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Advanced use of functions

0. Advanced use of functions. Anonymous functions function handles subfunctions and nested functions. Function handle. 0. Useful as a parameter to other functions Can be considered as an alternate name for a function – but with more capabilities Example: sine_handle = @sin

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Advanced use of functions

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  1. 0 Advanced use of functions Anonymous functions function handles subfunctions and nested functions

  2. Function handle 0 • Useful as a parameter to other functions • Can be considered as an alternate name for a function – but with more capabilities • Example: • sine_handle = @sin • sine_handle(x) • has same values as sin(x) for all x

  3. Three ways of plotting sin(x) 0 • 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

  4. Function handle continued 0 • In last example everything is on one line • but it requires writing the interval twice • It would be more convient to write • gen_plot( function_handle, interval ) • The first parameter has to be a function handle and not just the name of a function • 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] )

  5. Using a function handle 0 • When plotting lots of functions it may be useful to have a function with the name gen_plot available • function [] = gen_plot( func_handle, interval ) ; • plot( interval, func_handle(interval) ) ; • The example shows how to pass functions as parameters. • gen_plot( sine_handle, [0 : 0.01 : 2*pi] )

  6. Anonymous functions 0 Assume the user needs to work temporarily with the function x3+3*x – 1 • Instead of writing the function • 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 • mypoly = @(x) x.^3+3*x-1

  7. Using anonymous functions 0 • With a function handle an anonymous function can be used like any other • gen_plot( mypoly, [-10 : 0.01 : 10] ) • or try to find a zero near 1.5 • fzero( mypoly, 1.5 ) • Without the function handle the anonymous function can also be inserted directly as a parameter • gen_plot( @(x) x.^3+3*x-1, [-10 : 0.01 : 10] )

  8. More examples 0 • f1 = @(x) x + 2* exp(-x) -3 • fzero( f1, 0 ) • fzero( f1, 1 ) • Assume f1 had been defined as a function and kept in f1.m then • 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 ) • fzero( 'sin', 0 ) • fzero( 'x.^3', 0 ) need to use default variable name x • Use function handles instead!

  9. Commands of Matlab: clear, dir, which, cd, … 0 • they can be used with a parameter, i.e. • 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 • clear('functions') • dir('C:\MATLAB_SV701\toolbox\matlab') • which('clear') • cd(' e:\work')

  10. Remark: 0 • Builtin functions can be called like a command • median [1,2,100] • instead of • median([1,2,100]) • Matlab gives no warning in the first case and returns 1 • [1,2,100] is treated as a character string • median('[1,2,100]') also returns 1

  11. Subfunctions, example 0 • function [avg,med] = mystat(u) • n = length(u) ; • avg = mymean( u,n ) ; • med = mymedian( u,n ) ; • end % function mystat • function a = mymean( v,n ) • a = sum(v)/n; • end % function mymean • 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

  12. Subfunctions 0 • 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

  13. Avoid unnecessary calculations 0 • function [avg,med] = mystat2(u) • 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

  14. Nested functions 0 • main_function • nested_function_1 • … • end % nested_function_1 • nested_function_2 • … • end % nested_function_2 • … • … • end % main_function

  15. Nested function 0 • When using nested functions all functions need a matching end statement! • subfunction versus nested functions • 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

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