• MATLAB is a software package for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It's name is derived from MATrix LABoratory.
• MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation
• Variable names are case sensitive
• Variable names can contain up to 63 characters ( as of MATLAB 6.5 and newer).
• Variable names must start with a letter and can be followed by letters, digits and underscores.
Examples:
>> x = 2;
>> abc_123 = 0.005;
>> 1ab = 2;

MATLAB Special Variables
• pi Value of $$\pi$$
• eps Smallest incremental number
• inf Infinity
• NaN Not a number e.g. 0/0
• i and j i and j can be square root of -1
• realmin The smallest usable positive real number
• realmax The largest usable positive real number
• Less Than <
• Less Than or Equal <=
• Greater Than >
• Greater Than or Equal >=
• Equal To ==
• Not Equal To ~= (NOT != like in C)

MATLAB supports three logical operators.

• not ~ % highest precedence
• and & % equal precedence with or
• or | % equal precedence with and
• MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored.
• Vectors are special forms of matrices and contain only one row OR one column.
• Scalars are matrices with only one row AND one column
• A scalar can be created in MATLAB as follows:
>> x = 23;

• A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):
>> y = [12,10,-3]
y =
12 10 -3

• A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows:
>> z = [12;10;-3]
z =
12
10
-3

Generating Matrices
• MATLAB treats row vector and column vector very differently
• A matrix can be created in MATLAB as follows (note the commas and semicolons)
>> X = [1,2,3;4,5,6;7,8,9]
X =
1 2 3
4 5 6
7 8 9

Matrices must be rectangular!

A portion of a matrix can be extracted and stored in a smaller
matrix by specifying the names of both matrices and the rows
and columns to extract. The syntax is:

sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;


where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix.

*Example

>> X = [1,2,3;4,5,6;7,8,9]
X =
1 2 3
4 5 6
7 8 9
>> X22 = X(1:2 , 2:3)
X22 =
2 3
5 6
>> X13 = X(3,1:3)
X13 =
7 8 9
>> X21 = X(1:2,1)
X21 =
1
4

• Increment all the elements of
a matrix by a single value
>> x = [1,2;3,4]
x =
1 2
3 4
>> y = x + 5
y =
6 7
8 9


>> xsy = x + y
xsy =
7 9
11 13
>> z = [1,0.3]
z =
1 0.3
>> xsz = x + z
??? Error using => plus  Matrix dimensions must agree


*Matrix multiplication

>> a = [1,2;3,4]; (2x2)
>> b = [1,1]; (1x2)
>> c = b*a
c =
4 6
>> c = a*b
??? Error using ==> mtimes Inner matrix dimensions must agree.


*Element wise multiplication

>> a = [1,2;3,4];
>> b = [1,½;1/3,¼];
>> c = a.*b
c =
1 1
1 1

>> a = [1,2;1,3];
>> b = [2,2;2,1];


Element wise division

>> c = a./b
c =
0.5 1
0.5 3


Element wise multiplication

>> c = a.*b
c =
2 4
2 3


Element wise power operation

>> c = a.^2
c =
1 4
1 9
>> c = a.^b
c =
1 4
1 3

• zeros : creates an array of all zeros, Ex: x = zeros(3,2)
• ones : creates an array of all ones, Ex: x = ones(2)
• eye : creates an identity matrix, Ex: x = eye(3)
• rand : generates uniformly distributed random numbers in [0,1]
• diag : Diagonal matrices and diagonal of a matrix
• size : returns array dimensions
• length : returns length of a vector (row or column)
• det : Matrix determinant
• inv : matrix inverse
• eig : evaluates eigenvalues and eigenvectors
• rank : rank of a matrix
• find : searches for the given values in an array/matrix.
• abs - finds absolute value of all elements in the matrix
• sign - signum function
• sin,cos,... - Trignometric functions
• asin,acos... - Inverse trignometric functions
• exp - Exponential
• log,log10 - natural logarithm, logarithm (base 10)
• ceil,floor - round towards +infinity, -infinity respectively
• round - round towards nearest integer
• real,imag - real and imaginary part of a complex matrix
• sort - sort elements in ascending order
• sum,prod - summation and product of elements
• max,min - maximum and minimum of arrays
• mean,median – average and median of arrays
• std,var - Standard deviation and variance
and many more...

2D Plotting

• Example 1: Plot sin(x) and cos(x) over [0,2π], on the same plot with different colours.
• Method 1:
>> x = linspace(0,2*pi,1000);
>> y = sin(x);
>> z = cos(x);
>> hold on;
>> plot(x,y,‘b');
>> plot(x,z,‘g');
>> xlabel ‘X values';
>> ylabel ‘Y values';
>> title ‘Sample Plot';
>> legend (‘Y data',‘Z data');
>> hold off;

• Method 2:
>> x = 0:0.01:2*pi;
>> y = sin(x);
>> z = cos(x);
>> figure
>> plot (x,y,x,z);
>> xlabel ‘X values';
>> ylabel ‘Y values';
>> title ‘Sample Plot';
>> legend (‘Y data',‘Z data');
>> grid on;

• Example 2: Plot the following function
$$y=\left{\begin{array}{ll}{t} & {0 \leq t \leq 1} \ {1 / t} & {1 \leq t \leq 6}\end{array}\right.$$

Method 1:

>> t1 = linspace(0,1,1000);
>> t2 = linspace(1,6,1000);
>> y1 = t1;
>> y2 = 1./ t2;
>> t = [t1,t2];
>> y = [y1,y2];
>> figure
>> plot(t,y);
>> xlabel ‘t values', ylabel ‘y values';


Method 2:

>> t = linspace(0,6,1000);
>> y = zeros(1,1000);
>> y(t()<=1) = t(t()<=1);
>> y(t()>1) = 1./ t(t()>1);
>> figure
>> plot(t,y);
>> xlabel‘t values';
>> ylabel‘y values';


Subplots

• Syntax: subplot (rows, columns, index)
load filename x - loads only the variable x from the file
save filename - saves all workspace variables to a binary
.mat file named filename.mat
save filename x,y - saves variables x and y in filename.mat
• Import/Export from Excel sheet
Copy data from an excel sheet
>> x = xlsread(filename);

% if the file contains numeric values, text and raw data values, then
>> [numeric,txt,raw] = xlsread(filename);

• Copy data to an excel sheet
>>x = xlswrite('c:\matlab\work\data.xls',A,'A2:C4')

% will write A to the workbook file, data.xls, and attempt to fit the
elements of A into the rectangular worksheet region, A2:C4. On
success, ‘x' will contain ‘1', while on failure, ‘x' will contain ‘0'.

• Writing onto a text file
>> fid = fopen(‘filename.txt',‘w');
>> count = fwrite(fid,x);
>> fclose(fid);

% creates a file named ‘filename.txt' in your workspace and stores
the values of variable ‘x' in the file. ‘count' returns the number of
values successfully stored. Do not forget to close the file at the end.
• Read from a text file
>> fid = fopen(‘filename.txt',‘r');
>> X = fscanf(fid,‘%5d');
>> fclose(fid);

% opens the file ‘filename.txt' which is in your workspace and loads
the values in the format ‘%5d' into the variable

MATLAB has five flow control statements

• if statements
• switch statements
• for loops
• while loops
• break statements

‘if' statement

• The general form of the ‘if' statement is
>> if expression
>> ...
>> elseif expression
>> ...
>> else
>> ...
>> end

• Example 1:
>> if i == j
>> a(i,j) = 2;
>> elseif i >= j
>> a(i,j) = 1;
>> else
>> a(i,j) = 0;
>> end

• Example 2:
>> if (attn>0.9)&(grade>60)
>> pass = 1;
>> end


‘switch' statement

switch Switch among several cases based on expression

• The general form of the switch statement is:
>> switch switch_expr
>> case case_expr1
>> ...
>> case case_expr2
>> ...
>> otherwise
>> ...
>> end

• Example :
>> x = 2, y = 3;
>> switch x
>> case x==y
>> disp('x and y are equal');
>> case x>y
>> disp('x is greater than y');
>> otherwise
>> disp('x is less than y');
>> end

x is less than y Note: Unlike C, MATLAB doesn't need BREAKs in each case

‘for' loop

• for Repeat statements a
specific number of times
• The general form of a for
statement is
>> for variable=expression
>> ...
>> ...
>> end

• Example 1:
>> for x = 0:0.05:1
>> printf(‘%d\n',x);
>> end

• Example 2:
>> a = zeros(n,m);
>> for i = 1:n
>> for j = 1:m
>> a(i,j) = 1/(i+j);
>> end
>> end


‘while' loop

• while Repeat statements an
indefinite number of times
• The general form of a while
statement is
>> while expression
>> ...
>> ...
>> end

• Example 1:
>> n = 1;
>> y = zeros(1,10);
>> while n <= 10
>> y(n) = 2*n/(n+1);
>> n = n+1;
>> end

• Example 2:
>> x = 1;
>> while x
>> %execute statements
>> end

Note: In MATLAB ‘1' is synonymous to TRUE and ‘0' is synonymous to ‘FALSE'

‘break' statement

• break terminates the execution of for and while loops
• In nested loops, break terminates from the innermost loop only
• Example:
> y = 3;
>> for x = 1:10
>> printf(‘%5d',x);
>> if (x>y)
>> break;
>> end
>> end
1 2 3 4

• Avoid using nested loops as far as possible
• In most cases, one can replace nested loops with efficient matrix
manipulation.
• Preallocate your arrays when possible
• MATLAB comes with a huge library of in-built functions, use them
when necessary
• Avoid using your own functions, MATLAB's functions are more likely
to be efficient than yours.

Example 1

• Let x[n] be the input to a non causal FIR filter, with filter
coefficients h[n]. Assume both the input values and the filter
coefficients are stored in column vectors x,h and are given to
you. Compute the output values y[n] for n = 1,2,3 where
$$y[n]=\sum_{k=0}^{19} h[k] x[n+k]$$
• Solution
• Method 1:
>> y = zeros(1,3);
>> for n = 1:3
>> for k = 0:19
>> y(n)= y(n)+h(k)*x(n+k);
>> end
>> end

• Method 2 (avoids inner loop):
>> y = zeros(1,3);
>> for n = 1:3
>> y(n) = h'*x(n:(n+19));
>> end

• Method 3 (avoids both the loops):
>> X= [x(1:20),x(2:21),x(3:22)];
>> y = h'*X;


Example 2

• Compute the value of the following function
$$y(n)=1^{3 }\left(1^{3}+2^{3}\right)^{}\left(1^{3}+2^{3}+3^{3}\right)^{} \ldots^{}\left(1^{3}+2^{3}+\ldots+n^{3}\right)$$ for n = 1 to 20

Solution

• Method 1:
>> y = zeros(20,1);
>> y(1) = 1;
>> for n = 2:20
>> for m = 1:n
>> temp = temp + m^3;
>> end
>> y(n) = y(n-1)*temp;
>> temp = 0
>> end

• Method 2 (avoids inner loop):
>> y = zeros(20,1);
>> y(1) = 1;
>> for n = 2:20
>> temp = 1:n;
>> y(n) = y(n-1)*sum(temp.^3);
>> end

• Method 3 (avoids both the loops):
>> X = tril(ones(20)*diag(1:20));
>> x = sum(X.^3,2);
>> Y = tril(ones(20)*diag(x))+ ...
triu(ones(20)) – eye(20);
>> y = prod(Y,2);


Where to get help?