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## PowerPoint Slideshow about ' Matlab & LaTeX Tutorial' - landry

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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
- $\Mean$
- $\MyAdd{a}{b}$

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