Cutting time using optimization instead of a potentially endless for loop ?

Okay, so I have written a code that generates two linear piecewise functions: a hot stream and a cold stream. The hot stream begins below the cold stream and the x axis (temperatures) is fixed. Essentially I am trying to move the hot stream up (positive y direction) until the minimum temperature difference reaches some variable. As of now, I have a for loop that works great, but takes roughly four minutes to run;according to viewer this is all due to the for loop and using ppval inside the for loop. The code I have now for this part is:

    dhdc = [];
  raise_hot_y = 0;

for i = 1:length(unique_cold_temps)
    dhdc(i) = (interpFunction((Hcoldpt(i)+raise_hot_y),hotStreamInterp))- unique_cold_temps(i);
end

dcdh = [];
for i=1:length(unique_hot_temps)
    dcdh(i) = interpFunction((Hhotpt(i)+raise_hot_y), coldStreamInterp) - unique_hot_temps(i);
end

while min(min(abs(dhdc)), min(abs(dcdh))) >= epsilon
    for i = 1:length(unique_cold_temps)
        dhdc(i) = (interpFunction((Hcoldpt(i)+raise_hot_y),hotStreamInterp))- unique_cold_temps(i);
    end

      for i=1:length(unique_hot_temps)
          dcdh(i) = interpFunction((Hhotpt(i)+raise_hot_y), coldStreamInterp) - unique_hot_temps(i);
      end
      raise_hot_y = raise_hot_y + .1;
  end

Is there some way I can use an optimization technique or solver to solve for the raise_hot_y value (how much I must increase the intercept of the function) that is much more time efficient?

Answer 1

[Andrew Newell]

Certainly there is, but I'm not sure quite how to formulate it with the information given. It will look something like this. Put your hot and cold points into a single variable, e.g., hotcoldpt, and do the same for your interpolation hotcoldStreamInterp and your target values unique_temps. Vectorize interpFunction and then create an anonymous function:

f = @(x) interpFunction(Hholdcoltpt+x,holdcoldStreamInterp)-unique_temps;

Finally, solve:

raise_hot_sol = fsolve(f,raise_hot_sol_guess);

This finds the solution to f=0.

[David Hagan]

I'm not quite sure that would work exactly because the two piecewise functions are completely independant -- I'm not sure what side effects there may be by combining them. However, I did just write up a much better description of my problem (including an image!) that may help greatly if you are interested. I posted it on my website at http://wp.me/p1CeAi-3v . Any help would be greatly appreciated. Thanks!

[Andrew Newell]

I'm assuming they are independent. The function |interpfunction| is just a black box that takes some vector |x| and outputs a vector |y|. It could call a different function for each component of the input - if you wished.