MATLAB Curve Fitting ToolboxTM User's Guide

Getting Started Curve Fitting Toolbox Product Description Key Features Curve Fitting Tools Curve Fitting Interactive Curve Fitting Programmatic Curve Fitting Surface Fitting Interactive Surface Fitting Programmatic Surface Fitting Spline Fitting About Splines in Curve Fitting Toolbox Interactive Spline Fitting Programmatic Spline Fitting Interactive Fitting Interactive Curve and Surface Fitting Introducing the Curve Fitting App Fit a Curve Fit a Surface Model Types for Curves and Surfaces Selecting Data to Fit in Curve Fitting App Save and Reload Sessions Data Selection Selecting Data to Fit in Curve Fitting App Selecting Compatible Size Surface Data Troubleshooting Data Problems Create Multiple Fits in Curve Fitting App Refining Your Fit Creating Multiple Fits Duplicating a Fit Deleting a Fit Displaying Multiple Fits Simultaneously Using the Statistics in the Table of Fits Generating MATLAB Code and Exporting Fits Interactive Code Generation and Programmatic Fitting Compare Fits in Curve Fitting App Interactive Curve Fitting Workflow Loading Data and Creating Fits Determining the Best Fit Analyzing Your Best Fit in the Workspace Saving Your Work Surface Fitting to Franke Data Programmatic Curve and Surface Fitting Curve and Surface Fitting Fitting a Curve Fitting a Surface Model Types and Fit Analysis Workflow for Command Line Fitting Curve and Surface Fitting Objects and Methods Curve Fitting Objects Curve Fitting Methods Surface Fitting Objects and Methods Linear and Nonlinear Regression Parametric Fitting Parametric Fitting with Library Models Selecting a Model Type Interactively Selecting Model Type Programmatically Using Normalize or Center and Scale Specifying Fit Options and Optimized Starting Points List of Library Models for Curve and Surface Fitting Use Library Models to Fit Data Library Model Types Model Names and Equations Polynomial Models About Polynomial Models Fit Polynomial Models Interactively Fit Polynomials Using the Fit Function Polynomial Model Fit Options Defining Polynomial Terms for Polynomial Surface Fits Exponential Models About Exponential Models Fit Exponential Models Interactively Fit Exponential Models Using the fit Function Fourier Series About Fourier Series Models Fit Fourier Models Interactively Fit Fourier Models Using the fit Function Gaussian Models About Gaussian Models Fit Gaussian Models Interactively Fit Gaussian Models Using the fit Function Power Series About Power Series Models Fit Power Series Models Interactively Fit Power Series Models Using the fit Function Rational Polynomials About Rational Models Fit Rational Models Interactively Selecting a Rational Fit at the Command Line Example: Rational Fit Sum of Sines Models About Sum of Sines Models Fit Sum of Sine Models Interactively Selecting a Sum of Sine Fit at the Command Line Weibull Distributions About Weibull Distribution Models Fit Weibull Models Interactively Selecting a Weibull Fit at the Command Line Least-Squares Fitting Introduction Error Distributions Linear Least Squares Weighted Least Squares Robust Least Squares Nonlinear Least Squares Robust Fitting Custom Linear and Nonlinear Regression Custom Models Custom Models vs. Library Models Selecting a Custom Equation Fit Interactively Selecting a Custom Equation Fit at the Command Line Custom Linear Fitting About Custom Linear Models Selecting a Linear Fitting Custom Fit Interactively Selecting Linear Fitting at the Command Line Fit Custom Linear Legendre Polynomials Custom Nonlinear Census Fitting Custom Nonlinear ENSO Data Analysis Load Data and Fit Library and Custom Fourier Models Use Fit Options to Constrain a Coefficient Create Second Custom Fit with Additional Terms and Constraints Create a Third Custom Fit with Additional Terms and Constraints Gaussian Fitting with an Exponential Background Surface Fitting to Biopharmaceutical Data Interpolation and Smoothing Nonparametric Fitting Interpolation Methods About Interpolation Methods Selecting an Interpolant Fit Selecting an Interpolant Fit Interactively Fit Linear Interpolant Models Using the fit Function Smoothing Splines About Smoothing Splines Selecting a Smoothing Spline Fit Interactively Fit Smoothing Spline Models Using the fit Function Example: Nonparametric Fitting with Cubic and Smoothing Splines Lowess Smoothing About Lowess Smoothing Selecting a Lowess Fit Interactively Fit Lowess Models Using the fit Function Fit Smooth Surfaces To Investigate Fuel Efficiency Filtering and Smoothing Data About Data Smoothing and Filtering Moving Average Filtering Savitzky-Golay Filtering Local Regression Smoothing Example: Smoothing Data Example: Smoothing Data Using Loess and Robust Loess Fit Postprocessing Explore and Customize Plots Displaying Fit and Residual Plots Viewing Surface Plots and Contour Plots Using Zoom, Pan, Data Cursor, and Outlier Exclusion Customizing the Fit Display Print to MATLAB Figures Remove Outliers Remove Outliers Interactively Exclude Data Ranges Remove Outliers Programmatically Select Validation Data Generate Code and Export Fits to the Workspace Generating Code from the Curve Fitting App Exporting a Fit to the Workspace Evaluate a Curve Fit Evaluate a Surface Fit Compare Fits Programmatically Evaluating Goodness of Fit How to Evaluate Goodness of Fit Goodness-of-Fit Statistics Residual Analysis Plotting and Analysing Residuals Example: Residual Analysis Confidence and Prediction Bounds About Confidence and Prediction Bounds Confidence Bounds on Coefficients Prediction Bounds on Fits Compute Prediction Intervals Differentiating and Integrating a Fit Spline Fitting About Splines Introducing Spline Fitting About Splines in Curve Fitting Toolbox Spline Overview Interactive Spline Fitting Programmatic Spline Fitting Curve Fitting Toolbox Splines and MATLAB Splines Curve Fitting Toolbox Splines MATLAB Splines Expected Background Vector Data Type Support Spline Function Naming Conventions Arguments for Curve Fitting Toolbox Spline Functions Acknowledgments Simple Spline Examples Cubic Spline Interpolation Cubic Spline Interpolant of Smooth Data Periodic Data Other End Conditions General Spline Interpolation Knot Choices Smoothing Least Squares Vector-Valued Functions Fitting Values at N-D Grid with Tensor-Product Splines Fitting Values at Scattered 2-D Sites with Thin-Plate Smoothing Splines Postprocessing Splines Types of Splines Types of Splines: ppform and B-form Polynomials vs. Splines ppform B-form Knot Multiplicity B-Splines and Smoothing Splines B-Spline Properties Variational Approach and Smoothing Splines Multivariate and Rational Splines Multivariate Splines Rational Splines The ppform Introduction to ppform Definition of ppform Constructing and Working with ppform Splines Constructing a ppform Working With ppform Splines Example ppform The B-form Introduction to B-form Definition of B-form B-form and B-Splines B-Spline Knot Multiplicity Choice of Knots for B-form Constructing and Working with B-form Splines Construction of B-form Working With B-form Splines Example: B-form Spline Approximation to a Circle Multivariate Tensor Product Splines Introduction to Multivariate Tensor Product Splines B-form of Tensor Product Splines Construction With Gridded Data ppform of Tensor Product Splines Example: The Mobius Band NURBS and Other Rational Splines Introduction to Rational Splines rsform: rpform, rBform Constructing and Working with Rational Splines Rational Spline Example: Circle Rational Spline Example: Sphere Functions for Working With Rational Splines Constructing and Working with stform Splines Introduction to the stform Construction and Properties of the stform Working with the stform Advanced Spline Examples Least-Squares Approximation by Natural Cubic Splines Problem General Resolution Need for a Basis Map A Basis Map for “Natural” Cubic Splines The One-line Solution The Need for Proper Extrapolation The Correct One-Line Solution Least-Squares Approximation by Cubic Splines Solving A Nonlinear ODE Problem Approximation Space Discretization Numerical Problem Linearization Linear System to Be Solved Iteration Construction of the Chebyshev Spline What Is a Chebyshev Spline? Choice of Spline Space Initial Guess Remez Iteration Approximation by Tensor Product Splines Choice of Sites and Knots Least Squares Approximation as Function of y Approximation to Coefficients as Functions of x The Bivariate Approximation Switch in Order Approximation to Coefficients as Functions of y The Bivariate Approximation Comparison and Extension Splines Glossary List of Terms for Spline Fitting Functions Curve Fitting aptknt argnames augknt aveknt bkbrk brk2knt bspligui bspline category cfit chbpnt coeffnames coeffvalues confint csape csapi csaps cscvn datastats dependnames differentiate excludedata feval fit fitoptions fittype fn2fm fnbrk fnchg fncmb fnder fndir fnint fnjmp fnmin fnplt fnrfn fntlr fnval fnxtr fnzeros formula franke get getcurve indepnames integrate islinear knt2brk, knt2mlt newknt numargs numcoeffs optknt plot ppmak predint prepareCurveData prepareSurfaceData probnames probvalues quad2d rpmak rscvn rsmak set setoptions sfit sftool smooth slvblk sorted spap2 spapi spaps spcol spcrv splinetool splpp, sprpp spmak spterms stcol stmak subplus titanium tpaps type Bibliography