fitoptions

Create or modify fit options object

Syntax

fitOptions = fitoptions

fitOptions = fitoptions(libraryModelName)

fitOptions = fitoptions(libraryModelName,Name,Value)

fitOptions = fitoptions(fitType)

fitOptions = fitoptions(Name,Value)

newOptions = fitoptions(fitOptions,Name,Value)

newOptions = fitoptions(options1,options2)

Description

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 = 
  basefitoptions with properties:

    Normalize: 'on'
      Exclude: []
      Weights: []
       Method: 'None'

Create Default Fit Options for Gaussian Fit

options = fitoptions('gauss2')

options = 
  nlsqoptions with properties:

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

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 = 
  llsqoptions with properties:

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

Create Fit Options for Linear Least Squares

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

options = 
  llsqoptions with properties:

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

Specify Extrapolation Method for Interpolant Fits

Create a fitoptions object for a linear interpolant fit with nearest neighbor extrapolation.

linearoptions = fitoptions("linearinterp",ExtrapolationMethod="nearest")

linearoptions = 
  linearinterpoptions with properties:

    ExtrapolationMethod: 'nearest'
              Normalize: 'off'
                Exclude: []
                Weights: []
                 Method: 'LinearInterpolant'

Create a second fitoptions object for a cubic interpolant fit with nearest neighbor extrapolation.

cubicoptions = fitoptions("cubicinterp",ExtrapolationMethod="nearest")

cubicoptions = 
  cubicsplineinterpoptions with properties:

    ExtrapolationMethod: 'nearest'
              Normalize: 'off'
                Exclude: []
                Weights: []
                 Method: 'CubicSplineInterpolant'

You can use the fit options in linearoptions to create a linearinterp fit object using the fit function. Use cubicoptions to create a cubicinterp fit.

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
       with cubic extrapolation
       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  (-1.485, 1.195)
       b1 =       9.725  (-14.7, 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, 9.815e+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 = 
  nlsqoptions with properties:

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

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

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

newoptions = 
  nlsqoptions with properties:

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

Combine fit options.

options2 = fitoptions(options, newoptions)

options2 = 
  nlsqoptions with properties:

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

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 = 
  llsqoptions with properties:

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

Set the normalize fit option.

fo.Normalize = 'on'

fo = 
  llsqoptions with properties:

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

Input Arguments

libraryModelName — Library model to fit

character vector | string scalar

Library model to fit, specified as a character vector or string scalar. 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)
'log10'	Base-10 logarithmic curve
'logistic4'	Four-parameter logistic curve

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

Example: 'poly2'

Data Types: char | string

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 Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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) | 'NearestInterpolant | 'LinearInterpolant' | 'PchipInterpolant' | CubicSplineInterpolant' | ...

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 | string

Interpolation Options

ExtrapolationMethod — Extrapolation method

"auto" (default) | "none" | "linear" | "nearest" | "thinplate" | "biharmonic" | "pchip" | "cubic"

Extrapolation method for an interpolant fit, specified as one of the following values:

Value	Description	Supported Fits
"auto"	Default value for all interpolant fit types. Set ExtrapolationMethod to "auto" to automatically assign an extrapolation method when you use the fit function.	All interpolant fit types and cubicspline curve fits
"none"	No extrapolation. When you use fitOptions with the fit function to evaluate query points outside of the convex hull, fit returns NaN.	Curve fits — cubicspline and pchipinterp Curve and surface fits — cubicinterp, linearinterp, and nearestinterp
"linear"	Linear extrapolation based on boundary gradients	Surface fits — cubicinterp and nearestinterp Curve and surface fits — linearinterp
"nearest"	Nearest neighbor extrapolation. This method evaluates to the value of the nearest point on the boundary of the fitting data's convex hull.	Curve fits — cubicspline and pchipinterp Curve and surface fits — cubicinterp,linearinterp, and nearestinterp
"thinplate"	Thin-plate spline extrapolation. This method extends the thin-plate interpolating spline outside of the fitting data's convex hull. For more information, see tpaps.	Surface fits — thinplateinterp
"biharmonic"	Biharmonic spline extrapolation. This method extends the biharmonic interpolating spline outside of the fitting data's convex hull.	Surface fits — biharmonicinterp
"pchip"	Piecewise cubic hermite interpolating polynomial (PCHIP) extrapolation. This method extends a shape-preserving PCHIP outside of the fitting data's convex hull. For more information, see pchip.	Curve fits — pchipinterp
"cubic"	Cubic spline extrapolation. This method extends a cubic interpolating spline outside of the fitting data's convex hull.	Curve fits — cubicinterp and cubicspline

Data Types: char | string

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. For more information, see About Smoothing Splines.

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

StartPoint — Initial values for coefficients

[ ] (default) | vector

Initial values for the coefficients, specified as the comma-separated pair consisting of 'StartPoint' and a vector. Find the order of the entries for coefficients in the vector value by using the coeffnames function. For an example, see fit.

If no start points (the default value of an empty vector) are passed to the fit function, starting points for some library models are determined heuristically. For rational and Weibull models, and all custom nonlinear models, the toolbox selects default initial values for coefficients uniformly at random from the interval (0,1). As a result, multiple fits using the same data and model might lead to different fitted coefficients. To avoid this, specify initial values for coefficients with a vector value for the StartPoint property.

Available when the Method is NonlinearLeastSquares.

Data Types: double

Algorithm — Algorithm to use for fitting procedure

'Levenberg-Marquardt' (default) | 'Trust-Region'

Algorithm to use for the fitting procedure, specified as the comma-separated pair consisting of 'Algorithm' and either 'Levenberg-Marquardt' or 'Trust-Region'.

Available when the Method is NonlinearLeastSquares.

Data Types: char

DiffMaxChange — Maximum change in coefficients for finite difference gradients

0.1 (default)

Maximum change in coefficients for finite difference gradients, specified as the comma-separated pair consisting of 'DiffMaxChange' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

DiffMinChange — Minimum change in coefficients for finite difference gradients

10–8 (default)

Minimum change in coefficients for finite difference gradients, specified as the comma-separated pair consisting of 'DiffMinChange' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

Display — Display option in the Command Window

'notify' (default) | 'final' | 'iter' | 'off'

Display option in the command window, specified as the comma-separated pair consisting of 'Display' and one of these options:

• 'notify' displays output only if the fit does not converge.

• 'final' displays only the final output.

• 'iter' displays output at each iteration.

• 'off' displays no output.

Available when the Method is NonlinearLeastSquares.

Data Types: char

MaxFunEvals — Maximum number of evaluations of model allowed

600 (default)

Maximum number of evaluations of the model allowed, specified as the comma-separated pair consisting of 'MaxFunEvals' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

MaxIter — Maximum number of iterations allowed for fit

400 (default)

Maximum number of iterations allowed for the fit, specified as the comma-separated pair consisting of 'MaxIter' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

TolFun — Termination tolerance on model value

10–6 (default)

Termination tolerance on the model value, specified as the comma-separated pair consisting of 'TolFun' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

TolX — Termination tolerance on coefficient values

10^–6 (default)

Termination tolerance on the coefficient values, specified as the comma-separated pair consisting of 'TolX' and a scalar.

Available when the Method is NonlinearLeastSquares.

Data Types: double

Output Arguments

fitOptions — Algorithm options

options object

Algorithm options, returned as an options object.

newOptions — New algorithm options

options object

New algorithm options, returned as an options object.

Version History

Introduced before R2006a

R2023b: Specify extrapolation method for curve interpolant fits

Starting in 2023b, you can specify additional extrapolation methods for interpolant curve fits by using the ExtrapolationMethod name-value argument. For more information, see Extrapolation for Interpolant Fit Types.

R2023b: Specify sigmoidal and logarithmic fit types

Starting in R2023b, you can specify sigmoidal and logarithmic fit types for curve fits. For more information, see List of Library Models for Curve and Surface Fitting.

R2023a: fitoptions returns value objects

Starting in R2023a, fitoptions returns value objects instead of handle objects. For more information, see Comparison of Handle and Value Classes.

R2023a: Specify extrapolation method for surface interpolant fits

Starting in 2023a, you can specify the extrapolation method for interpolant fits by using the ExtrapolationMethod name-value argument. For curve fits, Curve Fitting Toolbox™ supports only the default extrapolation methods available in previous releases.