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