Matlab

Operators

• 2\1 is equivalent to 1/2

psi = C .* 1./(1+(x./a).^2);

• The dot denotes pair-by-pair operation for vectors
• Technically, you only need dots in front of ^ operators for which the first argument might be a vector, and * and / operators for which the quantities on each side of the operator could both be vectors. The MATLAB function quad gives a vector argument to the function it is integrating, so vectors may crop up when you don't expect them. The safest thing is to put a dot in front of every *, /, and ^ operator in all your functions. Otherwise, you may get hard-to-understand error messages.

Working at the command line

• semicolon at end of line prevents result from being displayed
• clear clears all session variables, clear x clears the variable x
• whos shows all session variables
• size(x) shows the dimensions of x
• clc clears the command window
• use diary mynotes.txt to append command window input/output to the file mynotes.txt; use diary off to stop appending
• disp(x) will display the value of x
• format controls format of numeric output

Built-in scalar functions

• fix rounds to nearest integer toward zero, floor, ceil
• log, log10, pow2 (two to the x)
• realmin, realmax smallest and largest floating point numbers supported
• rand in the interval [0,1)
• rem(x,y) remainder when x is divided by y

Vectors

• create a sequence vector:


1. x = 1:5 (one through five, inclusive)
2. x = 1: 0.1: 5 (one through five in steps of 0.1)

• create an arbitrary vector:

1. x = [5 2 9 4 8]
2. x = [5, 2, 9, 4, 8] (may use commas or spaces)
3. y = [1 x 1] (has 7 elements)

• multiply: y = 2*x
• add: x + y
• get the first element: x(1)
• get the first three elements: x(1:3)
• column vector using transpose: y = x'
• append an element: x = [ x 3 ]
• remove an element x(3) = []
• built-in vector functions: cumsum (cumulative sum), length, max, mean, min, prod, sum

Matrices

x = [1 2 3; 4 5 6]
x(1, 2)  (gives 2)
x'  % transpose
x(2, :)   % gives [4 5 6]
a = [1 2; 3 4], b = a'
a * b   % matrix multiplication give [5 11; 11 25]
a .* b  % element-by-element multiplication gives [1 6; 6 16]

Control Flow

for i = 1:5, disp(i), end

for i = 1:6
    x = (x + a / x) / 2;
    disp( x )
end

if x == 0, disp( ’x equals zero’), end

if bal < 5000
    rate = 0.09;
elseif bal < 10000
    rate = 0.12;
else
    rate = 0.15;
end

d = floor(3*rand) + 1
switch d
case 1
    disp( ’That’’s a 1!’ );
case 2
    disp( ’That’’s a 2!’ );
otherwise
    disp( ’Must be 3!’ );
end

Functions

The existence of a file on disk called stat.m containing this code defines a new function called stat that calculates the mean and standard deviation of a vector:

function [mean,stdev] = stat(x)
n = length(x);
mean = sum(x)/n;
stdev = sqrt(sum((x-mean).^2/n));

Call the function, supplying two output variables on the left side of the equation:

[mean stdev] = stat([12.7 45.4 98.9 26.6 53/1])
mean =
   47.3200
stdev =
   29.4085

Timing

start = clock;
.. do stuff ..
elapsed = etime(clock, start)

or equivalently

tic
..do stuff..
toc  % prints out elapsed time

Date and Time

• clock gives time and date in a six-element vector
• date gives a string like 02-Feb-2011

Plotting

x = 1:0.1:5
plot(x, sin(x)), grid
ezplot('sin(x)')

Plot two functions simultaneously:

fplot(@(x) [sin(x),cos(x)],[0,2*pi,-2,2])

Printing

To print some text:

disp( [’The answer is ’, num2str(x)] );
fprintf( ’Interest rate: %6.3f New balance: %8.2f\n’, rate, balance);

File I/O

save mydata.txt myVar -ascii
myVar = load('mydata.txt')

also

save mydata x y z  % saves to mydata.mat
load mydata

may also use csvread, csvwrite, dlmread, dlmwrite, textread, xlsread