Getting Started

Getting Started with MATLAB

Like most other programming languages, MATLAB provides mathematical expressions, but unlike most programming languages, these expressions involve entire matrices. The building blocks of expressions are

Variables
Numbers
Operators
Functions

Variables

MATLAB does not require any type declarations or dimension statements. When MATLAB encounters a new variable name, it automatically creates the variable and allocates the appropriate amount of storage. If the variable already exists, MATLAB changes its contents and, if necessary, allocates new storage. For example

num_students = 25

creates a 1-by-1 matrix named num_students and stores the value 25 in its single element.

Variable names consist of a letter, followed by any number of letters, digits, or underscores. MATLAB uses only the first 31 characters of a variable name. MATLAB is case sensitive; it distinguishes between uppercase and lowercase letters. A and a are not the same variable. To view the matrix assigned to any variable, simply enter the variable name.

Numbers

MATLAB uses conventional decimal notation, with an optional decimal point and leading plus or minus sign, for numbers. Scientific notation uses the letter e to specify a power-of-ten scale factor. Imaginary numbers uses either i or j as a suffix. Some examples of legal numbers are

3              -99            0.0001
9.6397238      1.60210e-20    6.02252e23
1i             -3.14159j      3e5i

All numbers are stored internally using the long format specified by the IEEE floating-point standard. Floating-point numbers have a finite precision of roughly 16 significant decimal digits and a finite range of roughly 10^-308 to 10⁺³⁰⁸. (The VAX computer uses a different floating-point format, but its precision and range are nearly the same.)

Operators

Expressions use familiar arithmetic operators and precedence rules.

+ addition

- subtraction

* multiplication

/ division

\ left division

\

Using MATLAB

^ power

' complex conjugate transpose

( ) specify evaluation order

Functions

MATLAB provides a large number of standard elementary mathematical functions, including abs, sqrt, exp, and sin. Taking the square root or logarithm of a negative number is not an error; the appropriate complex result is produced automatically. MATLAB also provides many more advanced mathematical functions, including Bessel and gamma functions. Most of these functions accept complex arguments. For a list of the elementary mathematical functions, type

help elfun

For a list of more advanced mathematical and matrix functions, type

help specfun
help elmat

Some of the functions, like sqrt and sin, are built-in. They are part of the MATLAB core so they are very efficient, but the computational details are not readily accessible. Other functions, like gamma and sinh, are implemented in M-files. You can see the code and even modify it if you want.

Several special functions provide values of useful constants.

`pi`	3.14159265
`i`	imaginary unit, -1
`j`	same as `i`
`eps`	floating-point relative precision, 2^-52
`realmin`	smallest floating-point number, 2^-1022
`realmax`	largest floating-point number, (2-)2¹⁰²³
`inf`	infinity
`nan`	Not-a-number

Infinity is generated by dividing a nonzero value by zero, or by evaluating well defined mathematical expressions that overflow, i.e., exceed realmax. Not-a-number is generated by trying to evaluate expressions like 0/0 or
inf-inf that do not have well defined mathematical values.

The function names are not reserved. It is possible to overwrite any of them with a new variable, such as

eps = 1.e-6

and then use that value in subsequent calculations. The original function can be restored with

clear eps

Expressions

You have already seen several examples of MATLAB expressions. Here are a few more examples, and the resulting values.

rho = (1+sqrt(5))/2
rho =
    1.6180

a = abs(3+4i)
a =
     5

z = sqrt(besselk(4/3,rho-i))
z =
   0.3730+ 0.3214i

huge = exp(log(realmax))
huge =
  1.7977e+308

toobig = pi*huge
toobig =
   Inf

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