matlab basics fin250f: lecture 3 spring 2010 grifths web notes
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Matlab Basics
FIN250f: Lecture 3
Spring 2010
Grifths Web Notes
Loading Software
Matlab Follow matlab instructions for your own
machine Downloads
We will eventually be downloading various matlab programs and data from the website
Matlab Basics
Math Operations Variables Vectors Functions Fancy subscripts Program files
Math Operations
Super calculator +,-,*,/,^, ()
Variables
x = 1 1+x x = 10 y = 20 x*y The importance of ; (no printing) x = 1;
Vectors
In matlab variables can be vectors Vector = list of numbers
x = [1 5 2 1 5]; 2*x x+1
Generating Vectors
: operator 1:10 1:2:10 60:-1:35 x = 1:5;
Parts of Vectors
x(2) x(10) x(b) x(10:15), x(20:end)
Vector Operations(dot operators)
x = [1 2 3]; y = [ 2 1 3]; x .* y x ./ y x .^ y
Matrices
x = [1 2 3; 4 5 6];
x = 1 2 3 4 5 6
rows = 2, columns = 3
Parts of Matrices
x = 1 2 3 4 5 6 x(row, column) x(2,1) = 4 x(2,:) = 4 5 6 x(1,1:2) = 1 2
Functions
Scalar functions: f(x) log(x), exp(x), sqrt(x) sin(x), cos(x), tan(x)
Vector functions sum(x), mean(x), median(x)
More Functions
plot(x) plot(x,'*'); Most important function!!!!
Help help functionname help plot
Even More Functions
zeros(m,n) : returns a matrix of zeros ones(m,n) : returns a matrix of ones rand(m,n) : returns a matrix of uniform
[0,1] random numbers randn(m,n) : returns a matrix of normal,
mean 0, variance 1, random numbers (Note: We will often use my own function
normal instead of randn)
Programs (mfiles)
Execute commands in a file filename.m Edit using matlab editor (colors) Examples:
Conditions
>, <, >=, <=, ==, ~=
x > 5 x < 10
If conditions
if (x>1) x = x/2; end
If/else
if (x<0) x = x+1; else x = -1*x; end
For loops
for j = [1 2 3] x(j) = j+1; end
For Loops
for j = 1:10 x(j) = 2^j; end
also x = 2.^(1:10);
For Loops
Useful for dealing with arrays Costly in terms of computer time
While Loops
x = 20; y = 0; while (x>3) y = y+sqrt(x); x = x-5; end
If’s With Vectors
if (a==b) disp(‘a equals b’) end
What if a and b are vectors? True if every element of a equals every
element of b
If’s With Vectors
if (a~=b) disp(‘a not equals b’) end
True if every element of a is not equal
Any and All
if any(a==b) disp(‘at least one equal’) end
if all(a==b) disp(‘all are equal’) end For matrices this gets more complicated
Fancy Subscripts (find function)
x = [5 2 -3 -4 1]; y = x(find(x<0));
all x values less than zero put in y k = find(x<0); k = subscripts k = [ 3 4];
Fancy Subscripts
x = [5 2 -3 -4 1]; y = x(x<0); all x values less than zero put in y k = x<0; k = [0 0 1 1 0]; y = x(k) = [-3 -4] s = sum(k) = 2
Important: Comment Lines
Lines starting with % are comments
x = 1; y = 2; z = x*y; % this really is not doing very much
Getting and Storing Results
diary filename (all results to filename) diary off (stop)
Load
load x.dat File x.dat = 1 2 3 4 5 6
Same thing in matrix x x file must be matrix
Save
save (saves everything to file matlab.mat) load (restores all settings) useful for taking a break, and starting
where you left off
Save
save filename x y z (save to filename.mat variables x, y, z)
save filename x y z -ascii (save in ascii format)
User Functions
Define your own functions Very important and powerful
Function file (positives.m)
function count = positives(x) % usage: count = positives(x) % x = vector % count = number greater than zero count = sum(x>0);
Fancy function stuff
Multiple returns
function [ count, count2] = positives(x) count = sum(x>0); count2 = sum(x>2);
Summary
We will see many more of these matlab related commands as we make use of them