Vectorize For-If-Elseif Loop

I am struggling with vectorizing this parfor loop. I want to completely remove the parfor loop from the code as it is taking a long time to execute when n is large. Please see the code pasted below. The vectorization I have done so far is also posted below. I will appreciate if any person in this forum can help me look at the vectorized codes and let me know where I got it wrong. Many thanks in advance.

% Initialization and precomputations
% w is an n x 1 vector
% beta: any number larger than 0. Usually set to 1.

f = zeros(n,1);
x = w;
y = w;
rho = 1;
v = f – (rho*y);
rhow = rho*w;
n = length(w);

parfor i = 1 : n

      if w(i) >= 0
          if v(i) < -rhow(i) – beta – 1
              x(i) = (-beta -1 -v(i))/rho;

          elseif (-rhow(i) – beta – 1 <= v(i)) && (v(i) <= -rhow(i) + beta – 1)
              x(i) = w(i);

          elseif (-rhow(i) + beta – 1 < v(i)) && (v(i) < beta – 1)
              x(i) = (beta – 1 -v(i))/rho;

          elseif (beta – 1 <= v(i)) && (v(i) <= beta + 1)
              x(i) = 0;

          else
              x(i) = (beta + 1 – v(i))/rho;
          end

      else

          if v(i) < -beta -1
              x(i) = (-beta -1 – v(i))/rho;

          elseif (-beta – 1 <= v(i) )&& (v(i) <= -beta + 1)
              x(i) = 0;

          elseif (-beta + 1 < v(i)) && (v(i) < -rhow(i) – beta + 1)
              x(i) = (-beta + 1 – v(i))/rho;

          elseif (-rhow(i) – beta + 1 <= v(i)) && (v(i) <= -rhow(i) + beta + 1)
              x(i) = w(i);

          else
              x(i) = (beta + 1 – v(i))/rho;
          end

      end
  end

===================================================================================

    cond1 = (w >= 0);
    cond2 = (cond1) & (v < -rhow-beta-1);       
    x(cond2) = (-beta-1-v(cond2))/rho; 

    cond3 = (cond1)&(-rhow - beta -1 <= v) & (v <= -rhow + beta - 1);
    x(cond3) =  w(cond3);

    cond4 = (cond1) & (-rhow +beta - 1 < v) & (v < beta - 1);
    x(cond4) = (beta - 1 - v(cond4))/rho;

    cond5 = (cond1) & (beta - 1 <= v) & (v <= beta + 1);
    x(cond5) = 0;

    cond6 = (cond1) & (~(v < -rhow -beta - 1));
    x(cond6) = (beta + 1 - v(cond6))/rho;

    cond7 = ((~cond1) & (v < -beta -1));
    x(cond7) = (-beta -1 - v(cond7))/rho;

    cond8 = ((~cond1) & (-beta - 1 <= v) & (v <= -beta + 1));
    x(cond8) = 0;

    cond9 = ((~cond1) & (-beta + 1 < v) & (v < -rhow - beta + 1));
    x(cond9) = (-beta + 1 - v(cond9))/rho;

    cond10 = ((~cond1) & (-rhow - beta + 1 <= v) & (v <= -rhow + beta + 1));
    x(cond10) = w(cond10);

    cond11 = ((~cond1) & (~(v < -beta - 1)));
    x(cond11) = (beta + 1 - v(cond11))/rho;

Answer 1

[Walter Roberson]

Construct your selection criteria and store it in a variable, and then use the same selector on both the left and right side.

For example,

cond1 = (w >= 0) & (v < -rhow-beta-1);
x(cond1) = (-beta-1-v(cond1))/rho;

And remember, white-space is free but the time of the humans trying to understand the code isn't.

[Chimalume Atuchukwu]

Hi Walter,

Thanks for the correction. I have effected it. Kindly help me review the corrected version and let me know if can see where I made some errors. Thank you for your help.

[Walter Roberson]

Instead of continually recalculating w>=0 such as in your current cond2

    cond2 = (w >= 0) & (v < -rhow-beta-1);

take advantage of the fact that you have already calculated it and stored it in cond1:

    cond2 = cond1 & (v < -rhow-beta-1);

Your cond6 is broken. ~cond2 is ~(cond1 & (v < -rhow-beta-1)) which is (~cond1) | ~(v < -rhow-beta-1)) which is true if cond1 is false or if v is in the next range over. If I read correctly, your cond6 should be

cond6 = cond1 & v(i) > beta + 1;

You have a similar problem for your cond11; it looks to me that it should be

cond11 = ~cond1 & v > -rhow(i) + beta + 1;

If I were doing the implementing I would probably use histc() in the two-output version to classify the range that v was in, and then (for example)

[counts, binnum] = histc(v, [-inf, -rhow-beta-1, -rhow(i) + beta – 1, beta – 1, beta + 1, inf]);
cond2 = cond1 & binnum == 1;
cond3 = cond2 & binnum == 2;

and so on.