Page 74 - A Guide to MATLAB for Beginners and Experienced Users

Functions and Expressions 55

This result may be puzzling if you are expecting f to act like a function. Since
f is a string, f(7) denotes the seventh character in f, which is 1 (the spaces
count). Notice that like symbolic output, string output is not indented from
the left margin. This is a clue that the answer above is a string (consisting
of one character) and not a floating point number. Typing f(5) would yield a
minus sign and f(-1) would produce an error message.
You have learned two ways to define your own functions, using inline (see
Chapter 2) and using an M-file (see Chapter 3). Inline functions are most useful
for defining simple functions that can be expressed in one line and for turning
the output of a symbolic command into a function. Function M-files are useful
for defining functions that require several intermediate commands to compute
the output. Most MATLAB commands are actually M-files, and you can peruse
them for ideas to use in your own M-files — to see the M-file for, say, the
command mean you can enter type mean. See also More about M-files below.
Some commands, suchas ode45 (a numerical ordinary differential equa-
tions solver), require their first argument to be a function — to be precise,
either an inline function (as in ode45(f, [0 2], 1))ora function handle,
that is, the name of a built-in function or a function M-file preceded by the
special symbol @ (as in ode45(@func, [0 2], 1)). The @ syntax is new in
MATLAB 6; in earlier versions of MATLAB, the substitute was to enclose the
name of the function in single quotes to make it a string. But with or without
quotes, typing a symbolic expression instead gives an error message. However,
most symbolic commands require their first argument to be either a string or
a symbolic expression, and not a function.
An important difference between strings and symbolic expressions is that
MATLAB automatically substitutes user-defined functions and variables into
symbolic expressions, but not into strings. (This is another sense in which the
single quotes you type around a string suppress evaluation.) For example, if
you type
>> h = inline(’t.ˆ3’, ’t’);
>> int(’h(t)’, ’t’)
ans =
int(h(t),t)
then the integral cannot be evaluated because within a string h is regarded
as an unknown function. But if you type

>> syms t
>> int(h(t), t)

ans =
1/4*t^4