Introduction to curve fitting toolbox

Curve Fitting Toolbox provides graphical user interfaces (GUI) and functions for curve fitting and data surfaces. This toolbox allows you to perform data analysis, data preprocessing, and data post-processing, compare models, and remove outliers. Linear or nonlinear models are used to confirm regression analysis. These models can be provided by libraries or user-defined equations, in addition, this database provides Optimized Solution parameters and initial conditions to improve the fitting quality. The Toolbox also supports non-parameter modeling technology, such as the difference value and smoothing method.

After fitting, you can use the plot method, inner insertion method, external push method, estimated confidence interval, calculation credits, and differentiation methods for subsequent processing.

Features

• Interactive graphic user interface facilitates curve and Surface Fitting
• User-Defined linear and nonlinear regression
• A series of regression model libraries with optimization start points and solver Parameters
• Interpolation methods, including B-spline, thin-sheet spline, and Zhangji Spline
• Smoothing method, including Smoothing Splines, local regression, savitzky-Golay filtering, and moving average method
• Preprocessing routines, including data conversion, cross-section data, smoothing, and exception Removal
• Data post-processing routines, including interpolation, plug-in, confidence interval, points, and Derivation

Use a surface fitting tool to generate a surface. This toolbox supports various fitting methods,
Including linear regression, nonlinear regression, interpolation, and smoothing

Curve Fitting toolbox

To fit curves and surface data, the curve fitting Toolbox provides a large number of related methods, including linear and nonlinear regression, splines, interpolation, and smoothing methods. AllAlgorithmCan be accessed through command line or GUI.

Use GUI to fit data

Main functions of curve fitting and surface fitting GUI include:

Data can be imported directly from the MATLAB workspace.
Visualized data facilitates Exploratory Data Analysis
Use multiple fitting algorithms for fitting
Evaluate Model Accuracy
Implement post-processing analysis, including interpolation, pushing, confidence interval, calculation credits, and differentiation.
For further analysis, the fitting data is output to the MATLAB workspace.
Automatically generate MATLABCode

Automatically generate Matlab code using the surface fitting Tool

Use command lines to fit data

For analysis and visualization, you can use the command line to develop custom functions. These functions make you:

Copy your analysis to a new dataset
Copy your analysis into multiple datasets (batch processing)
Embedding fitting algorithms into MATLAB Functions
Extend the basic capabilities of this toolbox

To implement command line fitting, the curve fitting Toolbox provides a simple and intuitive syntax, for example:

Linear regression: fittedmodel = fit ([x, y], Z, 'poly11 ');
Nonlinear Regression: fittedmodel = fit (X, Y, 'fourier2 ');
Interpolation: fittedmodel = fit ([time, temperature], energy, 'cubicinterp ');

Regression

The curve fitting toolbox supports linear and nonlinear regression. Linear regression supports more than 100 regression models, including:

Line and plane models
Higher Order Polynomial Model
Fourier and power-pole Models
Gaussian Model
Weber Function Model
Exponential Model
Rational Function Model
Sine and Model

Using the curve fitting toolbox for regression analysis, you can

You can choose between two robust regression types: dual-level square or minimum absolute error.
Specify the start condition of the Solver
Constraint Regression Coefficient
Select a trusted region or Levenberg-Marquardt Algorithm


Use the surface fitting tool to fit the data. Robust regression types, optimizer options, and optimizer based on initial conditions and constraints can be controlled.

Splines and Interpolation

The curve fitting toolbox supports various interpolation methods, including B-spline, thin-sheet spline, and Zhangji spline. The curve fitting toolbox also provides Function Support for advanced spline operations.

The curve fitting toolbox also supports various types of interpolation methods, including:

Linear interpolation
Nearest Neighbor Interpolation
Piecewise cubic Interpolation
Bilineharmonic Surface Interpolation
Segment Amy special interpolation polynomial (PChIP)

Linear interpolation by fitting toolbox using a surface

Smooth

Smoothing algorithms are also widely used to eliminate noise from datasets. The curve fitting toolbox supports smooth splines and local regression to generate a prediction model for non-functional variables.

Use the savitzky-Golay filter to deduce data analysis. Smooth data to facilitate periodic data Determination

Data preview and data preprocessing

The curve fitting toolbox supports data preprocessing, including development and comparison of predictive models that can be used for subsequent data processing. The graphic user interface provides 2D and 3D images. Visual monitoring can identify abnormal points and query functions, and can perform data weighting, data point elimination, and segmented data sequence functions.

Use the normalization data of the center and scale options to improve the fitting quality

Development, comparison, and management models

The curve fitting toolbox can fit multiple models through a set of datasets. You can describe statistics, visual monitoring, and validate and evaluate these models.

• Descriptive statistics:
  R-variance, adjusted R variance;
  Squared Error
  Degree of Freedom
• Visual monitoring data:
  Users can observe the model and data to find the fitting problem. For example, you can generate a curved surface image, generate a residual, and determine the fit degree.
• Verification Technology:
  The curve fitting toolbox supports verification technology to avoid over-fitting. You can generate a predefined model and evaluate the fit degree by confirming the dataset.