Computation
Visualization
Programming
For Use with MATLAB
®
User’s Guide
Version 1
Curve Fitting
Toolbox
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Curve Fitting Toolbox User’s Guide
COPYRIGHT 2001-2002 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc.
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Printing History: July 2001 First printing New for Version 1 (Release 12.1)
July 2002 Second printing Revised for Version 1.1 (Release 13)
i
Contents
Preface
What Is the Curve Fitting Toolbox? . . . . . . . . . . . . . . . . . . . . . . vi
Exploring the Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Using This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Expected Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
How This Guide Is Organized . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Documentation Examples and Data Sets . . . . . . . . . . . . . . . . . . . . x
Installation Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1
Getting Started with the Curve Fitting Toolbox
Opening the Curve Fitting Tool . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Importing the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Fitting the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
The Data Fitting Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Determining the Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Saving the Fit Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
Analyzing the Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
Saving the Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
ii Contents
Saving Your Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17
Saving the Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Generating an M-File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-19
2
Importing, Viewing, and Preprocessing Data
Importing Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Example: Importing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Viewing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Viewing Data Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Viewing Data Numerically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
Smoothing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9
Moving Average Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Lowess and Loess: Local Regression Smoothing . . . . . . . . . . . 2-14
Savitzky-Golay Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
Example: Smoothing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21
Excluding and Sectioning Data . . . . . . . . . . . . . . . . . . . . . . . . 2-25
Marking Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Sectioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
Example: Excluding and Sectioning Data . . . . . . . . . . . . . . . . 2-32
Example: Sectioning Periodic Data . . . . . . . . . . . . . . . . . . . . . . 2-35
Additional Preprocessing Steps . . . . . . . . . . . . . . . . . . . . . . . 2-40
Transforming the Response Data . . . . . . . . . . . . . . . . . . . . . . . 2-40
Removing Infs, NaNs, and Outliers . . . . . . . . . . . . . . . . . . . . . 2-41
Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
iii
3
Fitting Data
The Fitting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
Parametric Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Basic Assumptions About the Error . . . . . . . . . . . . . . . . . . . . . . 3-5
The Least Squares Fitting Method . . . . . . . . . . . . . . . . . . . . . . . 3-6
Library Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
Custom Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20
Specifying Fit Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23
Evaluating the Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . 3-27
Example: Rational Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41
Example: Fitting with Custom Equations . . . . . . . . . . . . . . . . 3-46
Example: Robust Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-61
Nonparametric Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-68
Interpolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-68
Smoothing Spline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-70
Example: Nonparametric Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-72
Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-75
4
Function Reference
Functions – By Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
Fitting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
Getting Information and Help . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
Getting and Setting Properties . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
Preprocessing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
Postprocessing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79
General Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79
Functions – Alphabetical List . . . . . . . . . . . . . . . . . . . . . . . . . 4-80
