introduction to matlab - tu dresden...introduction to matlab pouyan r. fard prof. dr. stefan j....
TRANSCRIPT
![Page 1: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/1.jpg)
Dresden, 23.09.2011
Introduction to Matlab
Pouyan R. Fard
Prof. Dr. Stefan J. Kiebel
Dresden, 27.04.2017
Matrices, Random Numbers, Plotting
![Page 2: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/2.jpg)
Titel der Präsentation Folie Nr. 2 von XYZ
Seminar overview
2
Date Topics Projects
06.04. Intro, basic operations, First Exercise (Morse Code)
13.04. First Exercise Continued(Morse Code)
27.04. Second Exercise (Game of Life)
04.05. Second Exercise Continued (Game of Life)
05.05. Third Exercise (Drift-Diffusion Model) Project Distribution
11.05. Third Exercise Continued (Drift-Diffusion Model)
30.05. - Project Deadline (6 PM)
![Page 3: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/3.jpg)
Titel der Präsentation Folie Nr. 3 von XYZ
Matrices and Vectors
3
• Thinking in a matrix way
![Page 4: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/4.jpg)
Titel der Präsentation Folie Nr. 4 von XYZ
Matrices and Vectors
4
• Initializing vectors and matrices in MATLAB
![Page 5: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/5.jpg)
Titel der Präsentation Folie Nr. 5 von XYZ
Matrices and Vectors
5
• Size of matrices
• Usage of spaces, commas, and semi-colons
• Dimensions must be consistent.
![Page 6: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/6.jpg)
Titel der Präsentation Folie Nr. 6 von XYZ
Matrices and Vectors
6
![Page 7: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/7.jpg)
Titel der Präsentation Folie Nr. 7 von XYZ
Initializing Matrices
7
• Initializing an empty matrix
• Initializing an identity matrix with size n
• Initializing a matrix whose all elements are 1 • n= number of rows , m= number of columns
• Initializing a matrix whose all elements are 0
• n= number of rows , m= number of columns
• Initializing a matrix of random integers magic(n)
• n= number of rows and columns
![Page 8: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/8.jpg)
Titel der Präsentation Folie Nr. 8 von XYZ
Indexing
8
![Page 9: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/9.jpg)
Titel der Präsentation Folie Nr. 9 von XYZ
• Accessing single elements in matrices
• Accessing multiple elements in matrices
Indexing
9
![Page 10: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/10.jpg)
Titel der Präsentation Folie Nr. 10 von XYZ
• Accessing multiple elements in matrices
• Deleting rows or columns of a matrix
Indexing
10
![Page 11: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/11.jpg)
Titel der Präsentation Folie Nr. 11 von XYZ
• Deleting rows or columns of a matrix
• Deleting one single entry in a matrix is not possible!
• Deleting one single entry is possible in vector.
Indexing
11
![Page 12: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/12.jpg)
Titel der Präsentation Folie Nr. 12 von XYZ
Matrix Operations
12
![Page 13: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/13.jpg)
Titel der Präsentation Folie Nr. 13 von XYZ
Matrix Operations
13
• Element-wise addition with a single-element matrix
• When dimensions don’t agree:
![Page 14: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/14.jpg)
Titel der Präsentation Folie Nr. 14 von XYZ
Matrix Operations
14
• Element-wise operations
![Page 15: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/15.jpg)
Titel der Präsentation Folie Nr. 15 von XYZ
Matrix Multiplication
15
• 𝐴 is a 𝑚 × 𝑛 matrix • 𝐵 is a 𝑛 × 𝑝 matrix
• (𝐴𝐵)𝑖,𝑗= 𝐴𝑖,𝑟 𝐵𝑟,𝑗𝑛𝑟=1
![Page 16: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/16.jpg)
Titel der Präsentation Folie Nr. 16 von XYZ
Matrix Multiplication
16
![Page 17: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/17.jpg)
Titel der Präsentation Folie Nr. 17 von XYZ
Matrix Multiplication
17
• Example 1: Application in linear algebra
![Page 18: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/18.jpg)
Titel der Präsentation Folie Nr. 18 von XYZ
Matrix Multiplication
18
Example 2: Suppose you have five different products in your shop being sold with five different prices, and you sell them in five different quantities. How you can compute your revenue using matrix calculations?
![Page 19: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/19.jpg)
Titel der Präsentation Folie Nr. 19 von XYZ
Example: General Linear Model
19
General Linear Models (GLMs) are widely used to localize brain activity in functional imaging. A standard GLM can be written as:
𝒀 = 𝑿𝜷 + 𝜺 Where:
𝑌1𝑌2⋮𝑌𝑛
=
1 𝑋111 𝑋21
⋯𝑋1𝑝𝑋2𝑝
⋮ ⋱ ⋮1 𝑋𝑛1 ⋯ 𝑋𝑛𝑝
×
𝛽1𝛽2⋮𝛽𝑛
+
𝜀1𝜀2⋮𝜀𝑛
BOLD Data Design Matrix Regression
Coefficients Noise
![Page 20: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/20.jpg)
Titel der Präsentation Folie Nr. 20 von XYZ
Bar Plots / Histograms
20
![Page 21: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/21.jpg)
Titel der Präsentation Folie Nr. 21 von XYZ
Random Numbers
21
• Uniform Distribution • Pseudo-random uniformly distributed integers
![Page 22: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/22.jpg)
Titel der Präsentation Folie Nr. 22 von XYZ
Random Numbers
22
• Normal Distribution
![Page 23: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/23.jpg)
Titel der Präsentation Folie Nr. 23 von XYZ
Random Numbers
23
• See MATLAB help for my for details.
![Page 24: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/24.jpg)
Titel der Präsentation Folie Nr. 24 von XYZ
Random Numbers
24
• See MATLAB help for my for details.
![Page 25: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/25.jpg)
Titel der Präsentation Folie Nr. 25 von XYZ
Basics of Plotting
25
![Page 26: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/26.jpg)
Titel der Präsentation Folie Nr. 26 von XYZ
Subplots
26
![Page 27: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/27.jpg)
Titel der Präsentation Folie Nr. 27 von XYZ
Subplots
27
![Page 28: Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J. Kiebel Dresden, 27.04.2017 Matrices, Random Numbers, Plotting Titel der Präsentation](https://reader036.vdocuments.mx/reader036/viewer/2022062403/5fd13c01b20b2b4bc6672774/html5/thumbnails/28.jpg)
Titel der Präsentation Folie Nr. 28 von XYZ
References
28
• MATLAB for Psychologists (2012), Borgo, M., Soranzo, A., Grassi, M., Springer-Verlag, 2012, ISBN. 978-1-4614-2196-2. • Chapter 1. Basic Operations, pp. 1-23. • Chapter 2. Data Handling, pp. 25-46
• MATLAB for Neuroscientists, 2nd Ed: An Introduction to Scientific Computing
(2014), Wallisch, P., Lusignan, M.E., Benayoun, M.D., Baker, T.I., Dickey, A.S. and Hatsopoulos, N.G., Academic Press, ISBN. 978-0123838360. • Chapter 2-3. pp. 7-114.
• MATLAB help:
• http://www.mathworks.com/help/matlab/random-number-generation.html • http://www.mathworks.com/help/stats/random.html • http://www.mathworks.com/help/matlab/ref/subplot.html