fitoptions
Create or modify fit options object
Syntax
Description
creates the default fit options object fitOptions
= fitoptionsfitOptions
.
creates the default fit options object for the library model.fitOptions
= fitoptions(libraryModelName
)
creates fit options for the specified library model with additional options specified by one or more fitOptions
= fitoptions(libraryModelName
,Name,Value
)Name,Value
pair arguments.
gets the fit options object for the specified fitOptions
= fitoptions(fitType
)fitType
. Use this syntax to work with fit options for custom models.
creates fit options with additional options specified by one or more fitOptions
= fitoptions(Name,Value
)Name,Value
pair arguments.
modifies the existing fit options object newOptions
= fitoptions(fitOptions
,Name,Value
)fitOptions
and returns updated fit options in newOptions
with new options specified by one or more Name,Value
pair arguments.
combines the existing fit options objects newOptions
= fitoptions(options1
,options2
)options1
and options2
in newOptions
.
If
Method
agrees, the nonempty values for the properties inoptions2
override the corresponding values inoptions1
innewOptions
.If
Method
differs,newOptions
contains theoptions1
value forMethod
and values fromoptions2
forNormalize
,Exclude
, andWeights
.
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 = -0.1451 (-1.485, 1.195) b1 = 9.725 (-14.7, 34.15) c1 = 7.117 (-15.84, 30.07) a2 = 14.08 (-1.962e+04, 1.965e+04) b2 = 607.4 (-3.197e+05, 3.209e+05) c2 = 376 (-9.745e+04, 9.82e+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 |
---|---|
| Linear polynomial curve |
| Linear polynomial surface |
| Quadratic polynomial curve |
| Piecewise linear interpolation |
| Piecewise cubic interpolation |
| Smoothing spline (curve) |
| 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.
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 byexcludedata
.
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 |
---|---|
| Nearest neighbor interpolation |
| Linear interpolation |
| Piecewise cubic Hermite interpolation (curves only) |
| Cubic spline interpolation |
| Biharmonic surface interpolation |
| Smoothing spline |
| Lowess smoothing (surfaces only) |
| Linear least squares |
| Nonlinear least squares |
Data Types: char
| string
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 | All interpolant fit types and |
"none" | No extrapolation. When you use | Curve fits — Surface
fits —
Curve
and surface fits — |
"linear" | Linear extrapolation based on boundary gradients | Surface fits — Curve
and surface fits —
|
"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 — Surface
fits —
Curve
and surface fits —
|
"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 | Surface fits — |
"biharmonic" | Biharmonic spline extrapolation. This method extends the biharmonic interpolating spline outside of the fitting data's convex hull. | Surface fits — |
"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 | Curve fits — |
"cubic" | Cubic spline extrapolation. This method extends a cubic interpolating spline outside of the fitting data's convex hull. | Curve fits — |
Data Types: char
| string
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
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
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
"Trust-Region"
(default) | "Levenberg-Marquardt"
Algorithm to use for the fitting procedure, specified as "Trust-Region"
or
"Levenberg-Marquardt"
.
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 R2006aR2024a: Specify natural neighbor interpolant surface fits
Starting in R2024a, you can create natural neighbor interpolant surface fits. For more information, see List of Library Models for Curve and Surface Fitting.
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.
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