MATLAB Notes for Professionals

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Chapter 11: Matrix decompositions

Section 11.1: Schur decomposition

Section 11.2: Cholesky decomposition

Section 11.3: QR decomposition

Section 11.4: LU decomposition

Section 11.5: Singular value decomposition

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Chapter 12: Graphics: 2D Line Plots

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Section 12.1: Split line with NaNs

Section 12.2: Multiple lines in a single plot

Section 12.3: Custom colour and line style orders

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57

Chapter 13: Graphics: 2D and 3D Transformations

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Section 13.1: 2D Transformations

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Chapter 14: Controlling Subplot coloring in MATLAB

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Section 14.1: How it's done

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64

Chapter 15: Image processing

Section 15.1: Basic image I/O

Section 15.2: Retrieve Images from the Internet

Section 15.3: Filtering Using a 2D FFT

Section 15.4: Image Filtering

Section 15.5: Measuring Properties of Connected Regions

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Chapter 16: Drawing

Section 16.1: Circles

Section 16.2: Arrows

Section 16.3: Ellipse

Section 16.4: Pseudo 4D plot

Section 16.5: Fast drawing

Section 16.6: Polygon(s)

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Chapter 17: Financial Applications

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82

Section 17.1: Random Walk

Section 17.2: Univariate Geometric Brownian Motion

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82

Chapter 18: Fourier Transforms and Inverse Fourier Transforms

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84

Section 18.1: Implement a simple Fourier Transform in MATLAB

Section 18.2: Images and multidimensional FTs

Section 18.3: Inverse Fourier Transforms

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84

Chapter 19: Ordinary Dierential Equations (ODE) Solvers

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92

Section 19.1: Example for odeset

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92

Chapter 20: Interpolation with MATLAB

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94

Section 20.1: Piecewise interpolation 2 dimensional

Section 20.2: Piecewise interpolation 1 dimensional

Section 20.3: Polynomial interpolation

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101

Chapter 21: Integration

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105

Section 21.1: Integral, integral2, integral3

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105

Chapter 22: Reading large files

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107

Section 22.1: textscan

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50

51

53

53

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54

54

56

56

65

65

65

65

66

70

70

79

80

85

90

Section 22.2: Date and time strings to numeric array fast

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Chapter 23: Usage of accumarray() Function

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109

Section 23.1: Apply Filter to Image Patches and Set Each Pixel as the Mean of the Result of Each Patch

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Section 23.2: Finding the maximum value among elements grouped by another vector

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110

Chapter 24: Introduction to MEX API

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111

Section 24.1: Check number of inputs/outputs in a C++ MEX-file

Section 24.2: Input a string, modify it in C, and output it

Section 24.3: Passing a struct by field names

Section 24.4: Pass a 3D matrix from MATLAB to C

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Chapter 25: Debugging

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Section 25.1: Working with Breakpoints

Section 25.2: Debugging Java code invoked by MATLAB

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Chapter 26: Performance and Benchmarking

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Section 26.1: Identifying performance bottlenecks using the Profiler

Section 26.2: Comparing execution time of multiple functions

Section 26.3: The importance of preallocation

Section 26.4: It's ok to be single!

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Chapter 27: Multithreading

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130

Section 27.1: Using parfor to parallelize a loop

Section 27.2: Executing commands in parallel using a "Single Program, Multiple Data" (SPMD) statement

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Section 27.3: Using the batch command to do various computations in parallel

Section 27.4: When to use parfor

Chapter 28: Using serial ports

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131

Section 28.1: Creating a serial port on Mac/Linux/Windows

Section 28.2: Choosing your communication mode

Section 28.3: Automatically processing data received from a serial port

Section 28.4: Reading from the serial port

Section 28.5: Closing a serial port even if lost, deleted or overwritten

Section 28.6: Writing to the serial port

Chapter 29: Undocumented Features

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Section 29.1: Color-coded 2D line plots with color data in third dimension

Section 29.2: Semi-transparent markers in line and scatter plots

Section 29.3: C++ compatible helper functions

Section 29.4: Scatter plot jitter

Section 29.5: Contour Plots - Customise the Text Labels

Section 29.6: Appending / adding entries to an existing legend

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Chapter 30: MATLAB Best Practices

Section 30.1: Indent code properly

Section 30.2: Avoid loops

Section 30.3: Keep lines short

Section 30.4: Use assert

Section 30.5: Block Comment Operator

Section 30.6: Create Unique Name for Temporary File

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Chapter 31: MATLAB User Interfaces

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Section 31.1: Passing Data Around User Interface

Section 31.2: Making a button in your UI that pauses callback execution

Section 31.3: Passing data around using the "handles" structure

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Section 31.4: Performance Issues when Passing Data Around User Interface

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Chapter 32: Useful tricks

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157

Section 32.1: Extract figure data

Section 32.2: Code Folding Preferences

Section 32.3: Functional Programming using Anonymous Functions

Section 32.4: Save multiple figures to the same .fig file

Section 32.5: Comment blocks

Section 32.6: Useful functions that operate on cells and arrays

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Chapter 33: Common mistakes and errors

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Section 33.1: The transpose operators

Section 33.2: Do not name a variable with an existing function name

Section 33.3: Be aware of floating point inaccuracy

Section 33.4: What you see is NOT what you get: char vs cellstring in the command window

Section 33.5: Undefined Function or Method X for Input Arguments of Type Y

Section 33.6: The use of "i" or "j" as imaginary unit, loop indices or common variable

Section 33.7: Not enough input arguments

Section 33.8: Using length for multidimensional arrays

Section 33.9: Watch out for array size changes

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Credits

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GoalKicker.com – MATLAB® Notes for Professionals

1

Chapter 1: Getting started with MATLAB

Language

Version Release Release Date

1.0

1984-01-01

2

3

3.5

4

4.2c

5.0

5.1

5.1.1

5.2

1986-01-01

1987-01-01

1990-01-01

1992-01-01

1994-01-01

Volume 8 1996-12-01

Volume 9 1997-05-01

R9.1

R10

1997-05-02

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

6.1

6.5

6.5.1

6.5.2

7

R12

2000-11-01

R12.1

2001-06-01

R13

2002-06-01

R13SP2

2003-01-01

R13SP2

2003-01-02

R14

2006-06-01

7.0.4

R14SP1

2004-10-01

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

7.10

7.11

7.12

7.13

7.14

8.0

8.1

8.2

8.3

8.4

8.5

8.6

R14SP3

2005-08-01

R2006a

2006-03-01

R2006b 2006-09-01

R2007a

2007-03-01

R2007b 2007-09-01

R2008a

2008-03-01

R2008b 2008-09-01

R2009a

2009-03-01

R2009b 2009-09-01

R2010a

2010-03-01

R2010b 2010-09-01

R2011a

2011-03-01

R2011b 2011-09-01

R2012a

2012-03-01

R2012b 2012-09-01

R2013a

2013-03-01

R2013b 2013-09-01

R2014a

2014-03-01

R2014b 2014-09-01

R2015a

2015-03-01

R2015b 2015-09-01

GoalKicker.com – MATLAB® Notes for Professionals

2

9.0

9.1

9.2

R2016a

2016-03-01

R2016b 2016-09-14

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

3

>> 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

4

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

5

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

6

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 subscri...