MATLAB

Functions – Part II

Greg Reese, Ph.D

Research Computing Support Group

Academic Technology Services

Miami University

September 2013

MATLAB

Functions – Part II

© 2010-2013 Greg Reese. All rights reserved 2

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Part I

• Write scripts

• Run MATLAB functions

• Write and run our own functions

• Use our functions in MATLAB

plotting and optimization routines

• Write and use anonymous

functions

4

Part II

• Document functions

• Detect number of inputs and outputs

• Subfunctions

• Nested functions

Documentation

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Documentation

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To find out how to use a MATLAB function you

type the command

help function_name

If you don't know function name, can look for

important word in function description with

lookfor word

We can incorporate our functions in the MATLAB help system so help and lookfor

work on custom code

Documentation

7

Look at results for MATLAB csvread()

Try It

1. Type help csvread

2. Type lookfor 'comma separated'

3. Type type csvread

Documentation

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>> help csvread

CSVREAD Read a comma separated value file.

M = CSVREAD('FILENAME') reads a comma separated value formatted file

FILENAME. The result is returned in M. The file can only contain

numeric values.

M = CSVREAD('FILENAME',R,C) reads data from the comma separated value, etc.

>> lookfor 'comma separated'

lists - Comma separated lists.

csvread - Read a comma separated value file.

csvwrite - Write a comma separated value file.

>> type csvread

function m = csvread(filename, r, c, rng)

%CSVREAD Read a comma separated value file.

% M = CSVREAD('FILENAME') reads a comma separated value formatted file

% FILENAME. The result is returned in M. The file can only contain

% numeric values.

%

% M = CSVREAD('FILENAME',R,C) reads data from the comma separated value

etc.

Documentation

9

help displays first group of

contiguous comment lines in file

• Traditionally put right after function line

• Blank line breaks contiguous group

– To display blank, put in line with only a

percent sign

Documentation

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Example – help output

In file doc_check.m function [ result details ] = doc_check( fileName )

% DOC_CHECK Check a function m-file for correct documentation.

%

% Check that first comment has function name in capital letters and line

% ends with a period, that every input and output parameter is documented,

% etc. See explanation for "details" output parameter for full list

>> help doc_check

DOC_CHECK Check a function m-file for correct documentation.

Check that first comment has function name in capital letters and line

ends with a period, that every input and output parameter is documented,

etc. See explanation for "details" output parameter for full list

Documentation

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H1 or description line

• H1 = first line in help description

• lookfor uses this line

– Make line descriptive of function

– Include words user would most likely

search for

Documentation

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Example – lookfor output

In file doc_check.m function [ result details ] = doc_check( fileName )

% DOC_CHECK Check a function m-file for correct documentation

>> lookfor documentation

doc_check - Check a function m-file for correct documentation.

builddocsearchdb - Build documentation search database

doc - Display HTML documentation in the Help browser.

docsearch - Search HTML documentation in the Help browser.

Documentation

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Suggestions for documentation

• H1 line

• Longer description of functionality

• Description of parameters

• Description of errors and how they're

handled

• References

Documentation

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H1 line suggestions

• File name in caps*

• End in period*

• Contain words likely to be searched for

* MATLAB conventions. Don't know if they have functionality

Documentation

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Longer description suggestions

• Name of algorithm, inputs and outputs,

e.g. "Run's Reese's algorithm on the

students in the class and produces a list

of slackers and hard workers"

• Don't put in details spelled out further in

documentation

Documentation

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Parameter suggestions

• Definition

• Data type, e.g., scalar, vector, matrix, etc.

– For vector, whether row, column or either

• Units

• Range

– Be careful with > and ≥

• Optional or required

– Default if optional input

Documentation

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Error suggestions

• Conditions that cause error

• State of output if error

• Internal state if error, e.g., "All open files in

routine will be closed if there is an error"

• Error reporting mechanism

– error()

– errordlg()

– Text of message

Documentation

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Example

In file doc_check.m function [ result details ] = doc_check( fileName )

% DOC_CHECK Check a function m-file for correct documentation.

%

% Check that first comment has function name in capital letters and line

% ends with a period, that every input and output parameter is documented,

% etc. See explanation for "details" output parameter for full list

%

% REQUIRED INPUT

% fileName - name of file to check

% REQUIRED OUTPUT

% result - true if all items checked for are correct, false otherwise

% OPTIONAL OUTPUT

% details - all values true or false

% details(1) - first word of first comment line is function name in caps

% details(2) - first comment line ends with a period

% etc.

% ERRORS

% If can't open or read file, calls error()

fid = fopen( fileName );

% etc.

Documentation

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Example - errors

Output for help doc_check.m >> help doc_check

DOC_CHECK Check a function m-file for correct documentation.

Check that first comment has function name in capital letters and line

ends with a period, that every input and output parameter is documented,

etc. See explanation for "details" output parameter for full list

REQUIRED INPUT

fileName - name of file to check

REQUIRED OUTPUT

result - true if all items checked for are correct, false otherwise

OPTIONAL OUTPUT

details - all values true or false

details(1) - first word of first comment line is function name in caps

details(2) - first comment line ends with a period

etc.

ERRORS

If can't open or read file, calls error()

Documentation

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References

• Full citations for books, papers, etc.

• Web sites

– URL

– Date downloaded

• External codes used

– MATLAB central

– sourceforge.net

– university

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Documentation

Questions?

Input / Output

Arguments

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Arguments

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One function can have different numbers of

inputs or outputs. Most MATLAB functions

are like this

fminbnd

Find minimum of single-variable function on fixed interval

Syntax

x = fminbnd(fun,x1,x2)

x = fminbnd(fun,x1,x2,options)

[x,fval] = fminbnd(...)

[x,fval,exitflag] = fminbnd(...)

[x,fval,exitflag,output] = fminbnd(...)

Arguments

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Why different number of inputs?

• Save caller from always entering argument that

has commonly used value

– e.g., delimiter in tokenizer usually a space

• Save caller from entering redundant arguments

– e.g., correlation( x, y ) computes cross-correlation, for

autocorrelation want correlation( x ) instead of

correlation( x, x )

• Allow caller to enter extra information if available

– e.g., pass graph title to plotting routine

Arguments

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In a function, get number of arguments passed to function with nargin

Example – download scale.m function [ y expansion ] = scale( x, m, b )

% SCALE - linearly scale x so that y = m*x + b

% x - unscaled data, row or column vector

% Optional input arguments

% m - slope, scalar ~= 0, default = 1

% b - y-intercept, scalar, default = 0

%

% Required output

% y - scaled data, same dimensions as x

% Optional output

% expansion - optional output, scalar,

% expansion = (yMax-yMin)/(xMax-xMin)

Arguments

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Typical verification of number of inputs function [ y expansion ] = scale( x, m, b )

% verify right number of input arguments

if nargin == 1

m = 1;

b = 0;

elseif nargin == 2

b = 0;

elseif nargin ~= 3

error( 'USAGE: y = scale( x, m, b ) m, b optional' );

end

If missing inputs, set them

If not max number of inputs, bail out

Arguments

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Can verify data type

% verify data type

if ~isvector( x )

error( 'x must be a vector' );

elseif ~isscalar( m ) | ~isscalar( b )

error( 'm and b must be scalars' );

end

Arguments

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Can verify range

%verify range

if m == 0

error( 'm must not be zero' );

end

Arguments

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Try It >> y = scale( magic(3) )

??? Error using ==> scale at 23

x must be a vector

>> y = scale( 1:5, 2 )

y = 2 4 6 8 10

>> y = scale( 1:5, 2, [ 5 6] )

??? Error using ==> scale at 25

m and b must be scalars

>> y = scale( 1:5, 2, 1, 5 )

??? Error using ==> scale

Too many input arguments.

>> y = scale( 1:5, 2, 1 )

y = 3 5 7 9 11

Arguments

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Why different number of outputs?

• Provide caller with less important

computations

– e.g., [R,P]=corrcoef(...) can return main

result R (correlation coefficients) and optionally

P (p-values)

• Provide caller with information about

processing that took place

• Provide caller with information for use with

other functions

• Provide caller with information about any

errors

Arguments

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Example – MATLAB fminbnd() [x,fval] = fminbnd(...) returns the value of the objective function computed in

fun at x.

[x,fval,exitflag] = fminbnd(...) returns a value exitflag that describes the exit

condition of fminbnd:

1 fminbnd converged to a solution x based on options.TolX.

0 Maximum number of function evaluations or iterations was reached.

-1 Algorithm was terminated by the output function.

-2 Bounds are inconsistent (x1 > x2).

[x,fval,exitflag,output] = fminbnd(...) returns a structure output that contains

information about the optimization:

output.algorithm Algorithm used

output.funcCount Number of function evaluations

output.iterations Number of iterations

output.message Exit message

Main results

Exit status

Processing information

Arguments

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In a function, get number of arguments requested by caller with nargout

Example – scale.m function [ y expansion ] = scale( x, m, b )

% SCALE - linearly scale x so that y = m*x + b

% x - unscaled data, row or column vector

% Optional input arguments

% m - slope, scalar ~= 0, default = 1

% b - y-intercept, scalar, default = 0

%

% Required output

% y - scaled data, same dimensions as x

% Optional output

% expansion - optional output, scalar,

% expansion = (yMax-yMin)/(xMax-xMin)

Continues on next slide

Arguments

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Processing different number of outputs function [ y expansion ] = scale( x, m, b )

% compute main output

if nargout == 1

y = m * x + b;

elseif nargout == 2

y = m * x + b;

expansion = ( max(y) - min(y) ) / ( max(x) - min(x) );

else

error( 'USAGE: [ y expansion ] = scale( x, m, b ) m, b

optional' );

end

If optional output desired,

compute it

If not max number of inputs, bail out

Arguments

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Try It >> scale( 1:5 )

??? Error using ==> scale at 42

USAGE: [ y expansion ] = scale( x, m, b ) m, b optional

>> y = scale( 1:5 )

y = 1 2 3 4 5

>> y = scale( 1:5, 3 )

y = 3 6 9 12 15

>> [ y ratio ] = scale( 1:5, 3 )

y = 3 6 9 12 15

ratio = 3

>> [ y ratio z ] = scale( 1:5, 3 )

??? Error using ==> scale

Too many output arguments.

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Arguments

Questions?

Subfunctions

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Subfunctions

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A function m-file can contain more than one

function. All functions other that the first one

are called subfunctions.

Subfunctions –Used mainly to carry out tasks that should be

separated from primary function but unlikely to be used

by other m-files

– Help avoid having a lot of m-files

– Override (used in place of) other functions of same

name

Subfunctions

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Subfunctions in a file

• Start with a function line

• End at next function line or at end of file

• Are only visible (usable) by the primary

function or the other subfunctions

• Can come in any order as long as

primary function comes first

• Cannot access variables in other

subfunctions or in the primary function

Subfunctions

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Example – download newstats.m function [avg, med] = newstats(u) % Primary function

% NEWSTATS Find mean and median with internal functions.

% From MATLAB help on subfunction

n = length(u);

% Note subfunction mean() gets called, not MATLAB's mean()

avg = mean(u, n);

med = my_median(u, n);

function a = mean(v, n) % Subfunction

% Calculate average.

a = sum(v)/n;

function m = my_median(v, n) % Subfunction

% Calculate median.

w = sort(v);

if rem(n, 2) == 1

m = w((n+1) / 2);

else

m = (w(n/2) + w(n/2+1)) / 2;

end

Subfunctions

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Try It

Call primary function

>> [ av med ] = newstats( 1:11 )

av = 6

med = 6

Call subfunction

>> med2 = my_median( 1:11, 11 )

??? Undefined function or method 'my_median' for

input arguments of type 'double'.

Subfunctions

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Try It

Verify overridden mean()called by putting line

disp( 'In newstats mean' );

in subfunction mean()

>> [ av med ] = newstats( 1:11 )

In newstats mean

av = 6

med = 6

Subfunctions

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Strange but True

Although you can't access subfunctions

from outside their file, you can get help

on them!

1. Write normal help stuff for subfunction

2. On command line type help filename>subfunction_name

where filename is the name of the file

(without the .m) that the subfunction is in

Subfunctions

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Try It

After the function line for my_median put

some help lines and print them by using

the help command on the command line function m = my_median(v, n)

% This is my median

% Land that I love

>> help newstats>my_median

This is my median

Land that I love

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Subfunctions

Questions?

Nested

Functions

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function3

Nested Functions

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A nested function is a function defined

within another function

Nested functions often passed by

function handle to functions that

manipulate other functions – e.g., ezplot(), fminbnd(), etc.

– Can be used instead of anonymous functions if

function has more than one expression

Nested Functions

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To define a nested function, just

write it within another function

Example

function outer( a, b, c )

...

function inner( a )

...

end

...

end

Nested

function

Nested Functions

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Nested functions

• Can be nested within other nested

functions

• Cannot be inside any MATLAB program control statement, i.e., if, else,

elseif, switch, for, while,

try, or catch statement

• Must always be terminated by an end statement

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Nested Functions

MATLAB Help says:

"M-file functions don't normally require a terminating end statement. This rule does

not hold, however, when you nest

functions. If an M-file contains one or more

nested functions, you must terminate all

functions (including subfunctions) in the M-file with end, whether or not they

contain nested functions."

Nested Functions

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You can call a nested function

• From the level immediately above

it. (In the following code, function

A can call B or D, but not C or E.)

• From a function nested at the

same level within the same parent

function. (Function B can call D,

and D can call B.)

• From a function at any lower level.

(Function C can call B or D, but

not E.)

• You can also call a subfunction

from any nested function in the

same M-file.

function A(x, y) % Primary function

B(x, y);

D(y);

function B(x, y) % Nested in A

C(x);

D(y);

function C(x) % Nested in B

D(x);

end

end

function D(x) % Nested in A

E(x);

function E(x) % Nested in D

...

end

end

end

Nested Functions

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The scope of a variable is the range

of functions that have direct access

to the variable.

When define a variable in a function,

scope normally that function alone

• Calling function cannot access called

function's variables

• A subfunction cannot access another

subfunction's variables

Nested Functions

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Big power of nested functions:

A nested function has

access to the variables in all

functions in which it is nested

Nested Functions

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• A variable that has a value assigned

to it by the primary function can be

read or overwritten by a function

nested at any level within the

primary

• A variable that is assigned in a

nested function can be read or

overwritten by any of the functions

containing that function

Nested Functions

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Example – download and run nested_fibonacci.m

function nested_fibonacci % primary function

% nested function

function sum = print_and_sum( ix )

if ix < 3

sum = 1;

else

% nested function can access "indexes"

% variable in containing function

sum = indexes(ix-1) + indexes(ix-2);

fprintf( '%d = %d + %d\n', sum,...

indexes(ix-1), indexes(ix-2) );

end

end

indexes = 1:8;

% apply print_and_sum to every element of numbers,

% save results in a vector and display the vector

fib = arrayfun( @print_and_sum, indexes );

fib

end % end of nested_fibonacci

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Nested Functions

Questions?

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The End