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Curve and Surface Fitting Objects and Object Functions

This topic describes how to create curve and surface fit objects and how to use their object functions to manipulate the fits. Use the Curve Fitting Toolbox™ objects and object functions at the MATLAB® command line or to write MATLAB programs for curve and surface fit applications. You can also use Curve Fitting Toolbox in combination with other MATLAB toolboxes to create curve and surface fit workflows.

This topic focuses on how to create and manipulate curve and surface fits programmatically. Alternatively, the Curve Fitter app allows convenient, interactive use of Curve Fitting Toolbox objects and object functions, without programming. You can select a fit on the Curve Fitter tab, in the Fit Type section.

Curve Fitting Objects

In MATLAB programming, all workspace variables are objects of a particular class. Familiar examples of MATLAB classes are double, char, and function_handle. You can also create custom MATLAB classes, using object-oriented programming.

Object functions are functions that operate exclusively on objects of a particular class. Data types package together objects and object functions so that the object functions operate exclusively on objects of their own type, and not on objects of other types. A clearly defined encapsulation of objects and object functions is the goal of object-oriented programming.

Curve Fitting Toolbox software provides you with new MATLAB data types for performing curve fitting:

  • fittype — Objects allow you to encapsulate information describing a parametric model for your data. Object functions allow you to access and modify that information.

  • cfit and sfit — Two subtypes of fittype, for curves and surfaces. Objects capture information from a particular fit by assigning values to coefficients, confidence intervals, fit statistics, etc. Object functions allow you to post-process the fit through plotting, extrapolation, integration, etc.

Relationship of curve fitting objects

Because cfit is a subtype of fittype, cfit inherits all fittype object functions. In other words, you can apply fittype object functions to both fittype and cfit objects, but cfit object functions are used exclusively with cfit objects. The same is true for sfit objects.

As an example, the fittype object function islinear, which determines if a model is linear or nonlinear, logically applies before or after a fit, that is, to both fittype and cfit objects. On the other hand, the cfit object functions coeffvalues and confint, which, respectively, return fit coefficients and their confidence intervals, makes no sense to apply to a general fittype object, which describes a parametric model with undetermined coefficients.

Curve fitting objects have properties that depend on their type, and also on the particulars of the model or the fit that they encapsulate. For example, the following code uses the constructor object functions for the two curve fitting types to create a fittype object f and a cfit object c:

f = fittype('a*x^2+b*exp(n*x)')
f = 

     General model:
     f(a,b,n,x) = a*x^2+b*exp(n*x)
c = cfit(f,1,10.3,-1e2)
c = 

     General model:
     c(x) = a*x^2+b*exp(n*x)
       a =           1
       b =        10.3
       n =        -100

Note that the display object function for fittype objects returns only basic information, piecing together outputs from formula and indepnames.

cfit and fittype objects are evaluated at predictor values x using feval. You can call feval indirectly using the following functional syntax:

y = cfun(x); % cfit objects
y = ffun(coef1,coef2,...,x); % fittype objects

Curve Fitting Object Functions

Curve fitting object functions allow you to create, access, and modify curve fitting objects. They also allow you, through object functions like plot and integrate, to perform operations that uniformly process the entirety of information encapsulated in a curve fitting object.

The object functions listed in the following table are available for all fittype objects, including cfit objects.

Fit Type Object FunctionDescription


Get input argument names


Get fit category


Get coefficient names


Get dependent variable name


Evaluate model at specified predictors


Construct fittype object


Get formula


Get independent variable name


Determine if model is linear


Get number of input arguments


Get number of coefficients


Get problem-dependent parameter names


Set model fit options


Get name of model

The object functions listed in the following table are available exclusively for cfit objects.

Curve Fit Object FunctionDescription


Construct cfit object


Get coefficient values


Get confidence intervals for fit coefficients


Differentiate fit


Integrate fit


Plot fit


Get prediction intervals


Get problem-dependent parameter values

A complete list of object functions for a curve fitting object can be obtained with the MATLAB methods command. For example,

f = fittype('a*x^2+b*exp(n*x)');
Methods for class fittype:

argnames     dependnames  fittype      islinear     probnames    
category     feval        formula      numargs      setoptions   
coeffnames   fitoptions   indepnames   numcoeffs    type    

Some of the object functions listed by methods do not appear in the tables above, and do not have reference pages in the Curve Fitting Toolbox documentation. These additional object functions are generally low-level operations used by the Curve Fitter app, and not of general interest when writing curve fitting applications.

There are no global accessor object functions, comparable to getfield and setfield, available for fittype objects. Access is limited to the object functions listed above. This is because many of the properties of fittype objects are derived from other properties, for which you do have access. For example,

f = fittype('a*cos( b*x-c )')
f = 

     General model:
     f(a,b,c,x) = a*cos( b*x-c )
ans =

    'a*cos( b*x-c )'
ans =

  4×1 cell array


You construct the fittype object f by giving the formula, so you do have write access to that basic property of the object. You have read access to that property through the formula object function. You also have read access to the argument names of the object, through the argnames object function. You don't, however, have direct write access to the argument names, which are derived from the formula. If you want to set the argument names, set the formula.

Surface Fitting Objects and Object Functions

The surface fit object (sfit) stores the results from a surface fitting operation, making it easy to plot and analyze fits at the command line.

Like cfit objects, sfit objects are a subclass of fittype objects, so they inherit all the same object functions of fittype listed in Curve Fitting Object Functions.

sfit objects also provide object functions exclusively for sfit objects. See sfit.

One way to quickly assemble code for surface fits and plots into useful programs is to generate a file from a fit in the Curve Fitter app. In this way, you can transform your interactive analysis of a single data set into a reusable function for command-line analysis or for batch processing of multiple data sets. You can use the generated file without modification, or edit and customize the code as needed. See Generate Code and Export Fits to the Workspace.