How to optimise this code?

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J 2016-1-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/265005-how-to-optimise-this-code

关闭： MATLAB Answer Bot 2021-8-20

Nested loops suck...how can I optimise this code?

function [a, v, x] = model1(x_s, x_a, OB, rho_0, K_a, K_r, K_v)
  ss = 0.01; % Step Size
  tmax = 60;
  c = 0; % Row index ID (for identification only)
  k = 1:length(OB); % Vectorisation
  x = [x_s(1); x_s(2)]; % Initial position
  v = [0; 0]; % Initial velocity
  a = [0; 0]; % Initial acceleration
  dUa = [1; 1];
  while ((dUa(1)^2 + dUa(2)^2) > 1e-10) && (c <= (tmax/ss)+1)
      dUr = 0; % Reset the force
      c = c + 1; % Add one to the row count (first iteration c = 1)
      dUa = K_a*(x(:,c) - x_a); % Calculate attractive force
      % Calculate distance from each obstacle
      rho_r = sqrt( (x(1,c)-OB(1,k)).^2 + (x(2,c)-OB(2,k)).^2 );
      for numobs = 1:length(OB) % Loop for the number of obstacles created
          if rho_r(numobs) > rho_0 % If outwith the obstacle radius
              dUrobs = 0; % No force experienced
          else % Otherwise
              dUrobs = K_r * ((1/rho_r(numobs)) + (1/rho_0)) * (OB(:,numobs)-x(:,c))/(rho_r(numobs)^3);
          end
          dUr = dUr + dUrobs; % Combine force from each obstacle to total
      end
      a(:,c+1) = -dUa - dUr - K_v * v(:,c); % Calculate acceleration
      v(:,c+1) = v(:,c) + a(:,c+1) * ss; % Calculate new velocity
      x(:,c+1) = x(:,c) + v(:,c+1) * ss; % Calculate new position
  end

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Answer 1

Jan 2016-1-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/265005-how-to-optimise-this-code#answer_207282

在 MATLAB Online 中打开

Pre-allocation!

n = ceil(c <= (tmax/ss) + 1);
x = zeros(2, n);
x(:, 1) = x_s(1:2); % Initial position
v = zeros(2, n); % Initial velocity
a = zeros(2, n); % Initial acceleration
...

The power operation is expensive, so do not compute it repeatedly: Omit zeros in the sum:

rho_r3 = rho_r ^ 3;
...
    for numobs = 1:length(OB) % Loop for the number of obstacles created
        if rho_r(numobs) <= rho_0 % If outwith the obstacle radius
            dUr = dUr + K_r * (1/rho_r(numobs) + (1/rho_0)) * ...
                              (OB(:,numobs)-x(:,c)) / rho_r3(numobs);
        end
    end

Crop the unused memory at the end:

x = x(:, 1:c);
v = v(:, 1:c);
a = a(:, 1:c);

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J 2016-1-25

Awesome! But is there a way to completely remove the nested for loop and instead replace it with a vectorised equivalent?

Jan 2016-1-31

在 MATLAB Online 中打开

Maybe. But it is not worth to spend hours in optimizing the code, when you save some seconds of runtime only. You can try this instead of the "for numobs" loop:

K = (rho_r <= rho_0);
dUR = sum(K_r .* (1 ./ rho_r(K) +  1 ./ rho_0) .* ...
          (OB(:, K) - x(:, c)) ./ rho_r3(K));

I cannot debug this due to the missing input data. Maybe some vectors must be transposed. But there migt be further problems with the sizes. Anyway, the underlying method is cleared.