Skip to content

Latest commit

 

History

History
110 lines (98 loc) · 4.2 KB

matlab.md

File metadata and controls

110 lines (98 loc) · 4.2 KB
Raw

Introduction to MATLAB

What is MATLAB?

MATLAB is short for "Matrix Laboratory." It is a scripting language that is designed for fast matrix operations and to be full of features for scientific computing. The software is proprietary and requires a license, so it is not free. Stanford offers discount licenses for personal use though the software store, free access on Farmshare, and free access in computer labs. For similar, free options, you can try out Octave, Python (with NumPy and SciPy), R, or Julia.

Basics

  • x = 5 - Variables are defined with =
  • + - * / - Basic math operations
  • ==, < <=, ~= - Logical operations
  • sin(x), cos(x), exp(x), sqrt(x), round(x) - Math functions
  • pi, i, Inf - Special values
  • ; - At the end of lines suppresses output
  • % - Comment
  • help <function> - Show function documentation
  • clear - Clears all saved variables (useful at the beginning of scripts)
  • clc - Clears the command window (useful at the beginning of scripts)
  • close all - Closes all figure (useful at hte beginning of scripts)
  • If statements and loops are
if x < y
  % do something
end

for i = 1:N
  % do something
end

while x < y
  % do something
end

Vectors and Matrices

  • y=[1,2,3] - Row Vector
  • x=[1;2;3] - Column Vector
  • A=[1,2,3;4,5,6;7,8,9] - Matrix
  • A(1,2) - Access entries in a matrix (Returns 2, in this example)
  • A(1,:) - Access the first row of the matrix
  • A' - Transpose
  • A*x - Matrix Multiplication
  • x.*z - Entry wise operation (Also works with ./ or .^)
  • x = A\b - Solve matrix system
  • zeros(n,m) - Creates an n by m matrix of zeros
  • ones(n,m) - Creates an n by m matrix of ones
  • eye(n) - Creates an n by n identity matrix
  • linspace(a,b,n) - Creates a row vector of n linear values between a and b
  • det(A) - Determinant
  • eig(a) - Eigenvalue decomposition
  • svd(a) - Singular value decomposition
  • There are also specific matrix formats to use for sparse/structured matrix computations

Functions

Simple inline function handles can be created like:

my_f = @(x) sin(x)+cos(x);

val = my_f(3/4*pi);

Full functions can be created with the follow syntax:

function [out_1,out_2] = my_fun_name(in_1,in_2)
  % [out_1,out_2] = my_fun_name(in_1,in_2)
  % Description of function in comments makes it appear with 'help' command
  
  <function body>
  
end
  • A function should be put into a separate file titled my_fun_name.m (With the function name as the title). This makes it so you can easily call the function with import statements
  • After the word function put he output values. When the function finishes running, it will return these values.
  • On the right side of the equals is the function name followed by the input arguments
  • If you put comment lines at the top of a function, those lines will appear with the help command
  • Then you put the body of the function
  • Then you end it with end

Plotting

x = linspace(0,10,1000);
y = x.^2 + sin(2*pi*x);
figure
plot(x,y,'b*')
hold on
z = x.^3;
plot(x,z,'r--')
legend('y','z')
xlabel('x')
ylabel('Functions')
title('Example Figure')
  • First, we create arrays of data to plot
  • figure creates a new figure to plot on
  • The first two arguments in plot are the data to plot
  • The third argument in plot is the type of markers for this data. Other options can also be selected here.
  • You can also create different plot types with loglog(), semilogx, semilogy
  • hold on makes it so that all of statements will plot on the same figure until a new figure is created
  • legend, xlabel, ylabel, and title create the labels, legends, and titles
  • help plot is very useful for remembering all of the different plotting options

Useful tools and packages

  • Symbolic math toolbox
  • Optimization toolbox
  • writeVideo() - Creates videos from plots
  • keyboard - Stops running and enters debug mode at this location
  • polyval() - Evaluates a polynomial defined by a vector
  • fft() - Fast fourier transform
  • trapz() - Numerical integration with trapezoidal rule
  • ode45() - 4th order ODE solver
  • Probability distributions
  • Tons of other useful math functions created by users and freely available on the MathWorks website