More on Functions…

Lecture 8

Preserving Data between Calls to a function

Persistent statement is declared in order to preserve some local information within a function between calls to afunction

persistent var1,var2…

Example: Running averages

function [ave,std]=runstats(x)

%runstats generate running ave /std deviation

persistent n

Persistent sum_x

Persistent sum_x2

if x == ‘reset’

n=0

Sum_x=0

Sum_x2=0

else

n=n+1

Sum_x = Sum_x

Sum_x2=Sum_x2+x^2

end

Preserving Data between Calls to A function

if n == 0 ave=0; std=0;elseif n == 1 ave=sum_x; std=0;else ave=sum_x/n; std=sqrt((n*sum_x2-sum_x^2)/(n*(n-1)));end

script file

[ave,std] = runstats(‘reset’)

nvals=input(‘enter number of values’);

for ii=1:nvals

x=input(‘enter a value’, ‘s’);

[ave,std]=runstats(x)

end

Function functionsA function includes the name of other functions in the input argument list.

Function Name Description

fminbnd Minimize a function of one variable

fzero find a zero of a function of one variable

quad Numerically integrate a function

ezplot easy to use function plotter

fplot plot a function by name

Common MATLAB Function functions

Function functions

Common MATLAB Function functions

>> fzero(‘cos’,[0 pi])ans = 1.5708

>> fzero('exp(x)-2',[0 1])

ans =

0.6931

Locates a zero of the function cos between 0 and pi.

Locates a zero of the function ex-2 between 0 and 1.

Function functions

Common MATLAB Function functions

>>fminbnd('x^3-2*x', 0,1)

ans =

0.816496985529690

>> quad(@fun,0,1)

ans =

-0.166666666666667

Locates a minimum between 0 and 1.

integrate function in ‘fun’ using simpson’s rule

function y=fun(x)y=x.^2-x;

‘fun’ includes any one variable function

Function functions

Common MATLAB Function functions

>>ezplot('x^3-2*x')quick plot of function in the string

-6 -4 -2 0 2 4 6-250

-200

-150

-100

-50

0

50

100

150

200

250

x

x3-2 x

-6 -4 -2 0 2 4 6

-1

-0.5

0

0.5

1

x

sin

>>ezplot(@sin)

Function functions

Common MATLAB Function functions

>> fplot('x^3-x',[-5 5])quick plot of function in the string

>> fplot(@sin,[-2*pi 2*pi])

-5 -4 -3 -2 -1 0 1 2 3 4 5-150

-100

-50

0

50

100

150

-6 -4 -2 0 2 4 6-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Function functions

eval and feval functions

eval evaluates a character string as though it had been typed in the Command Window.

feval evaluates a named function at a specific input value.

>>x=eval('sin(pi/4)')

x =

0.707106781186547

eval (string)

>>y=eval('x^2-2*x')

??? Error using ==> evalUndefined function or variable 'x'.

Function functions

eval and feval functions

eval evaluates a character string as though it had been typed in the Command Window.

feval evaluates a named function at a specific input value.

>>x=feval('sin’,pi/4)

x =

0.707106781186547

feval (fun,value)

>> y=feval(@fun,2)y = 2

function y=fun(x)y=x.^2-x;

Example: ascending sort

function out = ssort(a)nvals=length(a);for i=1:nvals-1iptr=i; for j=i+1:nvals if a(j)<a(iptr); temp = a(j); a(j) = a(iptr); a(iptr)= temp; end end

endout=a;

nvals=input('enter number of values to sort');array=zeros(1,nvals);for i=1:nvals string=['enter value' int2str(i) ': ']; array(i)= input(string);endsorted =ssort(array);disp(' Sorted data ');for i=1:nvals sorted(i)end

Function Handles

You can create a function handle to any function by using either @ before the function name. You can name the handle if you wish and use the handle to reference the function. For example, to create a handle to the sine function;

>> sine_handle = @sin;>> plot ([0:0.01:6], sine_handle, [0:0.01:6])

Methods for Calling Functions

There are four ways to invoke, or call, a function into a function.1.As a character string identifying the appropirate function M-file:2.As a function handle,3.As an inline function object4.As a string

1. function y= fun1(x)y = x.^2-4;The function may be called as follows, to compute the zero over the range 0<x<3.

[x,value]=fzero(‘fun1’,[0,3])

2. As a function handle:[x,value] = fzero(@fun1,[0,3])

3. As an inline function object:>>fun1=‘x.^2-4’;>>fun_inline =inline(fun1);>>[x,value] = fzero(@fun1,[0,3]);

4. As a string expression>>fun1=‘x.^2-4’;>>[x,value] = fzero(@fun1,[0,3]);Or>>[x,value] = fzero(=‘x.^2-4’,[0,3]);

Anonymous Functions

Anonymous Functions

You can pass the handle of an anonymous function to another function

Multiple input arguments

Calling one function within another

Nested functions