This page covers the use of variables in Matlab, the basic (built-in) datatypes, together with some information on how they can be used, how they can be converted, and how they relate to one another. The last part covers the different indexing syntax mechanisms and some pitfalls.

A variable can be thought of as a storage container that has the following properties:

• links a name (identifier) to a value (or list of values)
• is available in a workspace, i.e. when a function is called, variables available in the calling workspace are hidden (different function code files can use the same variable names without conflict), unless they are global variables
• can be assigned a (new) value (or list of values) using the = sign (assignment operator)
• has a specific datatype, which can change during the course of a program (or command line session)
  • changing datatypes is considered bad coding practice and should be avoided:

    % define x as a number
    x = 1;
     
    % re-define x as a string: no error!
    x = 'string';

• is of arbitrary size (which means it can also be empty), which can also change (older versions would allow up to 63 dimensions, but this limit no longer exists)
  • that means that a variable containing a single number is of the same type as a variable containing several numbers (of the same type)
• does not require declaration (like in C/C++) but can be created at any time (on the command line or at any point in a program, i.e. M-file)
  • this unfortunately makes it sometimes difficult to find out what an identifier stands for (function or variable? what datatype and content?)
• stores this value until it is reassigned a new value or the variable is “clear-ed” from the workspace
• allows indexing operations to access sub-parts of a list of values (both reading from and writing into parts of variables)
  • to read-access a sub-portion of an array, the index expression has to be provided within parentheses on the right-hand side (e.g. part = fullarray(portion);)
  • on the left-hand side, a part of an array can be replaced with new data (e.g. fullarray(portion) = newvalues;)
  • in that case, newvalues must either be a single number (all indices addressed by portion will be set to the same number) or must match in size
  • if the variable is smaller than indicated by the index expression, Matlab will attempt to grow the variable accordingly:

    % define a 2x3 array
    a = [10, 20, 30; 40, 50, 60];
     
    % assign the value 100 to the second through 4th row and the 3rd through 4th column
    a(2:4, 3:4) = 100;
     
    % a is now a 4x4 array!

• can be used in expressions (e.g. in computations, function calls, to index another variable, or to form new, compound variables)
• is available for storing the data contained therein to a file on disk and can be loaded from disk as well

Please note that at the end of a function (including when the keyword return is reached while executing a function) all variables that are not “returned” or marked as persistent are cleared from the workspace and memory.

There are a few rules applying to identifiers:

• a valid identifier must contain only letters (lower and upper case), numbers, and underscores, but no symbols or blanks
• it must begin with a letter
  • some valid variable names with assignments:

    v = 1;
    VAR12 = 12;
    A_Really_Long_Name = 'long name';

• keywords can not be used as identifier names, which excludes the following words from being identifier/variable names: break, case, catch, classdef, continue, else, elseif, end, for, function, global, if, otherwise, parfor, persistent, return, spmd, switch, try, while
• if a variable is given the same name as an existing function, the identifier then only refers to the variable in this workspace (see also precedence rules):

  % defining a new array
  newarray = [1, 2, 3, 4];
   
  % computing the sum
  sumarray = sum(newarray);
   
  % redefining sum
  sum = 5;
   
  % then this leads to an error...
  notthesum = sum(newarray); % index exceeds dimensions!!

Datatypes can be, generally, divided into 5 major groups:

• numeric datatypes (incl. a logical datatype for true/false values)
• text (character/string) datatype
• compound datatypes (to store values of different types in one variable)
• function handles
• user-defined datatypes/objects

By default, a variable in Matlab that is storing a numeric value (or a list/array of numbers) has the datatype “double”. So, in a simple assignment of a number (or array) to a variable (such as a = 1; or b = [2, 3, 4];), the datatype would be double, regardless of whether the number is integer or not! While this requires more memory (for large arrays of numbers), at least the user (or code writer) doesn't have to worry about datatype conversions, etc. Unless you have very specific needs (e.g. lower memory usage or increased speed for specific operations), it is recommended to use the default datatype.

Numeric variables are defined by simply assigning the output of a function that returns a number to a variable or by setting the value(s) manually.

Here is a list of all “numeric” datatypes:

• double (default type for all numbers, supports decimal numbers/fractions): each value being stored requires 8 byte (= 64 bits) of memory, 1 bit for the sign, 11 bits for the exponent, and 52 bits for a base-2 fraction (see Double precision floating point format at wikipedia). Special “configurations” are used to store the values Inf, -Inf, and NaN.
• single: each value being stored requires 4 byte (= 32 bits) of memory; in short, the datatype has similar properties compared to double, just less “precision” (and exponent range)
• int64: a 64-bit (8-byte) integer datatype (signed); lowest value is -2^63, highest value is 2^63 - 1
• uint64: a 64-bit (8-byte) integer datatype (unsigned); lowest value 0, highest value is 2^64 - 1
• int32: a 32-bit (4-byte) integer datatype (signed); lowest value is -2^31, highest value is 2^31 - 1
• uint32: a 32-bit (4-byte) integer datatype (unsigned); lowest value is 0, highest value is 2^32 - 1
• int16: a 16-bit (2-byte) integer datatype (signed); lowest value is -32768, highest value is 32767
• uint16: a 16-bit (2-byte) integer datatype (unsigned); lowest value is 0, highest value is 65535
• int8: an 8-bit (1-byte) integer datatype (signed); lowest value is -128, highest value is 127
• uint8: an 8-bit (1-byte) integer datatype (signed); lowest value is -128, highest value is 127

A special case is the logical datatype. It can only store two values: false or true. If converted to any of the other numeric datatypes, false is converted to 0 and true is converted to 1.

Please note that instead of being keywords (such as in C/C++), datatypes are not “reserved” words, but obviously the names of datatypes should not be used as variable identifiers. The reason is that those names are also the names of the functions used to convert the numeric datatypes into one another! For instance the code snippet

dvar = [7, -10, 13]; ivar = int32(dvar);

converts the double variable dvar (default numeric datatype!) into a variable of type int32. If the target datatype cannot hold the value(s), for instance because the value range is too small, the value will be truncated (in precision and range) to fit the new datatype.

Given that Matlab variables can be arrays of arbitrary size, single characters, as well as “strings” (a series of characters, such as in a word or sentence) and also lists of strings (two-dimensional field of characters) all are stored with the same basic datatype: char.

Here are some examples defining variables of type char:

letter = 'x';
start = 'The letter is';
sentence = [start, ' ', letter, '.'];

The resulting variable then contains the string “The letter is x.”.

Importantly, the underlying storage is yet a numeric datatype:

% the difference between to characters
'd' - 'a'
 
% is their distance in the alphabet, in this case 3!

And that also means that a variable can be converted from char to double (or any other compatible numeric datatype) and back. This can be useful to store large quantities of text and also to perform arithmetic operations on characters (for instance to test if all elements of a string are letters).

In many situations it is necessary to store data of different types (e.g. a name/string together with a number, such as age) in a “dataset”, which still should be accessible via a single variable. For this purpose, Matlab provides built-in compound datatypes.

These compound datatypes are further sub-divided into two types: one where elements are (mainly) addressed by a numeric (or equivalent) indices, and one where elements are accessed by a field name in a tree-like structure (same rules as identifiers, but also keywords can be used as field names, given the syntax).

The cell datatype allows to access individual elements (as well as groups of elements), called “cells”, with numeric indexing. This is mostly useful for storing tabular data (or data where several “columns” should be accessible at once), and numeric only data is too limited (e.g. in cases where text elements cannot be reasonably matched to numeric values a priori).

To define a cell array as well as to address the content of a cell, Matlab uses the “curly braces” symbols: { and }:

% define a 1x2 cell array with a name and an age
name_and_age = {'John Doe', 41};
 
% to access just the name we index the first cell with {1}
name = name_and_age{1};
 
% and for the age the second cell
age = name_and_age{2};

Please be aware that a cell array can, naturally, also be indexed with the parentheses syntax. However, in that case the returned value will be of type cell. In fact, every index expression on a variable of a built-in datatype using the parentheses syntax always returns a value (or values) of the same datatype!

Put differently, if you imagine a shelf with 5 jars on it. The entire shelf then represents a cell array (by the name of shelf). The expression shelf(3) will then return the third jar of the shelf. On the other hand, the expression shelf{3} returns the content of the third jar!

Also, please note that if you use a variable (numeric, char, or compound!) when creating a new compound variable or setting one or several elements of a compound variable, the values in the compound variable will be copies of the content of the original variable (or rather, if the variable is altered, a copy is created). For instance:

% assign a value to variables n and s
n = [12, 14, 10];
s = 'size';
 
% store variables in compound variable
c = {s, n};
 
% re-assign index 2 of n variable
n(2) = 18;
 
% and then c still contains [12, 14, 10] in its second cell element!

The other compound datatype in Matlab is the struct type. This allows to store multiple values of different types accessible via names.

Syntax-wise, the variable name (of the compound variable) is followed by a period (dot character, .) and a field name. If the field name itself is stored in a (char) variable, the syntax is struct_variable.(field_name).

The obvious advantage is that code usually becomes less cryptic, given that instead of using syntax such as compound_var{3} = some_function(some_value); you would write compound_var.property = some_function(some_value); whereas property can be a more meaningful term (such as name or duration) instead of using a numeric index (as with the cell syntax).

Please note that variables of type struct still can be of arbitrary size! This means that a list of structures (e.g. 5 people's names and their ages) could be stored in one variable. The syntax to access the 3rd person's name and age would then be:

% read out one persons name and age
this_name = people(3).name;
this_age = people(3).age;

In turn this means that if the index expression is omitted, the struct_var.fieldname syntax produces a list of values (possibly with different datatypes). The only useful way to capture such a list is by creating an ad-hoc cell array:

% get the names of all people
all_names = {people.name};

Each cell and struct field can contain any of Matlab's supported datatypes, including cell and struct arrays! This means that elaborate structures (or cells) can be created:

% assign a part of a subfield's value
main_tree.leaf(3).subfield{4}(11:20) = 1;

If you see such a piece of code this can be translated into

• main_tree is of datatype struct (and must be of size 1×1, i.e. a scalar struct, to be valid)
• one of the field names of main_tree is called leaf, is also of datatype struct with at least field name subfield, and it presumably has at least 3 elements (see comment below)
• the subfield (of the third leaf!) is of type cell with at least 4 elements
• the 4th element of the subfield is a numeric array
• numeric indices 11 through 20 (of this numeric array) are set to 1

Please be aware that this line of code is also valid if main_tree is not yet defined! In that case, the leaf field will be initialized as a 1×3 struct with field name subfield, but the first two “leaf” elements will have an empty subfield. Only the third leaf's subfield will be assigned a value, which will be a 1×4 cell array, of which only the 4th element will have a value. And that will be a 1×20 double array, of which the first 10 values are 0!

As you can see, while Matlab's “auto-declaration” of variables can be quite useful, it sometimes makes code difficult to understand (given that no explicit declaration is ever given that pre-determines the shape or type of content for compound variables).

The function_handle type is an advanced datatype which is used mainly in three cases:

• the type of operation that is to be applied to a variable (or expression) is not fully determinable before code is run, in which case a function handle can be used to call a variable function (instead of using a syntax construction that selects from all possible options, which still could be insufficient if a function can be user defined)
• an argument in a function call itself is “an operation” to be applied to certain values
• a function is only available in a certain context (private function or sub-function in an M-file), in which case a function handle can be created and returned, allowing functions outside the original scope to use this function after all

Given the fact that this feature is fairly advanced, I won't be giving any in-depth examples at this point. Just be aware that variables can also be of type function_handle.

Matlab allows users to add functionality by creating text files with the .m extension. While this allows to create new functions that can be applied to values, most modern languages also have object-oriented design patterns. Among those are method overloading, inheritance, and protected storage of properties.

For this purpose, Matlab allows to define new datatypes (classes) by adding folders with a leading @ (at) symbol, and placing an M-file into this folder with the same name (without the @ sign).

Again, this is fairly advanced coding and will not be discussed in-depth at this point. There are, however, a few important aspects I want to mention:

• the internal representation of objects is supposed to be of type struct
• indexing operations (incl. the struct syntax of variable.fieldname) can be overloaded on objects
• NeuroElf makes use of this feature by allowing a more C++/Visual Basic style syntax:

  % NeuroElf xff and xfigure examples
  % load a VMR into an xff object
  vmr = xff('some.vmr');
   
  % call the function in @xff/private/aft_Browse.m
  vmr.Browse;
   
  % get xfigure object of the main UI figure
  neuroelf_gui;
  global ne_gcfg;
  mainfig = ne_gcfg.h.MainFig;
   
  % switch to "page" 2 (this is overloaded differently in the @xfigure/subsref.m file)
  mainfig.ShowPage(2);