Can this algorithm be simplified (written cleaner) ?

Question

Hi,

I have this algorithm, but I am not too keen on the many if-statements.

Can someone see if this function can be written in a cleaner way?

rand('twister',101)

n = 10;
f = A.^(0:n)./factorial(0:n);
f = f/sum(f);
n = 10000;
Xi = 2;
X = zeros(1,n);

for i =1:n,
    dXi = (-1)^round(rand);
    Yi = Xi + dXi;
    if Yi > 0 & Yi <= length(f),
        if f(Yi) >= f(Xi),
            X(i) = Yi;
            Xi = Yi;
        else
            if rand <= f(Yi)/f(Xi),
                X(i) = Yi;
                Xi = Yi;
            else
                X(i) = Xi;
            end
        end
    end
    X(i) = Xi;
end

Answer 1

I don't know Matlab syntax, but generally something like this:

if (cond1) then
   mainAction
else if (cond2) then
        mainAction
     else
        otherAction

can be simplified as:

if (cond1 OR cond2) then
   mainAction
else
   otherAction

The OR would have to be short-circuiting for exact equivalence, but if cond2 has no side-effects then it doesn't really matter.

Answer 2

This can be simplified by noting that whenever you do X(i) = Yi you also do Xi = Yi and therefore you could just assign X(i) once at the end of the loop. This allows a lot of the other logic to simplify.

Also note that the , at the end of an if-clause is really only necessary in one-line if statements, e.g.

if x < y, do_something, else do_something_else, end 

Anyway I get this (you could simplify further into one if statement but perhaps that's less clear. Also having more than one if statement allows breakpoints on particular sections.):

for i =1:n,
    dXi = (-1)^round(rand);
    Yi = Xi + dXi;
    if Yi > 0 & Yi <= length(f)
        if f(Yi) >= f(Xi) || rand <= f(Yi)/f(Xi)
            Xi = Yi;
        end
    end
    X(i) = Xi;
end