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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 latex tutorial

Matlab & LaTeXTutorial

Course web page:

vision.cis.udel.edu/cv

February 14, 2003 Lecture 2

announcements
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
Function/Macro Equivalent: \newcommand
  • Definitions (right after \begin{document})
    • Simple substitution: \newcommand{\Mean}{\mu}
    • Arguments: \newcommand{\MyAdd}[2]{{#1 + #2}
  • Invoking
    • $\Mean$
    • $\MyAdd{a}{b}$
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