.. _variables: Variables and Values ==================================== .. include:: ../replace.txt .. only:: html .. topic:: 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. Command Window Calculator -------------------------- .. index:: variable, ans, assignment statement The characters ``>>`` in the Command Window is a prompt where commands are given to |M|. :: >> 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. .. describe:: 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. .. describe:: 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. .. describe:: ans |M| 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`. .. list-table:: **Math Operators** :widths: 30 30 :header-rows: 1 * - 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. Identifier Names ----------------- .. index:: identifiers, keywords, iskeyword 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 |M|'s keywords .. list-table:: :widths: 40 40 :header-rows: 1 * - Incorrect - Correct * - X-Y - XY * - month&year - monthYear * - 1987value - value1987 * - CO2 conc - CO2_conc .. admonition:: What is a keyword? Look up the function `iskeyword` in the |M| documentation. Calling Functions ------------------ .. index:: functions, trigonometry functions |M| 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 |M| 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 :math:`y` and :math:`x` coordinates. :: >> atan2(1,1) ans = 0.7854 .. caution:: A common error is to leave out the commas between the arguments of a function. Numeric Data Types -------------------- .. index:: data types, cast, format 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. * |M| 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 .. topic:: Look it Up! Look up the documentation for the :command:`format` command. How can it be applied? What affect does it have on the number of digits of accuracy that |M| stores for variables? Note that :command:`format compact` removes extra blank lines from results displayed in the command window. Simple Arrays -------------- .. index:: arrays, row vectors, indexing arrays We use arrays to hold a list of values. Arrays and matrices are central to using |M|. We will discuss them in more detail in the :ref:`vectors` section. For now, let us learn how to use a simple array, which |M| 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. Clearing Variables ------------------- .. index:: clear The :command:`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. Some Pre-defined Constants ------------------------------- .. index:: pre-defined constants, pi, exp, number e Since |M| is primarily used for numerical calculations, there are few math constants that we need to know about. The irrational number :math:`\pi` is perhaps the most obvious, but |M| also includes constants for working with the imaginary part of complex numbers (:math:`\sqrt{-1}`) and even infinity. .. list-table:: **Math Constants** :widths: 20 90 :header-rows: 1 * - 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 :math:`e \approx 2.718281828459046`. Instead, there is a function, ``exp(x)``, that returns :math:`e^x`. The usage of the number :math:`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 :math:`e^{i\,x} = \cos x + i\,\sin x`. .. only:: html .. note:: Now, complete the homework assignment :ref:`VariablesHW` using |M| Grader. .. raw:: latex \clearpage