MATLAB: How to write multiple levels of if-else statements

conditionelseif

Hi,
i am trying to write a code for the following:
h(x,y) = h_init, if (X,Y)not equal to Q
h(x,y) = h_init+h_step, if (X,Y)equal to Q
where Q is:
-3/4<X<3/4, and
[(1/sqrt3)X+(K-.5)*sqrt(3)/2]<Y<[X/sqrt3 + sqrt3/4], if Y>0     OR
[-X/sqrt3-sqrt3/4]<Y<[-X/sqrt3+(0.5-K)sqrt3/2], if Y<0
This is my current code but it is giving me errors:
    K=0.2; % ratio of length of inner and outer triangles 0<K<1
    R_P=sqrt((16*delta_sq*r_1^2)/(3*sqrt(3)*(1-K^2)));
    h_step = 5e-06; % step microasperity depth
    nHi=max(size(X));
    nHj=max(size(Y));
    % flat step condition
    for ii=1:nHi,
        for jj=1:nHj,
            if (X(ii)/R_P)>(-3/4) & (X(ii)/R_P)<(3/4),
                if ((Y(ii)/R_P)>0),
                (Y(ii)/R_P)>((X(ii)/(R_P*sqrt(3)))+(((K-0.5)*sqrt(3))/2)) & (Y(ii)/R_P)<((X(ii)/(R_P*sqrt(3)))+(sqrt(3))/4),    
                h(ii,jj)=h_init+h_step;
                if ((Y(ii)/R_P)<0),
                (Y(ii)/R_P)>((-(X(ii))/(R_P*sqrt(3)))-(sqrt(3))/4) & (Y(ii)/R_P)<((-(X(ii))/(R_P*sqrt(3)))+(((0.5-K)*sqrt(3))/2)),
                h(ii,jj)=h_init+h_step
                elseif (X(ii)/R_P)<(-3/4) & (X(ii)/R_P)>(3/4),
                h(ii,jj)=h_init;
                end
                end
            end
        end
    end
I think the mistake lies with the different levels of the if-condition. The code provided gives me errors as some parts of the domain are not defined, as per Matlab error. Any help will be appreciated.

Best Answer

Tim - there are a couple of things that you need to address in the conditions for your if/elseif statements.
Replace the single ampersands (&) with double ampersands so that short circuiting of the logical operations can occur. While the single ampersand works, it doesn't employ the short-circuiting behaviour. For example, your first if condition would become
 if (X(ii)/R_P)>(-3/4) && (X(ii)/R_P)<(3/4)
Note how I removed the comma from the end of the statement (not needed). You could also replace the above with the absolute function, abs
 if abs(X(ii)/R_P) < 3/4
unless you are concerned with performance. Now with this if you will need an else, because if X doesn't satisfy this condition then you know that (X,Y)not equal to Q so the above becomes
 if abs(X(ii)/R_P) < 3/4
     % maybe Q is satisfied



 else
     % Q is definitely not satisfied

     h(ii,jj)=h_init;
 end
Now we move to the section commented above maybe Q is satisfied, and do something similar with the Y
 if abs(X(ii)/R_P) < 3/4
     % maybe Q is satisfied
     if (Y(ii)/R_P)>0
         % maybe Q is satisfied
     elseif (Y(ii)/R_P)<0
         % maybe Q is satisfied
     else
         % Y is zero, so Q definitely not satisfied
         h(ii,jj)=h_init;
     end
 else
     % Q is definitely not satisfied
     h(ii,jj)=h_init;
 end
So I've added the three cases for Y being positive, negative and zero. Again I've removed commas from the end of the conditions. I've done it this way because I don't see how having two conditions separated by a comma will correctly give you what you need
 if ((Y(ii)/R_P)>0),(Y(ii)/R_P)>((X(ii)/(R_P*sqrt(3)))+(((K-0.5)*sqrt(3))/2))
Now repeat this pattern of maybe Q satisfied and Q definitely not satisfied for the above if and elseif. You will always want to include a final else body so that h is initializes to something.
Do note how your elseif statement will never evaluate to true
 elseif (X(ii)/R_P)<(-3/4) & (X(ii)/R_P)>(3/4)
The code tries to see if X(ii)/R_P is less than -3/4 AND X(ii)/R_P is greater than 3/4. Usually, you would want to replace this with a logical or like
 elseif (X(ii)/R_P)<(-3/4) || (X(ii)/R_P)>(3/4)
but I think that you can do away with altogether because we have added the final else statement to the block of code to handle when X doesn't fit in the interval (-3/4,3/4).
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