2.2. Variables and Values

Reading Assignment

Please read chapter 1 of Physical Modeling in MATLAB, by Allen B. Downey [DOWNEY11].

As with math equations, we use variables in computer programs. They allow us to associate a storage location in the computer’s memory with a name. We use the variable name to store and retrieve values from the storage location.

2.2.1. Command Window Calculator

The characters >> in the Command Window is a prompt where commands are given to MATLAB.

>> 2 + 1
ans =
    3

We can save a result to a variable for future reference:

>> x = 2 + 1
x =
    3

Tip

The keyboard arrow keys may be used to retrieve previously entered commands.

Variable

When a value is given a name, it becomes a variable. Variables are used to store results and to feed information to future computations. The name given to a variable is called an identifier, which just means that we made up the name. The rules for what is a valid identifier are covered later.

Assignment Statement

Storing data in a variable with an equal sign = is formally called an assignment statement in computer science terminology. Some data value is assigned to be held in a variable.

ans

MATLAB knows that users might perform a calculation without saving the result to a variable, but later want to use the result. So any result not saved to a variable is automatically stored in a variable called ans. NOTE: Only the most recent unsaved result is saved in ans.

Table 2.1 Math Operators
Operator Function
+ Addition
- Subtraction
* Multiplication
/ Division
^ Exponent

The order of operations is what you would expect from basic algebra: multiplication and division happen before addition and subtraction. If you want to override the order of operations, you can use parentheses.

>> 2 * (3-4) / 5
ans =
    -0.4000

The following is the order of operations.

  1. parentheses, brackets
  2. exponents, roots
  3. multiplication, division
  4. addition, subtraction

Caution

A common error for beginning programmers is leaving out the * for multiplication.

2.2.2. Identifier Names

A few simple rules govern identifier names for variables and functions.

  • Can only contain letters, numbers, and underscores
  • Can only start with letters
  • Are case-sensitive
  • Can be between 1 and 63 characters long
  • Can not be one of MATLAB’s keywords
Incorrect Correct
X-Y XY
month&year monthYear
1987value value1987
CO2 conc CO2_conc

What is a keyword?

Look up the function iskeyword in the MATLAB documentation.

2.2.3. Calling Functions

MATLAB has functions for any calculation you can imagine and a lot more.

>> sin(1)
ans =
    0.8415

This command is an example of a function call. The name of the function is sin, which is the usual abbreviation for the trigonometric sine. The value in parentheses is called the argument. All the trig functions in MATLAB work in radians, but there is a set of trig function ending with a ‘d’ that use angles in degrees. These include sind, cosd, tand, etc.

Some functions take more than one argument, in which case they are separated by commas. For example, atan2 computes the inverse tangent, which is the angle in radians between the positive x-axis and the point with the given y and x coordinates.

>> atan2(1,1)
ans =
    0.7854

Caution

A common error is to leave out the commas between the arguments of a function.

2.2.4. Numeric Data Types

The default data type for numeric variables is double floating point (64 bits). It supports very large positive or negative numbers and numbers very close to zero.

>> big1 = 9.578942e50
big1 =
     9.5789e+50
>> small = 1.07124e-122
small =
      1.0712e-122

Other numeric data types, such as signed integers and unsigned integers are available if needed. Look up the documentation for the Cast function for a detailed list of data types.

  • MATLAB treats all numeric data as a matrix (discussed later). Scalar values are thus reported as having a size of 1x1.

    >> a = 5
a =
    5
>> whos
Name      Size            Bytes  Class     Attributes

a         1x1                 8  double

Look it Up!

Look up the documentation for the format command. How can it be applied? What affect does it have on the number of digits of accuracy that MATLAB stores for variables? Note that format compact removes extra blank lines from results displayed in the command window.

2.2.5. Simple Arrays

We use arrays to hold a list of values. Arrays and matrices are central to using MATLAB. We will discuss them in more detail in the Vectors and Matrices in MATLAB section. For now, let us learn how to use a simple array, which MATLAB calls a row vector. Calling it a row vector just means that data is stored in a single row. Consider the following lines of code.

>> x = zeros(1, 5)
x =
    0     0     0     0     0
>> x(1) = 3
x =
    3     0     0     0     0
>> x(4) = 6
x =
    3     0     0     6     0
>> x(1)
ans =
    3

The zeros function was used to create a row vector consisting of one row and five columns that are filled with zeros. In the next two commands we used assignment statements to change the values stored in the first and forth positions. Notice two things about the use of an index number that are different than most other programming languages. First, we use a pair of parenthesis around the index number. Secondly, the range of indices goes from 1 to N, where N is the size of the row vector.

2.2.6. Clearing Variables

The clear command removes all variables from the Workspace. Specific variables may also be removed:

>> clear x

In some cases, it may be desirable particularly while developing a program to clear all variables and close open plots when the program starts. Add the line clear; close all at the beginning of the program to achieve this.

2.2.7. Some Pre-defined Constants

Since MATLAB is primarily used for numerical calculations, there are few math constants that we need to know about. The irrational number \pi is perhaps the most obvious, but MATLAB also includes constants for working with the imaginary part of complex numbers (\sqrt{-1}) and even infinity.

Table 2.2 Math Constants
Name Meaning
i Imaginary unit
j Imaginary unit
Inf Infinity
pi Ratio of circle’s circumference to its diameter
NaN Not-a-Number

You might expect to see the irrational number e \approx 2.718281828459046. Instead, there is a function, exp(x), that returns e^x. The usage of the number e almost always involves an exponent. If the exponent were always a real number, then an expression such as e^x would suffice, but the exponent may be a complex number. Thus a function gives the flexibility needed.

>> exp(i*pi)
ans =
  -1.0000 + 0.0000i

>> exp(i*pi/2)
ans =
   0.0000 + 1.0000i

The complex exponent demonstrates Euler’s formula for complex exponentials e^{i\,x} = \cos x + i\,\sin x.

Note

Now, complete the homework assignment Entering Basic Equations using MATLAB Grader.