|On this page…|
This section describes how to use Curve Fitting Toolbox™ functions from the command-line or to write programs for curve and surface fitting applications.
The Curve Fitting app allows convenient, interactive use of Curve Fitting Toolbox functions, without programming. You can, however, access Curve Fitting Toolbox functions directly, and write programs that combine curve fitting functions with MATLAB® functions and functions from other toolboxes. This allows you to create a curve fitting environment that is precisely suited to your needs.
Models and fits in the Curve Fitting app are managed internally as curve fitting objects. Objects are manipulated through a variety of functions called methods. You can create curve fitting objects, and apply curve fitting methods, outside of the Curve Fitting app.
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.
Methods are functions that operate exclusively on objects of a particular class. Data types package together objects and methods so that the methods operate exclusively on objects of their own type, and not on objects of other types. A clearly defined encapsulation of objects and methods 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. Methods 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. Methods allow you to post-process the fit through plotting, extrapolation, integration, etc.
Because cfit is a subtype of fittype, cfit inherits all fittype methods. In other words, you can apply fittype methods to both fittype and cfit objects, but cfit methods are used exclusively with cfit objects. Similarly for sfit objects.
As an example, the fittype method islinear, which determines if a model is linear or nonlinear, would apply equally well before or after a fit; that is, to both fittype and cfit objects. On the other hand, the cfit methods coeffvalues and confint, which, respectively, return fit coefficients and their confidence intervals, would make no sense if applied 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 methods 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) Coefficients: a = 1 b = 10.3 n = -100
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 methods allow you to create, access, and modify curve fitting objects. They also allow you, through methods like plot and integrate, to perform operations that uniformly process the entirety of information encapsulated in a curve fitting object.
The methods listed in the following table are available for all fittype objects, including cfit objects.
|Fit Type Method||Description|
Get input argument names
Get fit category
Get coefficient names
Get dependent variable name
Evaluate model at specified predictors
Construct fittype object
Get formula string
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 methods listed in the following table are available exclusively for cfit objects.
|Curve Fit Method||Description|
Construct cfit object
Get coefficient values
Get confidence intervals for fit coefficients
Get prediction intervals
Get problem-dependent parameter values
A complete list of methods 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(f) Methods for class fittype: argnames dependnames fittype islinear probnames category feval formula numargs setoptions coeffnames fitoptions indepnames numcoeffs type
Note that some of the methods listed by methods do not appear in the tables above, and do not have reference pages in the Curve Fitting Toolbox documentation. These additional methods are generally low-level operations used by the Curve Fitting app, and not of general interest when writing curve fitting applications.
There are no global accessor methods, comparable to getfield and setfield, available for fittype objects. Access is limited to the methods 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 ) formula(f) ans = a*cos( b*x-c ) argnames(f) ans = 'a' 'b' 'c' 'x'
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 method. You also have read access to the argument names of the object, through the argnames method. 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.
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 methods of fittype listed in Curve Fitting Methods.
sfit objects also provide methods 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 session in the Curve Fitting 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.