MATLAB Syntax Guide

MATLAB = MATrix LABoratory. Originally built for linear algebra with matrices, now covers data analysis, signal processing, optimisation, and 2-D/3-D graphics.

Variables

• Variable names are case sensitive
• Up to 63 characters (MATLAB 6.5+)
• Must start with a letter, then letters / digits / underscores

>> x = 2;
>> abc_123 = 0.005;
>> 1ab = 2;          % Error: Unexpected MATLAB expression

Special variables

Name	Meaning
pi	value of π
eps	smallest incremental number
inf	infinity
NaN	not a number (e.g. 0/0)
i, j	square root of −1
realmin	smallest usable positive real
realmax	largest usable positive real

Operators

Relational

Operator	Meaning
<	less than
<=	less than or equal
>	greater than
>=	greater than or equal
==	equal to
~=	not equal to (not != like in C)

Logical

Operator	Meaning	Precedence
~	not	highest
&	and	equal precedence with |
|	or	equal precedence with &

Matrices

MATLAB treats all variables as matrices:

• Vectors — only one row OR one column
• Scalars — one row AND one column
  Indices start from 1 (unlike C). A(2,4) is row 2, column 4; A(17) is linear (column-wise) indexing.

Generating matrices

>> x = 23;                  % scalar
 
>> y = [12,10,-3]           % row vector (commas)
y =
    12   10   -3
 
>> z = [12;10;-3]           % column vector (semicolons)
z =
    12
    10
    -3
 
>> X = [1,2,3;4,5,6;7,8,9]  % matrix: commas = columns, semicolons = rows
X =
     1    2    3
     4    5    6
     7    8    9

Row vectors and column vectors are treated very differently. Matrices must be rectangular.

Extracting a sub-matrix

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

where r1/r2 are the beginning/ending rows and c1/c2 the beginning/ending columns.

>> 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

Extension, tiling, concatenation

% assigning out of bounds auto-extends (pads with zeros)
>> a = [1,2i,0.56];
>> a(2,4) = 0.1
a =
     1   0+2i   0.56    0
     0    0      0     0.1
 
% repmat - replicates and tiles a matrix
>> b = [1,2;3,4];
>> b_rep = repmat(b,1,2)
b_rep =
     1   2   1   2
     3   4   3   4
 
% concatenation (result must still be rectangular)
>> a = [1,2;3,4];
>> a_cat = [a,2*a; 3*a,2*a]
a_cat =
     1    2    2    4
     3    4    6    8
     3    6    2    4
     9   12    6    8

Arithmetic

>> x = [1,2;3,4];
 
% scalar addition increments every element
>> y = x + 5
y =
     6   7
     8   9
 
% matrix addition - dimensions must agree
>> xsy = x + y
xsy =
      7    9
     11   13
 
>> x + [1,0.3]
??? Error using => plus
Matrix dimensions must agree

% matrix multiplication - inner dimensions must agree
>> 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 operations use a dot prefix:

>> a = [1,2;1,3];
>> b = [2,2;2,1];
 
>> a./b        % element-wise division
     0.5   1
     0.5   3
 
>> a.*b        % element-wise multiplication
     2    4
     2    3
 
>> a.^2        % element-wise power
     1   4
     1   9
 
>> a.^b
     1   4
     1   3

Matrix manipulation functions

Function	Purpose
zeros	array of all zeros — x = zeros(3,2)
ones	array of all ones — x = ones(2)
eye	identity matrix — x = eye(3)
rand	uniform random numbers in [0,1]
diag	diagonal matrices / diagonal of a matrix
size	array dimensions
length	length of a vector (row or column)
det	matrix determinant
inv	matrix inverse
eig	eigenvalues and eigenvectors
rank	rank of a matrix
find	searches for given values in an array/matrix

Built-in math functions

Elementary:

Function	Purpose
abs	absolute value of all elements
sign	signum function
sin, cos, …	trigonometric functions
asin, acos, …	inverse trigonometric functions
exp	exponential
log, log10	natural log, log base 10
ceil, floor	round towards +inf / −inf
round	round to nearest integer
real, imag	real and imaginary parts of a complex matrix
sort	sort elements in ascending order

Aggregation:

Function	Purpose
sum, prod	summation and product of elements
max, min	maximum and minimum of arrays
mean, median	average and median
std, var	standard deviation and variance

Graphics

2-D plotting

Plot sin(x) and cos(x) over [0,2π] on the same axes, in different colours.

% Method 1 - hold on / hold off
>> 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 - multiple series in one plot call
>> 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;

Piecewise functions

For y = t on 0 ≤ t ≤ 1 and y = 1/t on 1 < t ≤ 6:

% Method 1 - build each piece separately and concatenate
>> 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 - logical indexing
>> 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

subplot(rows, columns, index)
 
>> subplot(4,1,1)
>> ...
>> subplot(4,1,2)
>> ...
>> subplot(4,1,3)
>> ...
>> subplot(4,1,4)

Importing / exporting data

load and save

load filename        % loads all variables from "filename"
load filename x      % loads only the variable x
load filename a*     % loads all variables starting with 'a'
 
save filename        % saves all workspace variables to filename.mat (binary)
save filename x,y    % saves only x and y
 
% help load / help save for more

Excel

>> x = xlsread(filename);
 
% if the file contains numeric values, text and raw data values
>> [numeric,txt,raw] = xlsread(filename);
 
% write A into the region A2:C4 of data.xls
>> x = xlswrite('c:\matlab\work\data.xls', A, 'A2:C4');
% x = 1 on success, 0 on failure

Text files

% writing
>> fid = fopen('filename.txt','w');
>> count = fwrite(fid,x);     % count = number of values stored
>> fclose(fid);               % don't forget to close
 
% reading
>> fid = fopen('filename.txt','r');
>> X = fscanf(fid,'%5d');
>> fclose(fid);

Other useful commands: fread, fprintf.

Flow control

Five flow control statements: if, switch, for, while, break.

if

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

switch switch_expr
    case case_expr1
        ...
    case case_expr2
        ...
    otherwise
        ...
end

>> 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

Unlike C, MATLAB does not need break in each case.

for

for variable = expression
    ...
end

% Example 1
>> for x = 0:0.05:1
>>     printf('%d\n',x);
>> end
 
% Example 2 - nested
>> a = zeros(n,m);
>> for i = 1:n
>>   for j = 1:m
>>     a(i,j) = 1/(i+j);
>>   end
>> end

while

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

In MATLAB 1 is synonymous with TRUE and 0 with FALSE.

break

Terminates execution of for and while loops. In nested loops it terminates the innermost loop only.

>> y = 3;
>> for x = 1:10
>>     printf('%5d',x);
>>     if (x>y)
>>         break;
>>     end
>> end
1     2     3     4

Efficient programming

• Avoid nested loops as far as possible — in most cases they can be replaced with matrix manipulation
• Preallocate arrays when possible
• Use MATLAB’s huge library of built-in functions; they are more likely to be efficient than your own

Example 1 — non-causal FIR filter

Given input x and filter coefficients h as column vectors, compute y[n] = Σ(k=0..19) h[k]·x[n+k] for n = 1,2,3.

% Method 1 - two loops
>> 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 the inner loop (inner product)
>> y = zeros(1,3);
>> for n = 1:3
>>     y(n) = h'*x(n:(n+19));
>> end
 
% Method 3 - avoids both loops (matrix multiply)
>> X = [x(1:20), x(2:21), x(3:22)];
>> y = h'*X;

Example 2 — cumulative products of cubes

Compute y(n) = 1³ · (1³+2³) · (1³+2³+3³) · … · (1³+2³+…+n³) for n = 1..20.

% Method 1 - two loops
>> 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 the 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 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);

Getting help

At the MATLAB prompt: help, lookfor, helpwin, helpdesk, demos

On the web:

• http://www.mathworks.com/support
• http://www.mathworks.com/products/demos/#