Contents
Quick primer on some insightful characteristics of matlab for the course
MATlab : Matrix Laboratory can be used as a scripting language any variable is a matrix (a scalar is a special case of a multidimensional array)
credits Alessandro Giusti alessandrog@idsia.ch
Giacomo Boracchi September 23rd, 2019
close all clear clc disp('For enquiry, please send an email to giacomo.boracchi@polimi.it'); fprintf('there is also a C-like printing function\n%s %dst, %d', 'October', 1, 2018);
For enquiry, please send an email to giacomo.boracchi@polimi.it there is also a C-like printing function October 1st, 2018
variables
% variables are created by assignements v = 3 c = 'k' size(v) % use ; at the end of instruction not to display results % in command line v = 7; % data types are automatically defined depending on the % assigned value whos v % variables have datatypes (usually you can forget, % but not when dealing with images). Most common types we % will consider are: % . double,(i.e. double-precision floating point), % . uint8 (i.e. unsigned integers with 8 bits, [0 255] range), % . logical (i.e. boolean) % % casting to 8-bit integers v = uint8(v) whos v
v =
3
c =
'k'
ans =
1 1
Name Size Bytes Class Attributes
v 1x1 8 double
v =
uint8
7
Name Size Bytes Class Attributes
v 1x1 1 uint8
Arrays
a row vector (commas can be omitted)
r=[1, 2, 3, 4] size(r) % a column vector c=[1; 2; 3; 4] size(c) % you can define vectors by regular increment operator % [start : step : end] a = [1 : 2 : 10]; % when omitted, step is equal to 1 a = [1 : 10]; % a matrix v=[1 2; 3 4] size(v)
r =
1 2 3 4
ans =
1 4
c =
1
2
3
4
ans =
4 1
v =
1 2
3 4
ans =
2 2
Array concatenation
you can concatenate matrices or vectors as far as their sizes are consistent
B=[v', v'] C = [v ; v] % this is not allowed disp('K = [r,c]: this is not allowed') %K = [r,c]
B =
1 3 1 3
2 4 2 4
C =
1 2
3 4
1 2
3 4
K = [r,c]: this is not allowed
other examples of array concatenation
dim returns the dimension of the data, visible also typing whos
dim = size(C)
% other examples of array concatenation
my_vec1 = [1 2 3];
my_vec2 = 4:6;
my_matrix = [my_vec1; my_vec2]
size(my_matrix)
my_long_vector = [my_vec1 my_vec2]
size(my_long_vector)
my_matrix = cat(1,my_vec1,my_vec2)
my_long_vector = cat(2,my_vec1,my_vec2)
my_3d_matrix = cat(3,my_vec1,my_vec2)
size(my_3d_matrix)
dim =
4 2
my_matrix =
1 2 3
4 5 6
ans =
2 3
my_long_vector =
1 2 3 4 5 6
ans =
1 6
my_matrix =
1 2 3
4 5 6
my_long_vector =
1 2 3 4 5 6
my_3d_matrix(:,:,1) =
1 2 3
my_3d_matrix(:,:,2) =
4 5 6
ans =
1 3 2
indexing (starts from 1)
my_vec = (1:10)';
my_vec(1)
my_matrix = [1:4;5:8;9:12];
my_matrix(3,2)
% coumn-wise linear indexing for matrices
my_matrix(6)
ans =
1
ans =
10
ans =
10
subarray
v(indexes) returns a vector of all the elements of v at locations in array indexes
% you can reference single or multiple values in an array: v(1,2) % first row and second column (row and column indices are 1-based) v(:,2) % the second column of v v(1,:) % the first row B(:,2:4) % some of the columns v(5,5) = 10 % you can extend vectors / matrices by assigning some element our of the range my_matrix(1:3,3:4) my_matrix(1:3,[2 4]) my_matrix(1:end,[2 4]) my_matrix(:,[2 4]) my_matrix(1:2,[2 4]) my_matrix(1:end-1,[2 4]) my_vector = my_matrix(:)
ans =
2
ans =
2
4
ans =
1 2
ans =
3 1 3
4 2 4
v =
1 2 0 0 0
3 4 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 10
ans =
3 4
7 8
11 12
ans =
2 4
6 8
10 12
ans =
2 4
6 8
10 12
ans =
2 4
6 8
10 12
ans =
2 4
6 8
ans =
2 4
6 8
my_vector =
1
5
9
2
6
10
3
7
11
4
8
12
operation on vectors are from linear algebra
common operations work on matrices (careful about multiplication and division)
v*v'
ans =
5 11 0 0 0
11 25 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 100
there are also element-wise operators
[1 2 3].*[4 5 6] [1 2 3] + 5 [1 2 3] * 2 % no need to use element-wise operator with scalars [1 2 3] .* 2 %explicit element-wise multiplication [1 2 3] / 2 [1 2 3] ./ 2 %explicit element-wise division [1 2 3] .^ 2 %explicit element-wise power [1 2 3] * [4 5 6]' % this matrix product, returns a scalar (it is the inner product) [1 2 3]' * [4 5 6] % this is the matrix product, returns a 3 x 3 matrix % rounding functions ceil(10.56) floor(10.56) round(10.56) ceil(0:0.1:1) % arithmetic functions sum([1 2 3 4]) sum([1:4;5:8]) sum([1:4;5:8],2) sum(sum([1:4;5:8])) my_matrix = [1:4;5:8]; sum(my_matrix(:))
ans =
4 10 18
ans =
6 7 8
ans =
2 4 6
ans =
2 4 6
ans =
0.5000 1.0000 1.5000
ans =
0.5000 1.0000 1.5000
ans =
1 4 9
ans =
32
ans =
4 5 6
8 10 12
12 15 18
ans =
11
ans =
10
ans =
11
ans =
0 1 1 1 1 1 1 1 1 1 1
ans =
10
ans =
6 8 10 12
ans =
10
26
ans =
36
ans =
36
Printing
disp('Hello World!'); disp(['Hello ', 'World!']); % string concatenation in printf. disp(['number of columns in the matrix: ', num2str(size(my_matrix))]); fprintf('number of columns in the matrix: %f\n',size(my_matrix,2));
Hello World! Hello World! number of columns in the matrix: 2 4 number of columns in the matrix: 4.000000
logicals
you can compare a vector via the customary relational operators and obtain a vector of logicals (i.e. b)
b=v>2
whos b
b = 5×5 logical array 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Name Size Bytes Class Attributes b 5x5 25 logical