User
Defined
Functions
Domain
Lecture
3
f
Range
f
x
(x1,x2)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
f(x)
y
f
=
x1+x2
1
Creating
Function
M‐files
•  User
defined
functions
are
stored
as
M‐files
–  Same
kind
of
naming
as
script
m‐files
–  First
line
tells
Matlab
it
is
a
function
8/22/10
Intr
Matlab
for
FM,
Fall
2010
2
User‐defined
functions
must
have
a
function
declaration
as
their
first
executable
statement
•  The
line
contains…
–  The
word
function
–  A
variable
(or
variables)
that
defines
the
function
output
–  A
function
name
–  A
variable
(or
variables)
used
for
the
input
argument
function
output
=
poly(x)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
3
Function
name
The
name
of
the
m‐file
is
the
name
of
the
function
Style
“rule”
‐‐>
use
the
file
name
as
the
name
you
give
the
function
in
the
‘function’
line
(matlab
demo)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
4
Workshop
(part
of
a
hw
problem)
We
will
do
this
together
•  Create
a
function
to
generate
random
numbers
(uniform
on
0
to
1),
keeping
a
sum
of
them
until
they
add
up
to
a
specified
value.
•  Output
the
number
of
numbers
generated.
demo:
countEm()
8/22/10
Intr
Matlab
for
FM,
Fall
2010
5
A
simple
function
The
function
name
must
be
the
same
as
the
file
name
8/22/10
Intr
Matlab
for
FM,
Fall
2010
6
The
function
is
available
from
the
command
window
or
from
other
M‐file
programs
8/22/10
Intr
Matlab
for
FM,
Fall
2010
7
Style
While
you
are
creating
a
function
it
may
be
useful
to
allow
intermediate
calculations
to
print
to
the
command
window.
However,
once
you
complete
your
“debugging”
make
sure
that
all
your
output
is
suppressed.
Show
only
what
is
needed
to
facilitate
understanding
to
the
user
of
the
function
8/22/10
Intr
Matlab
for
FM,
Fall
2010
8
Comments
•  You
should
comment
functions
liberally,
just
as
you
would
any
computer
code
•  The
comment
lines
immediately
after
the
first
line
are
returned
when
you
query
the
help
function
•  You
should
describe
the
purpose
of
the
function
and
any
input
and
output
8/22/10
Intr
Matlab
for
FM,
Fall
2010
9
8/22/10
Intr
Matlab
for
FM,
Fall
2010
10
Functions
can
accept…
•  numeric
values
•  variables
•  scalars
•  arrays
8/22/10
Intr
Matlab
for
FM,
Fall
2010
11
Functions
with
Multiple
Inputs
and
Outputs
•  Recall
the
remainder
function
This
function
has
two
inputs
8/22/10
Intr
Matlab
for
FM,
Fall
2010
12
A
user
defined
function
with
multiple
inputs
8/22/10
Intr
Matlab
for
FM,
Fall
2010
13
Functions
with
Multiple
Outputs
•  Recall
the
max
function
•  It
returns
two
results
8/22/10
Intr
Matlab
for
FM,
Fall
2010
14
This
function
return
3
output
values
If
you
don’t
ask
for
all
three
results,
the
program
just
returns
the
first
value
8/22/10
Intr
Matlab
for
FM,
Fall
2010
15
Recall
the
size
function
At
first
this
function
looks
like
it
returns
two
values
–
but
it
really
only
returns
a
single
array
with
two
elements
8/22/10
Intr
Matlab
for
FM,
Fall
2010
16
Practice
•  6.1,
p
189
Work
a
few,
e.g.
1,
2,
3,
and
4
Call
the
solution
to
3
function
sinP.
Look
at
HW
6
‐‐
expP
•  6.2,
p
196
Work
a
few
8/22/10
Intr
Matlab
for
FM,
Fall
2010
17
Functions
with
no
input
or
no
output
• 
It
isn’t
always
necessary
to
define
an
output
In
math
terms
‐‐
The
range
may
be
the
empty
set
8/22/10
Intr
Matlab
for
FM,
Fall
2010
18
No
output
is
defined
Just
because
a
function
does
not
return
an
output
value
doesn’t
mean
it
doesn’t
do
anything.
This
function
draws
a
star
8/22/10
Intr
Matlab
for
FM,
Fall
2010
When
you
try
to
set
the
star
function
equal
to
a
variable,
an
error
statement
is
returned
19
Determining
the
number
of
input
and
output
arguments
•  nargin
–  discovers
the
number
of
input
arguments
•  nargout
–  discovers
the
number
of
output
arguments
8/22/10
Intr
Matlab
for
FM,
Fall
2010
20
You
can
use
these
functions
in
your
programming
to
make
your
functions
more
versatile
•  For
example
the
surf
function
accepts
a
variable
number
of
arguments
•  surf(z)
plots
the
2‐D
matrix
z
against
the
index
numbers
•  surf(x,y,z)
plots
the
2‐D
matrix
z
against
the
x
and
y
coordinates
8/22/10
Intr
Matlab
for
FM,
Fall
2010
21
When
a
variable
number
of
arguments
is
allowed…
•  nargin
returns
‐1
8/22/10
Intr
Matlab
for
FM,
Fall
2010
22
Checks
to
see
how
many
output
values
were
requested
If
star1
is
not
set
equal
to
a
variable
the
star
is
drawn
but
no
output
is
returned
If
star1
is
set
equal
to
a
variable,
the
rhyme
is
returned
8/22/10
Intr
Matlab
for
FM,
Fall
2010
23
Workshop
•  Create
a
function
to
generate
random
numbers
(uniform
on
0
to
1),
keeping
a
sum
of
them
until
they
add
up
to
a
specified
value.
•  If
one
value
is
requested,
–  output
the
number
of
numbers
generated.
•  If
two
values
are
requested,
–  output
the
number
of
numbers
generated
and
the
end
total
Two
possible
syntax
forms
[Nnums]
=
countEm(inVal)
[Nnums,
total]
=
countEm(inVal)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
24
Local
Variables
(Workspace)
•  Variables
defined
in
an
M‐file
function,
only
have
meaning
inside
that
program
•  if
I
set
x=1
in
the
command
window,
it
is
not
equal
to
1
in
the
function
•  If
I
set
y=2
in
a
function,
it
is
not
equal
to
2
in
the
workspace
window
•  When
a
function
is
invoked,
a
new
workspace
is
created.
•  When
the
function
terminates,
the
function
workspace
goes
away.
8/22/10
Intr
Matlab
for
FM,
Fall
2010
25
ans
is
the
only
variable
created
x,
y,
a,
and
output
are
local
variables
to
the
g
function
When
the
g
function
is
executed,
the
only
variable
created
is
determined
in
the
command
window
(or
script
M‐file
used
to
execute
a
program)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
26
Even
though
g
is
defined
in
the
workspace,
the
function
can’t
access
it
8/22/10
If
you
don’t
define
g
in
this
function,
it
won’t
work!!
Intr
Matlab
for
FM,
Fall
2010
27
Global
Variables
•  Although
it
is
possible
to
define
global
variables
•  Changing
the
value
of
a
global
variable
can
happen
anywhere
‐‐
very
hard
to
debug
mistakes
***Avoid
using
global
variables***
Demo:
adding
count
to
die.m
and
using
countEm()
first,
add
just
the
one
global
variable,
then
make
global
in
countEm
8/22/10
Intr
Matlab
for
FM,
Fall
2010
28
Persistent
Variables
Persistent
variables
retain
their
value
when
the
function‐workspace
disappears
Demo:
make
count
in
die.m
persistent
8/22/10
Intr
Matlab
for
FM,
Fall
2010
29
Toolbox
of
Functions
•  Directory/folder
nmc
is
called
a
toolbox.
•  Usually
functions
in
a
toolbox
are
connected
by
a
theme,
such
as
all
the
functions
needed
for
solving
ordinary
differential
equations.
•  When
you
call
a
function
MATLAB
searches
for
it
along
a
predetermined
path
–  First
it
looks
in
the
current
directory
–  Then
it
follows
a
search
path
determined
by
your
installation
of
the
program
–  we
have
already
used
addpath.
8/22/10
Intr
Matlab
for
FM,
Fall
2010
30
Define
anonymous
functions
in
a
script
M‐file
•  Suppose
you’d
like
to
define
a
function
for
natural
log
called
ln
•  ln=@(x)log(x)
–  The
@
symbol
alerts
MATLAB
that
ln
is
a
function
–  The
function
input
is
next,
inside
parentheses
–  Finally
the
function
is
defined
8/22/10
Intr
Matlab
for
FM,
Fall
2010
31
function
definition
The
name
of
the
function
is
called
a
function
handle
–
in
this
case
it
is
ln
Notice
that
function
handles
are
represented
with
the
box
symbol
in
the
workspace
window
8/22/10
Intr
Matlab
for
FM,
Fall
2010
32
Function
Functions
•  Some
functions
accept
other
functions
as
input
•  An
examples
include
fplot(),
nargin,
and
nargout.
•  More
on
function
functions
later….
8/22/10
Intr
Matlab
for
FM,
Fall
2010
33
Summary
•  MATLAB
contains
a
wide
variety
of
built
in
functions
•  It
also
allows
you
to
define
your
own
functions
8/22/10
Intr
Matlab
for
FM,
Fall
2010
34
Summary
–
Function
M‐Files
•  Function
M‐files
must
start
with
a
definition
line
containing
–  the
word
function
–  a
variable
that
defines
the
function
output
(if
there
is
any
output)
–  a
function
name
–  a
variable
used
for
the
input
argument
(if
there
is
input)
8/22/10
Intr
Matlab
for
FM,
Fall
2010
35
Summary
–
Function
M‐files
•  Function
M‐files
must
be
stored
in
the
current
directory
or
in
a
user
defined
toolbox
•  The
function
name
must
also
be
the
file
name
8/22/10
Intr
Matlab
for
FM,
Fall
2010
36
Summary
‐
Comments
•  Functions
should
contain
ample
comments
to
document
the
code
•  The
comments
directly
after
the
function
definition
are
used
by
the
help
feature
to
describe
the
function
8/22/10
Intr
Matlab
for
FM,
Fall
2010
37
Summary
–
Anonymous
Functions
•  Anonymous
functions
are
defined
in
a
MATLAB
session
or
M‐file
•  They
only
exist
during
the
current
session
•  They
are
useful
as
input
to
function
functions
8/22/10
Intr
Matlab
for
FM,
Fall
2010
38