Curve Fitting Toolbox

fit

Fit data using a library or custom model, a smoothing spline, or an interpolant

Syntax

• fresult = fit(xdata,ydata,'ltype')
  fresult = fit(xdata,ydata,'ltype','PropertyName',PropertyValue,...)
  fresult = fit(xdata,ydata,'ltype',opts)
  fresult = fit(xdata,ydata,'ltype',...,'problem',values)
  fresult = fit(xdata,ydata,ftype,...)
  [fresult,gof] = fit(...)
  [fresult,gof,output] = fit(...)
  

Arguments

xdata	A column vector of predictor data.
ydata	A column vector of response data.
'ltype'	The name of a library model, spline, or interpolant.
'PropertyName'	The name of a fit options property.
PropertyValue	A valid value for PropertyName.
opts	A fit options object.
'problem'	Specify problem parameters.
values	A cell array of problem parameter values.
ftype	A fit type object.
fresult	The fit result object.
gof	Goodness of fit statistics.
output	A structure containing information that is associated with the fitting procedure.

Description

fresult = fit(xdata,ydata,'ltype') fits the data specified by xdata and ydata to the library model, interpolant, or smoothing spline specified by ltype. The fit result is returned to fresult. You can display the library fit type names with the cflibhelp function. xdata and ydata cannot contain Infs or NaNs. Additionally, only the real part of a complex value is used.

fresult = fit(xdata,ydata,'ltype','PropertyName', PropertyValue,...) fits the data using the options specified by PropertyName and PropertyValue. You can display the fit options available for the specified library fit type with the fitoptions function.

fresult = fit(xdata,ydata,'ltype',opts) fits the data using options specified by the fit options object opts. You create a fit options object with the fitoptions function. This is an alternative syntax to specifying property name/property value pairs.

fresult = fit(xdata,ydata,'ltype',...,'problem',values) assigns values to problem parameters. values is a cell array with one element per parameter. Problem parameters are problem-dependent constants that you define as part of your model. See fittype for more information on problem parameters.

fresult = fit(xdata,ydata,ftype,...) fits the data to the fit type object specified by ftype. You create a fit type object with the fittype function.

[fresult,gof] = fit(...) returns goodness of fit statistics to the structure gof. The gof structure includes the fields shown below.

Field	Description
sse	Sum of squares due to error
rsquare	Coefficient of determination
dfe	Degrees of freedom
adjrsquare	Degree-of-freedom adjusted coefficient of determination
rmse	Root mean squared error (standard error)

[fresult,gof,output] = fit(...) returns the structure output, which contains information that is associated with the fitting procedure used. Supported fitting procedures include linear least squares, robust nonlinear least squares, and so on. Some information applies to all fitting procedures, while other information is relevant only for particular fitting procedures. For example, the information returned for nonlinear least squares fits is given below.

Field	Description
numobs	Number of observations (response values).
numparam	Number of unknown parameters to fit.
residuals	Vector of residuals.
Jacobian	Jacobian matrix.
exitflag	Describes the exit condition. If exitflag > 0, the function converged to a solution. If exitflag = 0, the maximum number of function evaluations or iterations was exceeded. If exitflag < 0, the function did not converge to a solution.
iterations	Number of iterations used to complete the fit.
funcCount	Number of function evaluations used to complete the fit.
firstorderopt	Measure of first-order optimality.
algorithm	Fitting algorithm used.

Remarks

For rationals and Weibull library models, the coefficient starting values are randomly selected in the range [0,1]. Therefore, if you perform multiple fits to a data set using the same equation, you might get different coefficient results due to different starting values. To avoid this situation, you should pass in a vector of starting values each time you fit, or define a specific state for the random number generator, rand or randn, before fitting.

For all other library models, optimal starting points are automatically calculated. These values depend on the data, and are based on model-specific heuristics.

Example

Fit the census data with a second-degree polynomial library model and return the goodness of fit statistics and the output structure.

• load census
  [fit1,gof1,out1] = fit(cdate,pop,'poly2');
  

Normalize the data and fit with a third-degree polynomial.

• [fit1,gof1,out1] = fit(cdate,pop,'poly3','Normalize','on');
  

Fit the data with a single-term exponential library model.

• [fit2,gof2,out2] = fit(cdate,pop,'exp1','Normalize','on');
  

Create a fit options object, and try to find a better fit by overriding the default starting points for the fit coefficients.

• opts = fitoptions('exp1','Norm','on','start',[100 0.1]);
  [fit3,gof3,out3] = fit(cdate,pop,'exp1',opts);
  

Fit the data to a custom model that contains the problem parameter n.

• mymodel = fittype('a*exp(b*n*x)+c','problem','n');
  opts = fitoptions(mymodel);
  set(opts,'normalize','on')
  [fit4,gof4,out4] = fit(cdate,pop,mymodel,opts,'problem',{2});
  
  Warning: Start point not provided, choosing random start point.
  

The warning occurs whenever you fit data with a custom nonlinear model and do not provide starting points.

See Also

cflibhelp, fitoptions, fittype

feval

fitoptions