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Matlab & 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

• Loading data: M = dlmread(‘filename’, ‘,’) (e.g., comma is delimiter)

• 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

• Reading: I = imread(‘filename’);

• 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:

I = imread(‘gore5.jpg');

[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}

• Arguments: \newcommand{\MyAdd}[2]{{#1 + #2}

• Invoking

• $\Mean$

• $\MyAdd{a}{b}$