Matlab & LaTeX Tutorial

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# Matlab & LaTeX Tutorial - PowerPoint PPT Presentation

Matlab &amp; LaTeX Tutorial. Course web page: vision.cis.udel.edu/cv. February 14, 2003  Lecture 2. Announcements. Try running Matlab, pdflatex; let me know if you’re having any trouble getting an account or otherwise

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### Matlab & LaTeXTutorial

Course web page:

vision.cis.udel.edu/cv

February 14, 2003 Lecture 2

Announcements
• Try running Matlab, pdflatex; let me know if you’re having any trouble getting an account or otherwise
• Read about 3-D geometry in Chapter 2-2.1 of Forsyth & Ponce for Monday’s lecture
Outline
• Matlab
• A high-level language for matrix calculations, numerical analysis, & scientific computing
• LaTeX
• A set of typesetting macros for documents containing equations, specialized mathematical symbols, etc.
Matlab
• For solving problems that arise in physics, engineering, and other sciences such as integration, differential equations, and optimization numerically as opposed to analytically (like Mathematica)
• Toolboxes are libraries for particular applications such as images, fluid dynamics, etc.
• Language features
• Intepreted
• No variable declarations
• Automatic memory management
• Variable argument lists control function behavior
• Vectorized: Can use for loops, but largely unnecessary
How to Get Help
• In Matlab
• Type “help” to get a listing of topics
• “help <topic>” gets help for that topic. The information is at the level of a Unix man page
• On the web
• “Matlab links” on course web page has pointers
• Especially MathWorks help desk:

www.mathworks.com/access/helpdesk/help/helpdesk.shtml

Entering Variables
• Entering a scalar, vector, matrix

>> a = 27;

>> V = [10, 4.5, a];

>> M = [3, 4 ; -6, 5];

• Without semi-colon, input is echoed (this is bad when you’re loading images!). You can use this as a kind of print statement, though
• Comma to separate statements on same line
• size: Number of rows, columns
Constructing Matrices
• Basic built-ins:
• All zeroes, ones: zeros, ones
• Identity: eye
• Random: rand (uniform), randn (unit normal)
• Ranges: m:n, m:i:n (i is step size)
• Composing big matrices out of small matrix blocks
• repmat(A, m, n): “Tile” a big matrix with m x n copies of A
• Write with dlmwrite(‘filename’, M, ‘,’)
Manipulations & Calculations
• Transpose (‘), inverse (inv)
• Matrix arithmetic: +, -, *, /, ^
• Can use scalar a * ones(m, n) to make matrix of a’s
• repmat(a, m, n) can be faster for big m, n
• Elementwise arithmetic: .*, ./, .^
• Relations: >, ==, etc. compare every element to scalar
• M > a returns a matrix the size of M where every element greater than a is 1 and everything else is 0
• Functions
• Vectorized
• sin, cos, etc.
Deconstructing Matrices
• Indexing individual entries by row, col: A(1, 1) is upper-left entry
• Ranges: e.g., A(1:10, 3), A(:, 1)
• Matrix to vector and vice versa by column: B = A(:), A(:) = B
• Transpose to use row order
• find: Indices of non-zero elements
• find(M==a) gives indices of M’s elements that are equal to a
Vector/Matrix Analysis
• Whole vector
• Matrix
• By column
• norm: magnitude
• max, min: max(max(M)) is maximum element of matrix M
• sum
• By row: transpose, do column analysis
M-Files
• Any text file ending in “.m”
• Use path or addpath to tell Matlab where code is (non-persistent?)
• Script: Collection of command line statements
• Function: Take argument(s), return value(s). First line defines:

>> function y = foo(A)

>> function [x, y] = foo2(a, M, N)

• Comment: Start line with %
Control Structures
• Expressions, relations (==, >, |, &, functions, etc.)
• if/whileexpressionstatementsend
• Use comma to separate expression from statements if on same line

>> if a == b & isprime(n), M = inv(K); else M = K; end

• forvariable=expressionstatementsend

>> for i=1:2:100, s = s / 10; end

Plotting
• 2-D vectors: plot(x, y)

>> plot(0:0.01:2*pi, sin(0:0.01:2*pi))

• 3-D: plot3(x, y, z)(space curve)
• Surfaces
• meshgrid makes surface from axes, mesh plots it

>> [X,Y] = meshgrid(-2:.2:2, -2:.2:2);

>> Z = X .* exp(-X.^2 - Y.^2);

>> mesh(Z)

• surf: Solid version of mesh
• Saving figures, plots: print –depsc2filename or –dpng or –djpgnn, where nn is quality 00-99
Images
• Accessing/modifying the pixels
• I is m x n if image is grayscale—e.g., I(i, j)
• I is m x n x 3 if image is color—e.g., I(i, j, 1)
• Displaying
• Just the image: imshow(I);
• With overlay:

[r,c,d]=size(I);

imshow(I), hold on;

plot(c*rand(100,1),r*rand(100,1), 'r*');

hold off;

• Writing: imwrite(I, ‘filename’);
LaTeX
• A markup language for typesetting scientific and mathematical documents
• Similar to editing raw HTML, with a lot of special-purpose characters and commands
Documents
• May be easiest to just modify template file provided: cv_math_template.tex
• File anatomy
• Header stuff (document type, font size, etc.)—ignore
• Title, author
• Sections and subsections
• Footer stuff—ignore
• Contents
• Text
• Equations (warning: different ways to get same effect)
• Figures, tables: put these kinds of things in your web page
• Compiling: “pdflatex filename.tex”  filename.pdf; preview with Acrobat Reader
Equations
• Types
• Inline: $2 + 2 = 4$
• Display: $a x + by > c$
• Font types (regular letters are italicized as variables by default)
• Roman, bold, italic, calligraphy
• Symbols
• Greek letters: \alpha, \beta, etc.
• Operators: \infty, \geq, etc.
• Functions: \log, \sin, etc.
• Sub- and superscripting: a_{n}, x^{2}
• Inverse: \mathbf{A}^{-1}
• Transpose: \mathbf{R}^{T}
• Vectors and matrices: Arrays
• For example, \left( \begin{array}{c} x \\ y \end{array} \right)
Function/Macro Equivalent: \newcommand
• Definitions (right after \begin{document})
• Simple substitution: \newcommand{\Mean}{\mu}
• $\Mean$
• $\MyAdd{a}{b}$