' };
3. p=fittype(EXPR)
4. f=fit(x,y,p)
5. plot(f,x,y);
6.

7. p =
8.
9. Linear model:
10. p(a,b,c,x) = a*x + b*sin(x) + c
11.
12. f =
13.
14. Linear model:
15. f(x) = a*x + b*sin(x) + c
16. Coefficients (with 95% confidence bounds):
17. a = 1.249 (0.9856, 1.512)
18. b = 0.6357 (0.03185, 1.24)
19. c = -0.8611 (-1.773, 0.05094)

法2：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. p=fittype( 'a*x+b*sin(x)+c' , 'independent' , 'x' )
3. f=fit(x,y,p)
4. plot(f,x,y);
运行结果：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. p=fittype( 'a*x+b*sin(x)+c' , 'independent' , 'x' )
3. f=fit(x,y,p)
4. plot(f,x,y);
5.
6. p =
7.
8. General model:
9. p(a,b,c,x) = a*x+b*sin(x)+c
10. Warning: Start point not provided, choosing random start
11. point.
12. > In fit>iCreateWarningFunction/nThrowWarning at 738
13. In fit>iFit at 320
14. In fit at 109
15.
16. f =
17.
18. General model:
19. f(x) = a*x+b*sin(x)+c
20. Coefficients (with 95% confidence bounds):

21. a = 1.249 (0.9856, 1.512)
22. b = 0.6357 (0.03185, 1.24)
23. c = -0.8611 (-1.773, 0.05094)

/*********************************** 非线性拟合***********************************/
Example ：y=a*x^2+b*x+c
法1：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. p=fittype( 'a*x.^2+b*x+c' , 'independent' , 'x' )
3. f=fit(x,y,p)
4. plot(f,x,y);
运行结果：
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1. p =
2.
3. General model:
4. p(a,b,c,x) = a*x.^2+b*x+c
5. Warning: Start point not provided, choosing random start

6. point.
7. > In fit>iCreateWarningFunction/nThrowWarning at 738
8. In fit>iFit at 320
9. In fit at 109
10.
11. f =
12.
13. General model:
14. f(x) = a*x.^2+b*x+c
15. Coefficients (with 95% confidence bounds):
16. a = -0.2571 (-0.5681, 0.05386)
17. b = 2.049 (0.791, 3.306)
18. c = -0.86 (-2.016, 0.2964)

法2：
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1. x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3];
2. %use c=0;
3. c=0;
4. p1=fittype(@(a,b,x) a*x.^2+b*x+c)
5. f1=fit(x,y,p1)
6. %use c=1;

7. c=1;
8. p2=fittype(@(a,b,x) a*x.^2+b*x+c)
9. f2=fit(x,y,p2)
10. %predict c
11. p3=fittype(@(a,b,c,x) a*x.^2+b*x+c)
12. f3=fit(x,y,p3)
13.
14. %show results
15. scatter(x,y);%scatter point
16. c1=plot(f1, 'b:*' );%blue
17. hold on
18. plot(f2, 'g:+' );%green
19. hold on
20. plot(f3, 'm:*' );%purple
21. hold off