Lecture note Data visualization - Chapter 28

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The main contents of the chapter consist of the following: Functions with no input or no output, determining the number of input and output arguments, local variables, global variables, creating toolbox of functions, anonymous functions and function handles, function functions, subfunctions.

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Nội dung Text: Lecture note Data visualization - Chapter 28

Lecture 28
Recap Functions with No input OR No output Determining The Number of Input and Output Arguments Local Variables Global Variables Creating ToolBox of Functions Anonymous Functions and Function Handles Function Functions Subfunctions
Summary of Chapter MATLAB contains a wide variety of builtin functions However, you will often find it useful to create your own MATLAB functions The most common type of userdefined MATLAB function is the function Mfile, which must start with a functiondefinition line that contains the word function a variable that defines the function output a function name a variable used for the input argument
Continued…. The function name must also be the name of the Mfile in which the function is stored Function names follow the standard MATLAB naming rules Like the builtin functions, userdefined functions can accept multiple inputs and can return multiple results Comments immediately following the functiondefinition line can be accessed from the command window with the help command Variables defined within a function are local to that function. They are not stored in the workspace and cannot
Continued…. Groups of userdefined functions, called “toolboxes,” may be stored in a common directory and accessed by modifying the MATLAB® search path. This is accomplished interactively with the path tool, either from the menu bar, as in File > Set Path or from the command line, with pathtool MATLAB provides access to numerous toolboxes developed at The MathWorks or by the user community Another type of function is the anonymous function,
Chapter 13 Numerical Techniques
Introduction Interpolate between data points, using either linear or cubic spline models Model a set of data points as a polynomial Use the basic fitting tool Use the curvefitting toolbox Perform numerical differentiations Perform numerical integrations Solve differential equations numerically
Interpolation Especially when we measure things, we don’t gather data at every possible data point Consider a set of x–y data collected during an experiment By using an interpolation technique, we can estimate the value of y at values of x where we didn’t take measurement The two most common interpolation techniques are Linear interpolation Cubic spline interpolation
Interpolation between data points
Linear Interpolation The most common way to estimate a data point between two known points is linear interpolation In this technique, we assume that the function between the points can be estimated by a straight line drawn between them If we find the equation of a straight line defined by the two known points, we can find y for any value of x The closer together the points are, the more accurate our approximation is likely to be
Continued…. We can perform linear interpolation in MATLAB with the interp1 function We’ll first need to create a set of ordered pairs to use as input to the function The data used to create the righthand graph of next figure is x = 0:5; y = [15, 10, 9, 6, 2, 0];
Continued…. To perform a single interpolation, the input to interp1 is the x data, the y data, and the new x value for which you’d like an estimate of y For example: to estimate the value of y when x is equal to 3.5, type interp1(x,y,3.5) ans = 4 You can perform multiple interpolations all at the same time by putting a vector of x values in the third field of the interp1 function For example: to estimate y values for new x ’s spaced evenly from 0 to 5 by 0.2, type
Continued…. The interp1 function defaults to linear interpolation to make its estimates. However, other approaches are possible If we want (probably for documentation purposes) to explicitly define the approach used in interp1 as linear interpolation, we can specify it in a fourth field: interp1(x, y, 3.5, 'linear') ans = 4