Tutorial matlab

1
Introduction to Matlab
Introduction to Matlab
1. Vectors, matrices, and arithmetic
2. Plotting
3. Flow Constructs
4. Other Useful Things

2
Why use Matlab?
• Drawbacks:
Slow compared to C or Java
• Advantages:
Handles vector and matrices very nicely
Quick plotting and analysis
EXTENSIVE documentation (type ‘help’)
Lots of nice functions: FFT, fuzzy logic, neural
nets, numerical integration, OpenGL (!?)
Vectors and Matrices
• Can be run from command line or from *.m file
scalar: x = 3
vector: x = [1 0 0]
2D matrix: x = [1 0 0; 0 1 0; 0 0 1]
arbitrarily higher dimensions possible
• Can also use matrices / vectors as elements:
x = [1 2 3]
y = [ x 4 5 6]

3
Some Standard matrices
• ones(3,3) 3x3 of all ones
• zeros(3,3) 3x3 of all zeros
• eye(3,3) 3x3 identity
• rand(3) 3x3 random elements
• linspace(1,10,100)
linear spacing from 1 to 10, with 100
spacings (also logspace)
• x = 1:10
linear spacing from 1 to 10, counting by 1
Accessing elements
• MATLAB IS NOT ZERO INDEXED!
• x retrieves entire matrix x
• x(1,2) retrieves element at row 1, col 2
• x(1, 5:10) retrieves row 1, columns 5 to 10
• x(1,:) retrieves row 1, all columns
• Useful functions:
length(x) length of vector x (cols)
size(x) rows, cols of x

4
Matrix Operations
• For matrix operations
– Dimensions must agree
• Scalar operations
– Same as usual
• Scalar / matrix mixed
– Scalar + matrix = [scalar + matrix(x, y)]
– Scalar * matrix = [scalar * matrix(x, y)]
More Matrix Operations
• The ‘.’ operator
– “element by element” access
• Example:
– x = [1 2 3]; y = [4; 5; 6];
– x * y = 32
– x .* y = [4 10 18]
• For some functions :
– x ^ 2 ERROR!
– x . ^2 fine

5
More Matrix Operations
• x=1:12
• reshape(x, 3,4)
• a=2*ones(3,4)
• X.*a
• b=[1:3;1:3;1:3;1:3]
• X.*b
• y=reshape(x, 4,3)
• y.^b
Plotting
• 2D graphing
plot(x,y)
• Example:
x = linspace(-10,10,100)
y = x .^2
plot(x,y)
• Also:
z = x .^3
plot(x,z)

6
Plotting Example
basis = [
[1 0];
[0 0];
[0 1];
]';
square = [
[ 1 1]
[-1 1];
[-1 -1];
[ 1 -1];
[ 1 1];
]';
axis equal;
plot( sqrt(3), sqrt(3), 'w.');
plot( -sqrt(3), -sqrt(3), 'w.');
plot( basis(1,:), basis(2,:), 'k');
plot( square(1,:), square(2,:), 'b');pause
obj = S*square;
plot( obj(1,:), obj(2,:), 'r');pause
Plotting Examplebasis = [
[1 0];
[0 0];
[0 1];
[1 0];
]';
square = [
[ 1 1];
[-1 1];
[-1 -1];
[ 1 -1];
[ 1 1];

7
More Plotting
• Graphics Window
– To open a new graph, type ‘figure’
• Multiple data sets:
– Type ‘hold on’ to add new plot to current graph
– Type ‘hold off’ to resume default mode
• Make your graph beautiful:
– title(‘apples over oranges’)
– xtitle(‘apples’)
– ytitle(‘oranges’)
3D Plotting
• 3D plots – plot an outer product
x = 1:10
y = 1:10
z = x’ * y
mesh(x,y,z)
Single quote ‘ means transpose

8
Flow Control
• IF block
if (<condition>)
<body>
elseif
<body>
end
• WHILE block
while (<condition>)
<body>
end
Conditions same as C, ( ==, >=, <=) except != is ~=
More Flow Control
• FOR block
for i = 1:10
<body>
end
• SWITCH statement
switch <expression>
case <condition>,
<statement>
otherwise <condition>,
<statement>
end

9
Other Language Features
• Matlab language is pretty sophisticated
– Functions
Stored in a *.m file of the same name:
function <return variable> = <function name>(<args>)
<function body>
– Structs
• point.x = 2; point.y = 3; point.z = 4;
Useful Commands
• Single quote is transpose
• % same as // comment in C, Java
No /* block comments */
• ; suppresses printing
• More:
max(x) min(x)
mean(x) median(x)
abs(x) dot(x,y)
cross(x,y) flops (flops in this session)

10
Useful Constants
• Inf infinity
• NaN Not a number (div by zero)
• eps machine epsilon (precision)
• ans most recent unassigned answer
• pi 3.14159….
• i and j Matlab supports imaginary
numbers!
Programming
• Wrong:
for x = 1:10
for y = 1:10
foo(x,y) = 2 * bar(x,y)
end
end
• Right:
foo = 2 * bar;
• Matlab is optimized for vectorization

11
Symbolic Maths
• Symbolic mathematics can be done using Matalb:
a = sqrt(sym(2))
a =
2^(1/2)
th=sym('th');
rt=sym([cos(th) sin(th) 0;-sin(th) cos(th) 0;0 0 1]);
rt =
[ cos(th), sin(th), 0]
[ -sin(th), cos(th), 0]
[ 0, 0, 1]
Good luck

Tutorial matlab

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