MATLAB Notes for Professionals (GoalKicker.com) (Z-Library)

MATLAB Notes for ProfessionalsMATLAB® Notes for Professionals GoalKicker.com Free Programming Books Disclaimer This is an unocial free book created for educational purposes and is not aliated with ocial MATLAB® group(s) or company(s). All trademarks and registered trademarks are the property of their respective owners 100+ pages of professional hints and tricks

Contents About 1 ................................................................................................................................................................................... Chapter 1: Getting started with MATLAB Language 2 ................................................................................... Section 1.1: Indexing matrices and arrays 3 ................................................................................................................... Section 1.2: Anonymous functions and function handles 8 .......................................................................................... Section 1.3: Matrices and Arrays 11 ................................................................................................................................ Section 1.4: Cell arrays 13 ................................................................................................................................................ Section 1.5: Hello World 14 ............................................................................................................................................... Section 1.6: Scripts and Functions 14 .............................................................................................................................. Section 1.7: Helping yourself 16 ....................................................................................................................................... Section 1.8: Data Types 16 ............................................................................................................................................... Section 1.9: Reading Input & Writing Output 19 ............................................................................................................ Chapter 2: Initializing Matrices or arrays 21 ....................................................................................................... Section 2.1: Creating a matrix of 0s 21 ........................................................................................................................... Section 2.2: Creating a matrix of 1s 21 ........................................................................................................................... Section 2.3: Creating an identity matrix 21 .................................................................................................................... Chapter 3: Conditions 22 ............................................................................................................................................... Section 3.1: IF condition 22 ............................................................................................................................................... Section 3.2: IF-ELSE condition 22 .................................................................................................................................... Section 3.3: IF-ELSEIF condition 23 ................................................................................................................................. Section 3.4: Nested conditions 24 ................................................................................................................................... Chapter 4: Functions 27 ................................................................................................................................................ Section 4.1: nargin, nargout 27 ........................................................................................................................................ Chapter 5: Set operations 29 ...................................................................................................................................... Section 5.1: Elementary set operations 29 ..................................................................................................................... Chapter 6: Documenting functions 30 .................................................................................................................... Section 6.1: Obtaining a function signature 30 .............................................................................................................. Section 6.2: Simple Function Documentation 30 ........................................................................................................... Section 6.3: Local Function Documentation 30 ............................................................................................................. Section 6.4: Documenting a Function with an Example Script 31 ............................................................................... Chapter 7: Using functions with logical output 34 ........................................................................................... Section 7.1: All and Any with empty arrays 34 ............................................................................................................... Chapter 8: For loops 35 ................................................................................................................................................. Section 8.1: Iterate over columns of matrix 35 .............................................................................................................. Section 8.2: Notice: Weird same counter nested loops 35 ........................................................................................... Section 8.3: Iterate over elements of vector 36 ............................................................................................................ Section 8.4: Nested Loops 37 .......................................................................................................................................... Section 8.5: Loop 1 to n 38 ............................................................................................................................................... Section 8.6: Loop over indexes 39 .................................................................................................................................. Chapter 9: Object-Oriented Programming 40 .................................................................................................... Section 9.1: Value vs Handle classes 40 ......................................................................................................................... Section 9.2: Constructors 40 ............................................................................................................................................ Section 9.3: Defining a class 42 ....................................................................................................................................... Section 9.4: Inheriting from classes and abstract classes 43 ...................................................................................... Chapter 10: Vectorization 47 ....................................................................................................................................... Section 10.1: Use of bsxfun 47 .......................................................................................................................................... Section 10.2: Implicit array expansion (broadcasting) [R2016b] 48 ............................................................................

Section 10.3: Element-wise operations 49 ...................................................................................................................... Section 10.4: Logical Masking 50 ..................................................................................................................................... Section 10.5: Sum, mean, prod & co 51 .......................................................................................................................... Section 10.6: Get the value of a function of two or more arguments 52 .................................................................... Chapter 11: Matrix decompositions 53 .................................................................................................................... Section 11.1: Schur decomposition 53 .............................................................................................................................. Section 11.2: Cholesky decomposition 53 ....................................................................................................................... Section 11.3: QR decomposition 54 .................................................................................................................................. Section 11.4: LU decomposition 54 .................................................................................................................................. Section 11.5: Singular value decomposition 55 .............................................................................................................. Chapter 12: Graphics: 2D Line Plots 56 ................................................................................................................... Section 12.1: Split line with NaNs 56 ................................................................................................................................. Section 12.2: Multiple lines in a single plot 56 ................................................................................................................ Section 12.3: Custom colour and line style orders 57 ................................................................................................... Chapter 13: Graphics: 2D and 3D Transformations 61 ................................................................................... Section 13.1: 2D Transformations 61 ............................................................................................................................... Chapter 14: Controlling Subplot coloring in MATLAB 64 ............................................................................... Section 14.1: How it's done 64 .......................................................................................................................................... Chapter 15: Image processing 65 .............................................................................................................................. Section 15.1: Basic image I/O 65 ...................................................................................................................................... Section 15.2: Retrieve Images from the Internet 65 ...................................................................................................... Section 15.3: Filtering Using a 2D FFT 65 ....................................................................................................................... Section 15.4: Image Filtering 66 ....................................................................................................................................... Section 15.5: Measuring Properties of Connected Regions 67 ..................................................................................... Chapter 16: Drawing 70 .................................................................................................................................................. Section 16.1: Circles 70 ...................................................................................................................................................... Section 16.2: Arrows 71 ..................................................................................................................................................... Section 16.3: Ellipse 74 ...................................................................................................................................................... Section 16.4: Pseudo 4D plot 75 ...................................................................................................................................... Section 16.5: Fast drawing 79 .......................................................................................................................................... Section 16.6: Polygon(s) 80 .............................................................................................................................................. Chapter 17: Financial Applications 82 ..................................................................................................................... Section 17.1: Random Walk 82 ......................................................................................................................................... Section 17.2: Univariate Geometric Brownian Motion 82 .............................................................................................. Chapter 18: Fourier Transforms and Inverse Fourier Transforms 84 .................................................... Section 18.1: Implement a simple Fourier Transform in MATLAB 84 ........................................................................... Section 18.2: Images and multidimensional FTs 85 ...................................................................................................... Section 18.3: Inverse Fourier Transforms 90 .................................................................................................................. Chapter 19: Ordinary Dierential Equations (ODE) Solvers 92 ................................................................. Section 19.1: Example for odeset 92 ................................................................................................................................ Chapter 20: Interpolation with MATLAB 94 .......................................................................................................... Section 20.1: Piecewise interpolation 2 dimensional 94 ................................................................................................ Section 20.2: Piecewise interpolation 1 dimensional 96 ................................................................................................ Section 20.3: Polynomial interpolation 101 ................................................................................................................... Chapter 21: Integration 105 .......................................................................................................................................... Section 21.1: Integral, integral2, integral3 105 ................................................................................................................ Chapter 22: Reading large files 107 ........................................................................................................................ Section 22.1: textscan 107 ................................................................................................................................................

Section 22.2: Date and time strings to numeric array fast 107 .................................................................................. Chapter 23: Usage of `accumarray()` Function 109 ......................................................................................... Section 23.1: Apply Filter to Image Patches and Set Each Pixel as the Mean of the Result of Each Patch 109 ............................................................................................................................................................................. Section 23.2: Finding the maximum value among elements grouped by another vector 110 ................................ Chapter 24: Introduction to MEX API 111 ............................................................................................................. Section 24.1: Check number of inputs/outputs in a C++ MEX-file 111 ........................................................................ Section 24.2: Input a string, modify it in C, and output it 112 ...................................................................................... Section 24.3: Passing a struct by field names 113 ........................................................................................................ Section 24.4: Pass a 3D matrix from MATLAB to C 113 ............................................................................................... Chapter 25: Debugging 116 .......................................................................................................................................... Section 25.1: Working with Breakpoints 116 .................................................................................................................. Section 25.2: Debugging Java code invoked by MATLAB 118 ................................................................................... Chapter 26: Performance and Benchmarking 121 ........................................................................................... Section 26.1: Identifying performance bottlenecks using the Profiler 121 ................................................................. Section 26.2: Comparing execution time of multiple functions 124 ............................................................................ Section 26.3: The importance of preallocation 125 ...................................................................................................... Section 26.4: It's ok to be `single`! 127 ............................................................................................................................ Chapter 27: Multithreading 130 ................................................................................................................................. Section 27.1: Using parfor to parallelize a loop 130 ...................................................................................................... Section 27.2: Executing commands in parallel using a "Single Program, Multiple Data" (SPMD) statement 130 ............................................................................................................................................................................. Section 27.3: Using the batch command to do various computations in parallel 131 ............................................. Section 27.4: When to use parfor 131 ............................................................................................................................ Chapter 28: Using serial ports 133 ........................................................................................................................... Section 28.1: Creating a serial port on Mac/Linux/Windows 133 ............................................................................... Section 28.2: Choosing your communication mode 133 .............................................................................................. Section 28.3: Automatically processing data received from a serial port 136 .......................................................... Section 28.4: Reading from the serial port 137 ............................................................................................................. Section 28.5: Closing a serial port even if lost, deleted or overwritten 137 ............................................................... Section 28.6: Writing to the serial port 137 .................................................................................................................... Chapter 29: Undocumented Features 138 ............................................................................................................ Section 29.1: Color-coded 2D line plots with color data in third dimension 138 ........................................................ Section 29.2: Semi-transparent markers in line and scatter plots 138 ....................................................................... Section 29.3: C++ compatible helper functions 140 ...................................................................................................... Section 29.4: Scatter plot jitter 141 ................................................................................................................................. Section 29.5: Contour Plots - Customise the Text Labels 141 ...................................................................................... Section 29.6: Appending / adding entries to an existing legend 143 ......................................................................... Chapter 30: MATLAB Best Practices 145 ............................................................................................................... Section 30.1: Indent code properly 145 .......................................................................................................................... Section 30.2: Avoid loops 146 ......................................................................................................................................... Section 30.3: Keep lines short 146 .................................................................................................................................. Section 30.4: Use assert 147 ........................................................................................................................................... Section 30.5: Block Comment Operator 147 ................................................................................................................. Section 30.6: Create Unique Name for Temporary File 148 ........................................................................................ Chapter 31: MATLAB User Interfaces 150 .............................................................................................................. Section 31.1: Passing Data Around User Interface 150 ................................................................................................. Section 31.2: Making a button in your UI that pauses callback execution 152 .......................................................... Section 31.3: Passing data around using the "handles" structure 153 ........................................................................

Section 31.4: Performance Issues when Passing Data Around User Interface 154 ................................................... Chapter 32: Useful tricks 157 ....................................................................................................................................... Section 32.1: Extract figure data 157 .............................................................................................................................. Section 32.2: Code Folding Preferences 158 ................................................................................................................. Section 32.3: Functional Programming using Anonymous Functions 160 ................................................................. Section 32.4: Save multiple figures to the same .fig file 160 ........................................................................................ Section 32.5: Comment blocks 161 ................................................................................................................................. Section 32.6: Useful functions that operate on cells and arrays 162 ......................................................................... Chapter 33: Common mistakes and errors 165 ................................................................................................. Section 33.1: The transpose operators 165 .................................................................................................................... Section 33.2: Do not name a variable with an existing function name 165 ............................................................... Section 33.3: Be aware of floating point inaccuracy 166 ............................................................................................. Section 33.4: What you see is NOT what you get: char vs cellstring in the command window 167 ........................ Section 33.5: Undefined Function or Method X for Input Arguments of Type Y 168 ................................................. Section 33.6: The use of "i" or "j" as imaginary unit, loop indices or common variable 169 .................................... Section 33.7: Not enough input arguments 172 ............................................................................................................ Section 33.8: Using `length` for multidimensional arrays 173 ...................................................................................... Section 33.9: Watch out for array size changes 173 .................................................................................................... Credits 175 ............................................................................................................................................................................ You may also like 177 ......................................................................................................................................................

GoalKicker.com – MATLAB® Notes for Professionals 1 About Please feel free to share this PDF with anyone for free, latest version of this book can be downloaded from: https://goalkicker.com/MATLABBook This MATLAB® Notes for Professionals book is compiled from Stack Overflow Documentation, the content is written by the beautiful people at Stack Overflow. Text content is released under Creative Commons BY-SA, see credits at the end of this book whom contributed to the various chapters. Images may be copyright of their respective owners unless otherwise specified This is an unofficial free book created for educational purposes and is not affiliated with official MATLAB® group(s) or company(s) nor Stack Overflow. All trademarks and registered trademarks are the property of their respective company owners The information presented in this book is not guaranteed to be correct nor accurate, use at your own risk Please send feedback and corrections to web@petercv.com

GoalKicker.com – MATLAB® Notes for Professionals 2 Chapter 1: Getting started with MATLAB Language Version Release Release Date 1.0 1984-01-01 2 1986-01-01 3 1987-01-01 3.5 1990-01-01 4 1992-01-01 4.2c 1994-01-01 5.0 Volume 8 1996-12-01 5.1 Volume 9 1997-05-01 5.1.1 R9.1 1997-05-02 5.2 R10 1998-03-01 5.2.1 R10.1 1998-03-02 5.3 R11 1999-01-01 5.3.1 R11.1 1999-11-01 6.0 R12 2000-11-01 6.1 R12.1 2001-06-01 6.5 R13 2002-06-01 6.5.1 R13SP2 2003-01-01 6.5.2 R13SP2 2003-01-02 7 R14 2006-06-01 7.0.4 R14SP1 2004-10-01 7.1 R14SP3 2005-08-01 7.2 R2006a 2006-03-01 7.3 R2006b 2006-09-01 7.4 R2007a 2007-03-01 7.5 R2007b 2007-09-01 7.6 R2008a 2008-03-01 7.7 R2008b 2008-09-01 7.8 R2009a 2009-03-01 7.9 R2009b 2009-09-01 7.10 R2010a 2010-03-01 7.11 R2010b 2010-09-01 7.12 R2011a 2011-03-01 7.13 R2011b 2011-09-01 7.14 R2012a 2012-03-01 8.0 R2012b 2012-09-01 8.1 R2013a 2013-03-01 8.2 R2013b 2013-09-01 8.3 R2014a 2014-03-01 8.4 R2014b 2014-09-01 8.5 R2015a 2015-03-01 8.6 R2015b 2015-09-01

GoalKicker.com – MATLAB® Notes for Professionals 3 9.0 R2016a 2016-03-01 9.1 R2016b 2016-09-14 9.2 R2017a 2017-03-08 See also: MATLAB release history on Wikipedia. Section 1.1: Indexing matrices and arrays MATLAB allows for several methods to index (access) elements of matrices and arrays: Subscript indexing - where you specify the position of the elements you want in each dimension of the matrix separately. Linear indexing - where the matrix is treated as a vector, no matter its dimensions. That means, you specify each position in the matrix with a single number. Logical indexing - where you use a logical matrix (and matrix of true and false values) with the identical dimensions of the matrix you are trying to index as a mask to specify which value to return. These three methods are now explained in more detail using the following 3-by-3 matrix M as an example: >> M = magic(3) ans = 8 1 6 3 5 7 4 9 2 Subscript indexing The most straight-forward method for accessing an element, is to specify its row-column index. For example, accessing the element on the second row and third column: >> M(2, 3) ans = 7 The number of subscripts provided exactly matches the number of dimensions M has (two in this example). Note that the order of subscripts is the same as the mathematical convention: row index is the first. Moreover, MATLAB indices starts with 1 and not 0 like most programming languages. You can index multiple elements at once by passing a vector for each coordinate instead of a single number. For example to get the entire second row, we can specify that we want the first, second and third columns: >> M(2, [1,2,3]) ans = 3 5 7 In MATLAB, the vector [1,2,3] is more easily created using the colon operator, i.e. 1:3. You can use this in indexing as well. To select an entire row (or column), MATLAB provides a shortcut by allowing you just specify :. For example, the following code will also return the entire second row

GoalKicker.com – MATLAB® Notes for Professionals 4 >> M(2, :) ans = 3 5 7 MATLAB also provides a shortcut for specifying the last element of a dimension in the form of the end keyword. The end keyword will work exactly as if it was the number of the last element in that dimension. So if you want all the columns from column 2 to the last column, you can use write the following: >> M(2, 2:end) ans = 5 7 Subscript indexing can be restrictive as it will not allow to extract single values from different columns and rows; it will extract the combination of all rows and columns. >> M([2,3], [1,3]) ans = 3 7 4 2 For example subscript indexing cannot extract only the elements M(2,1) or M(3,3). To do this we must consider linear indexing. Linear indexing MATLAB allows you to treat n-dimensional arrays as one-dimensional arrays when you index using only one dimension. You can directly access the first element: >> M(1) ans = 8 Note that arrays are stored in column-major order in MATLAB which means that you access the elements by first going down the columns. So M(2) is the second element of the first column which is 3 and M(4) will be the first element of the second column i.e. >> M(4) ans = 1 There exist built-in functions in MATLAB to convert subscript indices to linear indices, and vice versa: sub2ind and ind2sub respectively. You can manually convert the subscripts (r,c) to a linear index by idx = r + (c-1)*size(M,1) To understand this, if we are in the first column then the linear index will simply be the row index. The formula above holds true for this because for c == 1, (c-1) == 0. In the next columns, the linear index is the row number

GoalKicker.com – MATLAB® Notes for Professionals 5 plus all the rows of the previous columns. Note that the end keyword still applies and now refers to the very last element of the array i.e. M(end) == M(end, end) == 2. You can also index multiple elements using linear indexing. Note that if you do that, the returned matrix will have the same shape as the matrix of index vectors. M(2:4) returns a row vector because 2:4 represents the row vector [2,3,4]: >> M(2:4) ans = 3 4 1 As another example, M([1,2;3,4]) returns a 2-by-2 matrix because [1,2;3,4] is a 2-by-2 matrix as well. See the below code to convince yourself: >> M([1,2;3,4]) ans = 8 3 4 1 Note that indexing with : alone will always return a column vector: >> M(:) ans = 8 3 4 1 5 9 6 7 2 This example also illustrates the order in which MATLAB returns elements when using linear indexing. Logical indexing The third method of indexing is to use a logical matrix, i.e. a matrix containing only true or false values, as a mask to filter out the elements you don't want. For example, if we want to find all the elements of M that are greater than 5 we can use the logical matrix >> M > 5 ans = 1 0 1 0 0 1 0 1 0

GoalKicker.com – MATLAB® Notes for Professionals 6 to index M and return only the values that are greater than 5 as follows: >> M(M > 5) ans = 8 9 6 7 If you wanted these number to stay in place (i.e. keep the shape of the matrix), then you could assign to the logic compliment >> M(~(M > 5)) = NaN ans = 8 NaN 6 NaN NaN 7 NaN 9 Nan We can reduce complicated code blocks containing if and for statements by using logical indexing. Take the non-vectorized (already shortened to a single loop by using linear indexing): for elem = 1:numel(M) if M(elem) > 5 M(elem) = M(elem) - 2; end end This can be shortened to the following code using logical indexing: idx = M > 5; M(idx) = M(idx) - 2; Or even shorter: M(M > 5) = M(M > 5) - 2; More on indexing Higher dimension matrices All the methods mentioned above generalize into n-dimensions. If we use the three-dimensional matrix M3 = rand(3,3,3) as an example, then you can access all the rows and columns of the second slice of the third dimension by writing >> M(:,:,2) You can access the first element of the second slice using linear indexing. Linear indexing will only move on to the second slice after all the rows and all the columns of the first slice. So the linear index for that element is >> M(size(M,1)*size(M,2)+1)

GoalKicker.com – MATLAB® Notes for Professionals 7 In fact, in MATLAB, every matrix is n-dimensional: it just happens to be that the size of most of the other n- dimensions are one. So, if a = 2 then a(1) == 2 (as one would expect), but also a(1, 1) == 2, as does a(1, 1, 1) == 2, a(1, 1, 1, ..., 1) == 2 and so on. These "extra" dimensions (of size 1), are referred to as singleton dimensions. The command squeeze will remove them, and one can use permute to swap the order of dimensions around (and introduce singleton dimensions if required). An n-dimensional matrix can also be indexed using an m subscripts (where m<=n). The rule is that the first m-1 subscripts behave ordinarily, while the last (m'th) subscript references the remaining (n-m+1) dimensions, just as a linear index would reference an (n-m+1) dimensional array. Here is an example: >> M = reshape(1:24,[2,3,4]); >> M(1,1) ans = 1 >> M(1,10) ans = 19 >> M(:,:) ans = 1 3 5 7 9 11 13 15 17 19 21 23 2 4 6 8 10 12 14 16 18 20 22 24 Returning ranges of elements With subscript indexing, if you specify more than one element in more than one dimension, MATLAB returns each possible pair of coordinates. For example, if you try M([1,2],[1,3]) MATLAB will return M(1,1) and M(2,3) but it will also return M(1,3) and M(2,1). This can seem unintuitive when you are looking for the elements for a list of coordinate pairs but consider the example of a larger matrix, A = rand(20) (note A is now 20-by-20), where you want to get the top right hand quadrant. In this case instead of having to specify every coordinate pair in that quadrant (and this this case that would be 100 pairs), you just specify the 10 rows and the 10 columns you want so A(1:10, 11:end). Slicing a matrix like this is far more common than requiring a list of coordinate pairs. In the event that you do want to get a list of coordinate pairs, the simplest solution is to convert to linear indexing. Consider the problem where you have a vector of column indices you want returned, where each row of the vector contains the column number you want returned for the corresponding row of the matrix. For example colIdx = [3;2;1] So in this case you actually want to get back the elements at (1,3), (2,2) and (3,1). So using linear indexing: >> colIdx = [3;2;1]; >> rowIdx = 1:length(colIdx); >> idx = sub2ind(size(M), rowIdx, colIdx); >> M(idx) ans = 6 5 4 Returning an element multiple times With subscript and linear indexing you can also return an element multiple times by repeating it's index so >> M([1,1,1,2,2,2]) ans =

GoalKicker.com – MATLAB® Notes for Professionals 8 8 8 8 3 3 3 You can use this to duplicate entire rows and column for example to repeat the first row and last column >> M([1, 1:end], [1:end, end]) ans = 8 1 6 6 8 1 6 6 3 5 7 7 4 9 2 2 For more information, see here. Section 1.2: Anonymous functions and function handles Basics Anonymous functions are a powerful tool of the MATLAB language. They are functions that exist locally, that is: in the current workspace. However, they do not exist on the MATLAB path like a regular function would, e.g. in an m- file. That is why they are called anonymous, although they can have a name like a variable in the workspace. The @ operator Use the @ operator to create anonymous functions and function handles. For example, to create a handle to the sin function (sine) and use it as f: >> f = @sin f = @sin Now f is a handle to the sin function. Just like (in real life) a door handle is a way to use a door, a function handle is a way to use a function. To use f, arguments are passed to it as if it were the sin function: >> f(pi/2) ans = 1 f accepts any input arguments the sin function accepts. If sin would be a function that accepts zero input arguments (which it does not, but others do, e.g. the peaks function), f() would be used to call it without input arguments. Custom anonymous functions Anonymous functions of one variable It is not obviously useful to create a handle to an existing function, like sin in the example above. It is kind of redundant in that example. However, it is useful to create anonymous functions that do custom things that otherwise would need to be repeated multiple times or created a separate function for. As an example of a custom anonymous function that accepts one variable as its input, sum the sine and cosine squared of a signal: >> f = @(x) sin(x)+cos(x).^2 f = @(x)sin(x)+cos(x).^2

GoalKicker.com – MATLAB® Notes for Professionals 9 Now f accepts one input argument called x. This was specified using parentheses (...) directly after the @ operator. f now is an anonymous function of x: f(x). It is used by passing a value of x to f: >> f(pi) ans = 1.0000 A vector of values or a variable can also be passed to f, as long as they are used in a valid way within f: >> f(1:3) % pass a vector to f ans = 1.1334 1.0825 1.1212 >> n = 5:7; >> f(n) % pass n to f ans = -0.8785 0.6425 1.2254 Anonymous functions of more than one variable In the same fashion anonymous functions can be created to accept more than one variable. An example of an anonymous function that accepts three variables: >> f = @(x,y,z) x.^2 + y.^2 - z.^2 f = @(x,y,z)x.^2+y.^2-z.^2 >> f(2,3,4) ans = -3 Parameterizing anonymous functions Variables in the workspace can be used within the definition of anonymous functions. This is called parameterizing. For example, to use a constant c = 2 in an anonymous function: >> c = 2; >> f = @(x) c*x f = @(x)c*x >> f(3) ans = 6 f(3) used the variable c as a parameter to multiply with the provided x. Note that if the value of c is set to something different at this point, then f(3) is called, the result would not be different. The value of c is the value at the time of creation of the anonymous function: >> c = 2; >> f = @(x) c*x; >> f(3) ans = 6 >> c = 3; >> f(3) ans = 6 Input arguments to an anonymous function do not refer to workspace variables Note that using the name of variables in the workspace as one of the input arguments of an anonymous function

GoalKicker.com – MATLAB® Notes for Professionals 10 (i.e., using @(...)) will not use those variables' values. Instead, they are treated as different variables within the scope of the anonymous function, that is: the anonymous function has its private workspace where the input variables never refer to the variables from the main workspace. The main workspace and the anonymous function's workspace do not know about each other's contents. An example to illustrate this: >> x = 3 % x in main workspace x = 3 >> f = @(x) x+1; % here x refers to a private x variable >> f(5) ans = 6 >> x x = 3 The value of x from the main workspace is not used within f. Also, in the main workspace x was left untouched. Within the scope of f, the variable names between parentheses after the @ operator are independent from the main workspace variables. Anonymous functions are stored in variables An anonymous function (or, more precisely, the function handle pointing at an anonymous function) is stored like any other value in the current workspace: In a variable (as we did above), in a cell array ({@(x)x.^2,@(x)x+1}), or even in a property (like h.ButtonDownFcn for interactive graphics). This means the anonymous function can be treated like any other value. When storing it in a variable, it has a name in the current workspace and can be changed and cleared just like variables holding numbers. Put differently: A function handle (whether in the @sin form or for an anonymous function) is simply a value that can be stored in a variable, just like a numerical matrix can be. Advanced use Passing function handles to other functions Since function handles are treated like variables, they can be passed to functions that accept function handles as input arguments. An example: A function is created in an m-file that accepts a function handle and a scalar number. It then calls the function handle by passing 3 to it and then adds the scalar number to the result. The result is returned. Contents of funHandleDemo.m: function y = funHandleDemo(fun,x) y = fun(3); y = y + x; Save it somewhere on the path, e.g. in MATLAB's current folder. Now funHandleDemo can be used as follows, for example: >> f = @(x) x^2; % an anonymous function >> y = funHandleDemo(f,10) % pass f and a scalar to funHandleDemo y = 19 The handle of another existing function can be passed to funHandleDemo:

GoalKicker.com – MATLAB® Notes for Professionals 11 >> y = funHandleDemo(@sin,-5) y = -4.8589 Notice how @sin was a quick way to access the sin function without first storing it in a variable using f = @sin. Using bsxfun, cellfun and similar functions with anonymous functions MATLAB has some built-in functions that accept anonymous functions as an input. This is a way to perform many calculations with a minimal number of lines of code. For example bsxfun, which performs element-by-element binary operations, that is: it applies a function on two vectors or matrices in an element-by-element fashion. Normally, this would require use of for-loops, which often requires preallocation for speed. Using bsxfun this process is sped up. The following example illustrates this using tic and toc, two functions that can be used to time how long code takes. It calculates the difference of every matrix element from the matrix column mean. A = rand(50); % 50-by-50 matrix of random values between 0 and 1 % method 1: slow and lots of lines of code tic meanA = mean(A); % mean of every matrix column: a row vector % pre-allocate result for speed, remove this for even worse performance result = zeros(size(A)); for j = 1:size(A,1) result(j,:) = A(j,:) - meanA; end toc clear result % make sure method 2 creates its own result % method 2: fast and only one line of code tic result = bsxfun(@minus,A,mean(A)); toc Running the example above results in two outputs: Elapsed time is 0.015153 seconds. Elapsed time is 0.007884 seconds. These lines come from the toc functions, which print the elapsed time since the last call to the tic function. The bsxfun call applies the function in the first input argument to the other two input arguments. @minus is a long name for the same operation as the minus sign would do. A different anonymous function or handle (@) to any other function could have been specified, as long as it accepts A and mean(A) as inputs to generate a meaningful result. Especially for large amounts of data in large matrices, bsxfun can speed up things a lot. It also makes code look cleaner, although it might be more difficult to interpret for people who don't know MATLAB or bsxfun. (Note that in MATLAB R2016a and later, many operations that previously used bsxfun no longer need them; A-mean(A) works directly and can in some cases be even faster.) Section 1.3: Matrices and Arrays In MATLAB, the most basic data type is the numeric array. It can be a scalar, a 1-D vector, a 2-D matrix, or an N-D multidimensional array.

GoalKicker.com – MATLAB® Notes for Professionals 12 % a 1-by-1 scalar value x = 1; To create a row vector, enter the elements inside brackets, separated by spaces or commas: % a 1-by-4 row vector v = [1, 2, 3, 4]; v = [1 2 3 4]; To create a column vector, separate the elements with semicolons: % a 4-by-1 column vector v = [1; 2; 3; 4]; To create a matrix, we enter the rows as before separated by semicolons: % a 2 row-by-4 column matrix M = [1 2 3 4; 5 6 7 8]; % a 4 row-by-2 column matrix M = [1 2; ... 4 5; ... 6 7; ... 8 9]; Notice you cannot create a matrix with unequal row / column size. All rows must be the same length, and all columns must be the same length: % an unequal row / column matrix M = [1 2 3 ; 4 5 6 7]; % This is not valid and will return an error % another unequal row / column matrix M = [1 2 3; ... 4 5; ... 6 7 8; ... 9 10]; % This is not valid and will return an error To transpose a vector or a matrix, we use the .'-operator, or the ' operator to take its Hermitian conjugate, which is the complex conjugate of its transpose. For real matrices, these two are the same: % create a row vector and transpose it into a column vector v = [1 2 3 4].'; % v is equal to [1; 2; 3; 4]; % create a 2-by-4 matrix and transpose it to get a 4-by-2 matrix M = [1 2 3 4; 5 6 7 8].'; % M is equal to [1 5; 2 6; 3 7; 4 8] % transpose a vector or matrix stored as a variable A = [1 2; 3 4]; B = A.'; % B is equal to [1 3; 2 4] For arrays of more than two-dimensions, there is no direct language syntax to enter them literally. Instead we must use functions to construct them (such as ones, zeros, rand) or by manipulating other arrays (using functions such as cat, reshape, permute). Some examples: % a 5-by-2-by-4-by-3 array (4-dimensions) arr = ones(5, 2, 4, 3);

GoalKicker.com – MATLAB® Notes for Professionals 13 % a 2-by-3-by-2 array (3-dimensions) arr = cat(3, [1 2 3; 4 5 6], [7 8 9; 0 1 2]); % a 5-by-4-by-3-by-2 (4-dimensions) arr = reshape(1:120, [5 4 3 2]); Section 1.4: Cell arrays Elements of the same class can often be concatenated into arrays (with a few rare exceptions, e.g. function handles). Numeric scalars, by default of class double, can be stored in a matrix. >> A = [1, -2, 3.14, 4/5, 5^6; pi, inf, 7/0, nan, log(0)] A = 1.0e+04 * 0.0001 -0.0002 0.0003 0.0001 1.5625 0.0003 Inf Inf NaN -Inf Characters, which are of class char in MATLAB, can also be stored in array using similar syntax. Such an array is similar to a string in many other programming languages. >> s = ['MATLAB ','is ','fun'] s = MATLAB is fun Note that despite both of them are using brackets [ and ], the result classes are different. Therefore the operations that can be done on them are also different. >> whos Name Size Bytes Class Attributes A 2x5 80 double s 1x13 26 char In fact, the array s is not an array of the strings 'MATLAB ','is ', and 'fun', it is just one string - an array of 13 characters. You would get the same results if it were defined by any of the following: >> s = ['MAT','LAB ','is f','u','n']; >> s = ['M','A','T','L','A','B,' ','i','s',' ','f','u','n']; A regular MATLAB vector does not let you store a mix of variables of different classes, or a few different strings. This is where the cell array comes in handy. This is an array of cells that each can contain some MATLAB object, whose class can be different in every cell if needed. Use curly braces { and } around the elements to store in a cell array. >> C = {A; s} C = [2x5 double] 'MATLAB is fun' >> whos C Name Size Bytes Class Attributes C 2x1 330 cell Standard MATLAB objects of any classes can be stored together in a cell array. Note that cell arrays require more memory to store their contents. Accessing the contents of a cell is done using curly braces { and }.

GoalKicker.com – MATLAB® Notes for Professionals 14 >> C{1} ans = 1.0e+04 * 0.0001 -0.0002 0.0003 0.0001 1.5625 0.0003 Inf Inf NaN -Inf Note that C(1) is different from C{1}. Whereas the latter returns the cell's content (and has class double in out example), the former returns a cell array which is a sub-array of C. Similarly, if D were an 10 by 5 cell array, then D(4:8,1:3) would return a sub-array of D whose size is 5 by 3 and whose class is cell. And the syntax C{1:2} does not have a single returned object, but rather it returns 2 different objects (similar to a MATLAB function with multiple return values): >> [x,y] = C{1:2} x = 1 -2 3.14 0.8 15625 3.14159265358979 Inf Inf NaN -Inf y = MATLAB is fun Section 1.5: Hello World Open a new blank document in the MATLAB Editor (in recent versions of MATLAB, do this by selecting the Home tab of the toolstrip, and clicking on New Script). The default keyboard shortcut to create a new script is Ctrl-n . Alternatively, typing edit myscriptname.m will open the file myscriptname.m for editing, or offer to create the file if it does not exist on the MATLAB path. In the editor, type the following: disp('Hello, World!'); Select the Editor tab of the toolstrip, and click Save As. Save the document to a file in the current directory called helloworld.m. Saving an untitled file will bring up a dialog box to name the file. In the MATLAB Command Window, type the following: >> helloworld You should see the following response in the MATLAB Command Window: Hello, World! We see that in the Command Window, we are able to type the names of functions or script files that we have written, or that are shipped with MATLAB, to run them. Here, we have run the 'helloworld' script. Notice that typing the extension (.m) is unnecessary. The instructions held in the script file are executed by MATLAB, here printing 'Hello, World!' using the disp function. Script files can be written in this way to save a series of commands for later (re)use. Section 1.6: Scripts and Functions MATLAB code can be saved in m-files to be reused. m-files have the .m extension which is automatically associated

GoalKicker.com – MATLAB® Notes for Professionals 15 with MATLAB. An m-file can contain either a script or functions. Scripts Scripts are simply program files that execute a series of MATLAB commands in a predefined order. Scripts do not accept input, nor do scripts return output. Functionally, scripts are equivalent to typing commands directly into the MATLAB command window and being able to replay them. An example of a script: length = 10; width = 3; area = length * width; This script will define length, width, and area in the current workspace with the value 10, 3, and 30 respectively. As stated before, the above script is functionally equivalent to typing the same commands directly into the command window. >> length = 10; >> width = 3; >> area = length * width; Functions Functions, when compared to scripts, are much more flexible and extensible. Unlike scripts, functions can accept input and return output to the caller. A function has its own workspace, this means that internal operations of the functions will not change the variables from the caller. All functions are defined with the same header format: function [output] = myFunctionName(input) The function keyword begins every function header. The list of outputs follows. The list of outputs can also be a comma separated list of variables to return. function [a, b, c] = myFunctionName(input) Next is the name of the function that will be used for calling. This is generally the same name as the filename. For example, we would save this function as myFunctionName.m. Following the function name is the list of inputs. Like the outputs, this can also be a comma separated list. function [a, b, c] = myFunctionName(x, y, z) We can rewrite the example script from before as a reusable function like the following: function [area] = calcRecArea(length, width) area = length * width; end We can call functions from other functions, or even from script files. Here is an example of our above function being used in a script file.