Data fitting method

Application of MATLAB in Mathematical Modeling (Second Edition)

Polynomial Fits

 polyfit(X,Y,N)

X,Y are the data to be fitted, and N is the highest number of fittings

Returns a vector P of polynomial coefficients.

polyval(P,X)

P is the polynomial coefficient vector, X is the required data point,

Returns the value of Y corresponding to X.

Specified function fit

f=fittype('function','independent','independent variable','coefficients',{'coefficient1','coefficient2',...})

The fittype function is used to customize the fitting function

fit(x,y,f)

The fit function uses a custom function f to fit x, y.

Curve Fitting Toolbox

Curve Fitting Tool

Click Start->Toolboxes->Curve Fitting->Curve Fitting Tool(cftool) to open

You can also enter the cftool command on the command line to open

Example 1 Population Prediction Model

The topic is omitted

%syms tY = [33815 33981 34004 34165 34212 34327 34344 34458 34498 34476 34483 34488 34513 34497 34511 34520 34507 34509 34521 34513 34515 34517 34519 34519 34521 34521 34523 34525 34525 34527];X = [1:30];x = [1:30];y = [1:30];%f = fittype('1/(a+b*exp(-t))','independent','t','coefficient',{'a','b'});%cfun = fit(X,Y,f);%Yi = cfun(X);%plot(X,Y,'r*',X,Yi,'b');for t = 1:30x(t) = exp(-t);y(t) = 1/(Y(1,t));endf = polyfit(x,y,1);for t = 1:30Yj(t)=1/(f(2)+f(1)*exp(-t));endplot(X,Y,'r*',X,Yj,'b');

Example 2 Determination of membrane permeable membrane

The topic is omitted

x = lsqcurvefit(fun,x0,xdata,ydata,lb,ub,options)

lsqcurvefit

Solving nonlinear curve fitting (data fitting) problems with least squares

For details, see the linkhttps://ww2.mathworks.cn/help/optim/ug/lsqcurvefit.html#responsive_offcanvas

t = [100:100:1000];Cbt = 0.001.*[4.54 4.99 5.35 5.65 5.90 6.10 6.26 6.39 6.50 6.59];x0 = [0.2,0.05,0.05];%a,b,K initial valueopts = optimset('lsqcurvefit');opts = optimset(opts,'PrecondBandWidth',0);x = lsqcurvefit('curvefun',x0,t,Cbt,[],[],opts);f = curvefun(x,t);plot(t,Cbt,'o',t,f,'b');