MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES User's Guide Page 5
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- Table of contents
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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
- Curve Fitting 1
- How to Contact The MathWorks: 2
- Contents 3
- Preface 10
- Related Products 10
- Using This Guide 11
- Installation Information 13
- Typographical Conventions 14
- Getting Started with the 15
- Curve Fitting Toolbox 15
- Importing the Data 17
- Create data set 18
- Fitting the Data 19
- Copy Fit 20
- Determining the Best Fit 22
- Tools->Axes Limit Control 24
- Table of Fits 25
- Saving the Fit Results 27
- Analyzing the Fit 29
- Saving the Analysis Results 30
- Saving Your Work 31
- Saving the Session 32
- Generating an M-File 33
- Importing, Viewing, and 35
- Preprocessing Data 35
- Importing Data Sets 36
- Data Sets List 37
- Data Import Process 38
- Create data set button 39
- Viewing Data 40
- Viewing Data Numerically 42
- Smoothing Data 43
- Data sets 44
- Data sets list 44
- Smoothing method 44
- Data Sets 45
- Moving Average Filtering 46
- Lowess Smoothing 50
- Robust Smoothing Procedure 51
- Robust Lowess Smoothing 52
- Savitzky-Golay Filtering 53
- Savitzky−Golay Smoothing 54
- Example: Smoothing Data 55
- View button 56
- Saving the Results 58
- Excluding and Sectioning Data 59
- Exclusion Rule 60
- Marking Outliers 61
- Influential Data Points 63
- Sectioning 64
- Check to 66
- Data points outside the 68
- Individual data points 68
- Viewing the Exclusion Rule 69
- applied 72
- Infs, NaNs, and outliers 74
- The Fitting Process 78
- 2 Select an exclusion rule 79
- 4 Compare fits 79
- 5 Save the fit results 79
- Normal Distribution 81
- Zero Mean 81
- Constant Variance 81
- Linear Least Squares 82
- Weighted Linear Least Squares 85
- Robust Least Squares 87
- Nonlinear Least Squares 90
- Library Models 92
- Gaussian 93
- Polynomials 93
- Power Series 94
- Rationals 95
- Sum of Sines 95
- Custom Equations 96
- Linear Equations 97
- General Equations 98
- Specifying Fit Options 99
- 3 Fitting Data 100
- Fitting Method and Algorithm 100
- Fit Convergence Criteria 100
- Coefficient Parameters 101
- Residuals 103
- Fitting Data 104
- Goodness of Fit Statistics 105
- Results list box in the 106
- Table of fits 106
- Parametric Fitting 107
- View->Confidence Level 110
- View->Residuals menu item 113
- Example: Rational Fit 117
- Tools->Custom Equation 122
- New Equation button 122
- Example: Robust Fit 137
- Nonparametric Fitting 144
- Smoothing Spline 146
- Apply button 149
- Selected Bibliography 151
- Function Reference 153
- 4 Function Reference 154
- Functions – By Category 154
- Postprocessing Data 155
- General Purpose 155
- Functions – Alphabetical List 156
- Syntax cflibhelp 158
- Arguments 158
- Description 158
- See Also cfit, fit, fittype 159
- Syntax cftool 160
- The Data GUI 162
- The Fitting GUI 163
- The Exclude GUI 164
- The Plotting GUI 164
- The Analysis GUI 165
- Syntax ci = confint(fresult) 166
- See Also fit 167
- Syntax xds = datastats(xdata) 168
- See Also cfit, fit, integrate 171
- Syntax obj 172
- See Also fit, fittype 177
- Syntax opts = fitoptions 182
- Additional Fit Options 184
- 4integrate 193
- Plot the residuals 197
- , plot (built-in), subplot 198
- See Also confint, fit 201
- Syntax set(opts) 202
- See Also fitoptions, get 203
- Syntax yy = smooth(ydata) 204
- See Also fit, sort 208
- Numerics 209
- Infs, NaNs, and outliers 2-41 215
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