Function Handle Assignment

This solution is perhaps a little bit fancier than it has to be, but illustrates what I want to show.

Problem 1: The Lambert W function

I wrote a function called myLambert, which is at the bottom of this file. Here is how it works:

fprintf('I calculated W(2)=%0.4f.\n',myLambert(2));
I calculated W(2)=0.8526.
fprintf('MATLAB''s builtin lambertw function gives %0.4f.\n',lambertw(2))
MATLAB's builtin lambertw function gives 0.8526.

Problem 2: Find all the zeros of

First, let's just define the function and plot it to see what it looks like

f=@(x)(sin(x)+cos(3*x));

fplot(f,[0 2*pi])

xlabel('$x$');ylabel('$\sin{x}+\cos{3x}$')

I see six zeros. I will find them by defining an array of x values. If

, then there is a root on the interval

x=linspace(0,2*pi,101);
ff=f(x);
spots=find(ff(1:end-1).*ff(2:end)<0);

Note that if the zero occurs at one of the endpoints, it will be double counted. Eliminate duplicates:

spots = unique(spots);

plot(x,ff,x(spots),ff(spots),'ro',x(spots+1),ff(spots+1),'rx');

title('The zeros are between the $\circ$ and $\times$ marks')

xlabel('$x$');ylabel('$\sin{x}+\cos{3x}$')

xx=zeros(size(spots));

n=length(xx);

for k=1:n

xx(k)=fzero(f,x(spots(k):spots(k)+1));

end

plot(x,ff,xx,zeros(1,n),'o')

xlabel('$x$');ylabel('$\sin{x}+\cos{3x}$')

fprintf('The zeros are:\n')

The zeros are:

fprintf('%6.3f\n',xx)

0.785 1.178 2.749 3.927 4.320 5.890

The implementation of the Lambert-W function

function y=myLambert(xIn)
f=@(x)x.*exp(x)-xIn;
assert(xIn>-exp(-1),'xIn must be bigger than -1/e')
y=fzero(f,0);
end