Documentation

fitOptions = fitoptions creates the default fit options object fitOptions.

fitOptions = fitoptions(libraryModelName) creates the default fit options object for the library model.

fitOptions = fitoptions(libraryModelName,Name,Value) creates fit options for the specified library model with additional options specified by one or more Name,Value pair arguments.

fitOptions = fitoptions(fitType) gets the fit options object for the specified fitType. Use this syntax to work with fit options for custom models.

fitOptions = fitoptions(Name,Value) creates fit options with additional options specified by one or more Name,Value pair arguments.

newOptions = fitoptions(fitOptions,Name,Value) modifies the existing fit options object fitOptions and returns updated fit options in newOptions with new options specified by one or more Name,Value pair arguments.

newOptions = fitoptions(options1,options2) combines the existing fit options objects options1 and options2 in newOptions.

If Method agrees, the nonempty values for the properties in options2 override the corresponding values in options1 in newOptions.
If Method differs, newOptions contains the options1 value for Method and values from options2 for Normalize, Exclude, and Weights.

Examples

Modify Default Fit Options to Normalize Data

Create the default fit options object and set the option to center and scale the data before fitting.

options = fitoptions;
options.Normal = 'on'

options =

    Normalize: 'on'
      Exclude: [1x0 double]
      Weights: [1x0 double]
       Method: 'None'

Create Default Fit Options for Gaussian Fit

options = fitoptions('gauss2')

options =

        Normalize: 'off'
          Exclude: []
          Weights: []
           Method: 'NonlinearLeastSquares'
           Robust: 'Off'
       StartPoint: [1x0 double]
            Lower: [-Inf -Inf 0 -Inf -Inf 0]
            Upper: [1x0 double]
        Algorithm: 'Trust-Region'
    DiffMinChange: 1.0000e-08
    DiffMaxChange: 0.1000
          Display: 'Notify'
      MaxFunEvals: 600
          MaxIter: 400
           TolFun: 1.0000e-06
             TolX: 1.0000e-06

Set Polynomial Fit Options

Create fit options for a cubic polynomial and set center and scale and robust fitting options.

options = fitoptions('poly3', 'Normalize', 'on', 'Robust', 'Bisquare')

options =

    Normalize: 'on'
      Exclude: []
      Weights: []
       Method: 'LinearLeastSquares'
       Robust: 'Bisquare'
        Lower: [1x0 double]
        Upper: [1x0 double]

Create Fit Options for Linear Least Squares

options = fitoptions('Method', 'LinearLeastSquares')

options =

    Normalize: 'off'
      Exclude: []
      Weights: []
       Method: 'LinearLeastSquares'
       Robust: 'Off'
        Lower: [1x0 double]
        Upper: [1x0 double]

Use Identical Fit Options in Multiple Fits

Modifying the default fit options object is useful when you want to set the Normalize, Exclude, or Weights properties, and then fit your data using the same options with different fitting methods. For example, the following uses the same fit options to fit different library model types.

load census
options = fitoptions;
options.Normalize = 'on';
f1 = fit(cdate,pop,'poly3',options);
f2 = fit(cdate,pop,'exp1',options);
f3 = fit(cdate,pop,'cubicspline',options)

f3 = 
     Cubic interpolating spline:
       f3(x) = piecewise polynomial computed from p
       where x is normalized by mean 1890 and std 62.05
     Coefficients:
       p = coefficient structure

Find and Change the Smoothing Fit Option

Find the smoothing parameter. Data-dependent fit options such as the smooth parameter are returned in the third output argument of the fit function.

load census
[f,gof,out] = fit(cdate,pop,'SmoothingSpline');
smoothparam = out.p

smoothparam = 0.0089

Modify the default smoothing parameter for a new fit.

options = fitoptions('Method','SmoothingSpline',...
                     'SmoothingParam',0.0098);
[f,gof,out] = fit(cdate,pop,'SmoothingSpline',options);

Apply Coefficient Bounds to Improve Gaussian Fit

Create a Gaussian fit, inspect the confidence intervals, and specify lower bound fit options to help the algorithm.

Create a noisy sum of two Gaussian peaks, one with a small width, and one with a large width.

a1 = 1; b1 = -1; c1 = 0.05;
a2 = 1; b2 = 1; c2 = 50;
x = (-10:0.02:10)';
gdata = a1*exp(-((x-b1)/c1).^2) + ...
        a2*exp(-((x-b2)/c2).^2) + ...
        0.1*(rand(size(x))-.5);
plot(x,gdata)

Fit the data using the two-term Gaussian library model.

gfit = fit(x,gdata,'gauss2')

gfit = 
     General model Gauss2:
     gfit(x) =  a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
     Coefficients (with 95% confidence bounds):
       a1 =      -0.145  (-1.486, 1.195)
       b1 =       9.725  (-14.71, 34.15)
       c1 =       7.117  (-15.84, 30.07)
       a2 =       14.07  (-1.959e+04, 1.962e+04)
       b2 =       607.2  (-3.195e+05, 3.207e+05)
       c2 =         376  (-9.74e+04, 9.816e+04)

plot(gfit,x,gdata)

The algorithm is having difficulty, as indicated by the wide confidence intervals for several coefficients.

To help the algorithm, specify lower bounds for the nonnegative amplitudes a1 and a2 and widths c1, c2.

options = fitoptions('gauss2', 'Lower', [0 -Inf 0 0 -Inf 0]);

Alternatively, you can set properties of the fit options using the form options.Property = NewPropertyValue.

options = fitoptions('gauss2');
options.Lower = [0 -Inf 0 0 -Inf 0];

Recompute the fit using the bound constraints on the coefficients.

gfit = fit(x,gdata,'gauss2',options)

gfit = 
     General model Gauss2:
     gfit(x) =  a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
     Coefficients (with 95% confidence bounds):
       a1 =       1.005  (0.966, 1.044)
       b1 =          -1  (-1.002, -0.9988)
       c1 =      0.0491  (0.0469, 0.0513)
       a2 =      0.9985  (0.9958, 1.001)
       b2 =      0.8059  (0.3879, 1.224)
       c2 =        50.6  (46.68, 54.52)

plot(gfit,x,gdata)

This is a much better fit. You can further improve the fit by assigning reasonable values to other properties in the fit options object.

Copy and Combine Fit Options

Create fit options and set lower bounds.

options = fitoptions('gauss2', 'Lower', [0 -Inf 0 0 -Inf 0])

options =

        Normalize: 'off'
          Exclude: []
          Weights: []
           Method: 'NonlinearLeastSquares'
           Robust: 'Off'
       StartPoint: [1x0 double]
            Lower: [0 -Inf 0 0 -Inf 0]
            Upper: [1x0 double]
        Algorithm: 'Trust-Region'
    DiffMinChange: 1.0000e-08
    DiffMaxChange: 0.1000
          Display: 'Notify'
      MaxFunEvals: 600
          MaxIter: 400
           TolFun: 1.0000e-06
             TolX: 1.0000e-06

Make a new copy of the fit options and modify the robust parameter.

newoptions = fitoptions(options, 'Robust','Bisquare')

newoptions =

        Normalize: 'off'
          Exclude: []
          Weights: []
           Method: 'NonlinearLeastSquares'
           Robust: 'Bisquare'
       StartPoint: [1x0 double]
            Lower: [0 -Inf 0 0 -Inf 0]
            Upper: [1x0 double]
        Algorithm: 'Trust-Region'
    DiffMinChange: 1.0000e-08
    DiffMaxChange: 0.1000
          Display: 'Notify'
      MaxFunEvals: 600
          MaxIter: 400
           TolFun: 1.0000e-06
             TolX: 1.0000e-06

Combine fit options.

options2 = fitoptions(options, newoptions)

options2 =

        Normalize: 'off'
          Exclude: []
          Weights: []
           Method: 'NonlinearLeastSquares'
           Robust: 'Bisquare'
       StartPoint: [1x0 double]
            Lower: [0 -Inf 0 0 -Inf 0]
            Upper: [1x0 double]
        Algorithm: 'Trust-Region'
    DiffMinChange: 1.0000e-08
    DiffMaxChange: 0.1000
          Display: 'Notify'
      MaxFunEvals: 600
          MaxIter: 400
           TolFun: 1.0000e-06
             TolX: 1.0000e-06

Change Custom Model Fit Options

Create a linear model fit type.

lft = fittype({'x','sin(x)','1'})

lft = 
     Linear model:
     lft(a,b,c,x) = a*x + b*sin(x) + c

Get the fit options for the fit type lft.

fo = fitoptions(lft)

fo =

    Normalize: 'off'
      Exclude: []
      Weights: []
       Method: 'LinearLeastSquares'
       Robust: 'Off'
        Lower: [1x0 double]
        Upper: [1x0 double]

Set the normalize fit option.

fo.Normalize = 'on'

fo =

    Normalize: 'on'
      Exclude: []
      Weights: []
       Method: 'LinearLeastSquares'
       Robust: 'Off'
        Lower: [1x0 double]
        Upper: [1x0 double]

Input Arguments

`libraryModelName` — Library model to fit
character vector

Library model to fit, specified as a character vector. This table shows some common examples.

Library Model Name	Description
`'poly1'`	Linear polynomial curve
`'poly11'`	Linear polynomial surface
`'poly2'`	Quadratic polynomial curve
`'linearinterp'`	Piecewise linear interpolation
`'cubicinterp'`	Piecewise cubic interpolation
`'smoothingspline'`	Smoothing spline (curve)
`'lowess'`	Local linear regression (surface)

For a list of library model names, see Model Names and Equations.

Example: 'poly2'

Data Types: char

`fitType` — Model type to fit
`fittype`

Model type to fit, specified as a fittype constructed with the fittype function. Use this to work with fit options for custom models.

`fitOptions` — Algorithm options
`fitoptions`

Algorithm options, specified as a fitoptions object created using the fitoptions function.

`options1` — Algorithm options to combine
`fitoptions`

Algorithm options to combine, constructed using the fitoptions function.

`options2` — Algorithm options to combine
`fitoptions`

Algorithm options to combine, constructed using the fitoptions function.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example:

'Method','NonlinearLeastSquares','Lower',[0,0],'Upper',[Inf,max(x)],'Startpoint',[1
                        1]

specifies fitting method, bounds, and start points.

Options for All Fitting Methods

`'Normalize'` — Option to center and scale data
`'off'` (default) | `'on'`

Option to center and scale the data, specified as the comma-separated pair consisting of 'Normalize' and 'on' or 'off'.

Data Types: char

`'Exclude'` — Points to exclude from fit
expression | index vector | logical vector | empty

Points to exclude from the fit, specified as the comma-separated pair consisting of 'Exclude' and one of:

An expression describing a logical vector, e.g., x > 10.
A vector of integers indexing the points you want to exclude, e.g., [1 10 25].
A logical vector for all data points where true represents an outlier, created by excludedata.

For examples, see fit.

`'Weights'` — Weights for fit
[ ] (default) | vector

Weights for the fit, specified as the comma-separated pair consisting of 'Weights' and a vector the same size as number of data points.

Data Types: double

`'Method'` — Fitting method
`'None'` (default) | character vector

Fitting method, specified as the comma-separated pair consisting of 'Method' and one of the fitting methods in this table.

Fitting Method	Description
`'NearestInterpolant'`	Nearest neighbor interpolation
`'LinearInterpolant'`	Linear interpolation
`'PchipInterpolant'`	Piecewise cubic Hermite interpolation (curves only)
`'CubicSplineInterpolant'`	Cubic spline interpolation
`'BiharmonicInterpolant'`	Biharmonic surface interpolation
`'SmoothingSpline'`	Smoothing spline
`'LowessFit'`	Lowess smoothing (surfaces only)
`'LinearLeastSquares'`	Linear least squares
`'NonlinearLeastSquares'`	Nonlinear least squares

Data Types: char

Smoothing Options

`'SmoothingParam'` — Smoothing parameter
scalar value in the range (0,1)

Smoothing parameter, specified as the comma-separated pair consisting of 'SmoothingParam' and a scalar value between 0 and 1. The default value depends on the data set. Only available if the Method is SmoothingSpline.

Data Types: double

`'Span'` — Proportion of data points to use in local regressions
0.25 (default) | scalar value in the range (0,1)

Proportion of data points to use in local regressions, specified as the comma-separated pair consisting of 'Span' and a scalar value between 0 and 1. Only available if the Method is LowessFit.

Data Types: double

Linear and Nonlinear Least-Squares Options

`'Robust'` — Robust linear least-squares fitting method
`'off'` (default) | `'LAR'` | `'Bisquare'`

Robust linear least-squares fitting method, specified as the comma-separated pair consisting of 'Robust' and one of these values:

'LAR' specifies the least absolute residual method.
'Bisquare' specifies the bisquare weights method.

Available when the Method is LinearLeastSquares or NonlinearLeastSquares.

Data Types: char

`'Lower'` — Lower bounds on coefficients to be fitted
[ ] (default) | vector

Lower bounds on the coefficients to be fitted, specified as the comma-separated pair consisting of 'Lower' and a vector. The default value is an empty vector, indicating that the fit is unconstrained by lower bounds. If bounds are specified, the vector length must equal the number of coefficients. Find the order of the entries for coefficients in the vector value by using the coeffnames function. For an example, see fit. Individual unconstrained lower bounds can be specified by -Inf.

Available when the Method is LinearLeastSquares or NonlinearLeastSquares.

Data Types: double

`'Upper'` — Upper bounds on coefficients to be fitted
[ ] (default) | vector

Upper bounds on the coefficients to be fitted, specified as the comma-separated pair consisting of 'Upper' and a vector. The default value is an empty vector, indicating that the fit is unconstrained by upper bounds. If bounds are specified, the vector length must equal the number of coefficients. Find the order of the entries for coefficients in the vector value by using the coeffnames function. For an example, see fit. Individual unconstrained upper bounds can be specified by +Inf.

Available when the Method is LinearLeastSquares or NonlinearLeastSquares.

Data Types: logical

Nonlinear Least-Squares Options