Introduction to Matlab - TU Dresden...Introduction to Matlab Pouyan R. Fard Prof. Dr. Stefan J....

Dresden, 23.09.2011

Introduction to Matlab

Pouyan R. Fard

Prof. Dr. Stefan J. Kiebel

Dresden, 27.04.2017

Matrices, Random Numbers, Plotting

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Seminar overview

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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)

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Matrices and Vectors

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• Thinking in a matrix way

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Matrices and Vectors

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• Initializing vectors and matrices in MATLAB

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Matrices and Vectors

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• Size of matrices

• Usage of spaces, commas, and semi-colons

• Dimensions must be consistent.

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Matrices and Vectors

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Initializing Matrices

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• 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

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Indexing

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• Accessing single elements in matrices

• Accessing multiple elements in matrices

Indexing

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• Accessing multiple elements in matrices

• Deleting rows or columns of a matrix

Indexing

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• 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

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Matrix Operations

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Matrix Operations

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• Element-wise addition with a single-element matrix

• When dimensions don’t agree:

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Matrix Operations

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• Element-wise operations

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Matrix Multiplication

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• 𝐴 is a 𝑚 × 𝑛 matrix • 𝐵 is a 𝑛 × 𝑝 matrix

• (𝐴𝐵)𝑖,𝑗= 𝐴𝑖,𝑟 𝐵𝑟,𝑗𝑛𝑟=1

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Matrix Multiplication

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Matrix Multiplication

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• Example 1: Application in linear algebra

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Matrix Multiplication

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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?

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Example: General Linear Model

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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

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Bar Plots / Histograms

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Random Numbers

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• Uniform Distribution • Pseudo-random uniformly distributed integers

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Random Numbers

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• Normal Distribution

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Random Numbers

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• See MATLAB help for my for details.

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Random Numbers

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• See MATLAB help for my for details.

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Basics of Plotting

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Subplots

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Subplots

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References

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• 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