Advanced use of functions
Anonymous functions
function handles
subfunctions
and
nested functions
Function handle
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Useful as a parameter to other functions
Can be considered as an alternate name for a
function – but with more capabilities
Example:
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sine_handle = @sin
sine_handle(x)
has same values as sin(x) for all x
Three ways of plotting sin(x)
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x = [0 : 0.01 : 2*pi] ;
y = sin( x );
plot(x,y)
plot( x, sin(x) )
plot( [0 : 0.01 : 2*pi] , sin( [0 : 0.01 : 2*pi] )) ;
Last method has the advantage that no
permanent storage is needed for x and/or y
Function handle continued
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In last example everything is on one line
but it requires writing the interval twice
It would be more convient to write
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gen_plot( function_handle, interval )
The first parameter has to be a function
handle and not just the name of a function
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gen_plot( sin, [0 : 0.01 : 2*pi ] ) does not make
sense to Matlab, but the following does
gen_plot( sine_handle, [0 : 0.01 : 2*pi] )
Using a function handle
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When plotting lots of functions it may
be useful to have a function with the
name gen_plot available
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function [] = gen_plot( func_handle, interval ) ;
plot( interval, func_handle(interval) ) ;
The example shows how to pass
functions as parameters.
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gen_plot( sine_handle, [0 : 0.01 : 2*pi] )
Anonymous functions
Assume the user needs to work temporarily
with the function x3+3*x – 1
 Instead of writing the function
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function y = mypoly(x) ;
y = x.^3+3*x-1
and storing it as mypoly.m in subdirectory
work we can use an anonymous function with
the function handle mypoly
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mypoly = @(x) x.^3+3*x-1
Using anonymous functions
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With a function handle an anonymous
function can be used like any other
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or try to find a zero near 1.5
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gen_plot( mypoly, [-10 : 0.01 : 10] )
fzero( mypoly, 1.5 )
Without the function handle the anonymous
function can also be inserted directly as a
parameter
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gen_plot( @(x) x.^3+3*x-1, [-10 : 0.01 : 10] )
More examples
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Assume f1 had been defined as a function and kept
in f1.m then
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fzero( f1, 0 ) would be in error
Matlab used an alternate method in the past. In
order to be backward compatible it is still available,
but the use is not recommended:
fzero( 'f1', 0 )
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f1 = @(x) x + 2* exp(-x) -3
fzero( f1, 0 )
fzero( f1, 1 )
fzero( 'sin', 0 )
fzero( 'x.^3', 0 )
need to use default variable name x
Use function handles instead!
Commands of Matlab: clear,
dir, which, cd, …
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they can be used with a parameter, i.e.
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clear functions
dir C:\MATLAB_SV701\toolbox\matlab
which clear
cd E:\work
all are builtin functions
the parameter is interpreted as a character string. A
blank terminates the character string
equivalent calls
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clear('functions')
dir('C:\MATLAB_SV701\toolbox\matlab')
which('clear')
cd(' e:\work')
Remark:
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Builtin functions can be called like a
command
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instead of
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median [1,2,100]
median([1,2,100])
Matlab gives no warning in the first case and
returns 1
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[1,2,100] is treated as a character string
median('[1,2,100]') also returns 1
Subfunctions, example
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function [avg,med] = mystat(u)
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n = length(u) ;
avg = mymean( u,n ) ;
med = mymedian( u,n ) ;
end % function mystat
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function a = mymean( v,n )
a = sum(v)/n;
end % function mymean
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function m = mymedian( v,n ) ;
w = sort(v) ;
if rem(n,2) ==1
m = w((n+1)/2)
else
m = (w(n/2)+ w(n/2+1))/2 ;
end
end % mymedian
Subfunctions
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subfunctions are stored in the same file as the main
function and can only be called in that file
the scope of subfunctions is restricted to the file in
which they are defined
the example given is for illustration only
the example uses modular design, but carries it to an
extreme
the overhead of calling a function outweighs any
benefit in this case
if a function mystat has to be written the following
would be acceptable
Avoid unnecessary calculations
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function [avg,med] = mystat2(u)
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n = length(u) ;
avg = sum(u)/n ;
if nargout == 2
% only compute if requested
w = sort(u) ;
if rem(n,2) ==1
med = w((n+1)/2) ;
else
med = (w(n/2)+ w(n/2+1))/2 ;
end
end
end
% mystat2
Nested functions
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main_function
nested_function_1
…
end % nested_function_1
nested_function_2
…
end % nested_function_2
…
…
end % main_function
Nested function
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When using nested functions all functions
need a matching end statement!
subfunction versus nested functions
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nested functions have access to all variables
defined in the main function!
avoids passing parameters or using global
variables
For a structured design use subfunctions.
Avoid nested functions or use them sparingly