Optimization of matlab code

I am relatively new in MATLAB and my major problem is optimization. My code seems to run very slowly and I can't think of any way to make it faster. All my arrays have been preallocated. S is a large number of element (say 1500 element, for example). i know my code runs slowly because of the "for k=1:S" but i cant think of another way to perform this loop at a relatively fast speed. Just to explain my code, i have a set of points and for each point i want to obtain the predicted_value and its predicted_error. Can i please get help because it takes hours to run (when S = 1000 elements, for example)

[M,~] = size(Sample2000_X);
[N,~] = size(Sample2000_Y);
[S,~] = size(Prediction_Point);

% Speed Preallocation
Distance = zeros(M,N);
Distance_Prediction = zeros(M,1);
Semivariance = zeros(M,N);
semivariance_Prediction = zeros(M,1);
Predicted_Value00 = zeros(S,1);
Predicted_Error = zeros(S,1);

for k=1:S
    for i=1:M
        for j=1:N
            Distance(i,j) = sqrt(power((Sample2000_X(i)-Sample2000_X(j)),2)+power((Sample2000_Y(i)-Sample2000_Y(j)),2));
        end
        Distance_Prediction(i,1) = sqrt(power((Prediction_Point(k,1)-Sample2000_X(i)),2)+power((Prediction_Point(k,2)-Sample2000_Y(i)),2));
    end

      Lagrange_Column = ones(M,1);
      Lagrange_Row = [ones(1,N),0];

      for i=1:M
          for j=1:N
              if (Distance(i,j) == 0)
                  Semivariance(i,j) = 0;
              elseif (Distance(i,j) > Range00)
                  Semivariance(i,j) = Nugget00+Sill00;
              else
                  Semivariance(i,j) = Nugget00+Sill00*((3*0.5*(Distance(i,j)/Range00))-(0.5*power((Distance(i,j)/Range00),3)));
              end
          end
          if (Distance_Prediction(i) == 0)
              semivariance_Prediction(i) = 0;
          elseif (Distance_Prediction(i) > Range00)
              semivariance_Prediction(i) = Nugget00+Sill00;
          else
              semivariance_Prediction(i) = Nugget00+Sill00*((3*0.5*(Distance_Prediction(i)/Range00))-(0.5*power((Distance_Prediction(i)/Range00),3)));
          end
      end
      Semivariance_Prediction = [semivariance_Prediction;ones()];
      Semivariance_Lagrange = [Semivariance,Lagrange_Column;Lagrange_Row];

      weights = Semivariance_Lagrange\Semivariance_Prediction;
      Weights = weights(1:end-1,:);

      Predicted_Value00(k,1) = sum(Sample2000_Z.*Weights);
      Predicted_Error(k,1) = sum(Semivariance_Prediction.*weights);
  end

Answer 1

[Jos (10584)]

Pre-allocate all your outputs before the loop.

Distance = zeros(M,N)
...

The editor should have given you a warning " The variable .. appears to be growing inside a loop". Did you notice the small red underlining in the editor?

[Darlington Mensah]

Yes. I pre-allocated all the output. I'm sure the problem is from the first for-loop but i dont know an alternative way to work on it.

[Stephen23]

@Darlington Mensah: you say that you have preallcoated your code, but we can't see this. Please edit your question and upload a complete copy of your code using the paperclip button.

[Darlington Mensah]

@Stephen: I have edited the code. Thanks

Answer 2

[Steven Lord]

Try to profile your code with a small data set to identify potential bottlenecks then improve or eliminate the bottlenecks identified during the previous step.