MATLAB: Increase compute speed compute angle between 2 vectors

angleaxiscomputecrossdotincreasenormspeedvector

hi, I'm student in a space compagny and I have built a matlab soft to compute orbit , but the run take more than 48h, in fact, one function was call more than billion time, and also I search to win some milliseconde in my funtion.
this funtion compute angle between 2 vectors input : 2 vectors v & u (3 by n) output : angle between u and v in rad (n by 1)
here after the code , but I don't find more solution to optimize it :
function angle = searchAngle(u, v)
norm = @(v) sqrt(sum(v.^2, 2));
dot = @(u, v) sum(u .* v, 2);
cross = @(a, b) [ a(:,2) .* b(:,3) - a(:,3) .* b(:,2), ...
      a(:,3) .* b(:,1) - a(:,1) .* b(:,3), ...
      a(:,1) .* b(:,2) - a(:,2) .* b(:,1) ];
normVect = norm(u) .* norm(v);
dotVect = dot(u, v); 
threshold = normVect * 0.9999;
idx1 = dotVect > threshold;
axis = cross(v(idx1,:), u(idx1,:));
angle(idx1) = asin(norm(axis) ./ normVect(idx1));
idx2 = dotVect < -threshold;
axis = cross(v(idx2,:), u(idx2,:));
angle(idx2) = pi - asin(norm(axis) ./ normVect(idx2));
idx = ~(idx1 | idx2);
angle(idx) = acos(dotVect(idx) ./ normVect(idx));
end
thx for any help

Best Answer

The indirection of anonymous functions costs time. So either use the built-in functions with the same names cross, norm and dot, or hard code the functions directly.
Instead of the expensive trick to determine the positions of instabilities in the ASIN and ACOS methods, use a stable method directly:
atan2(norm(cross(N1 x N2)), dot(N1, N2))
Where N1 and N2 are the normalized input vectors.
N1      = bsxfun(@rdivide, a, sqrt(sum(a .* a ,1)))
N2      = bsxfun(@rdivide, b, sqrt(sum(b .* b ,1)))
N1dotN2 = N1(:, 1) .* N2(:, 1) + N1(:, 2) .* N2(:, 2) + N1(:, 3) .* N2(:, 3);
N1xN2   = [(N1(:, 2) .* N2(:, 3) - N1(:, 3) .* N2(:, 2)), ...
         (N1(:, 3) .* N2(:, 1) - N1(:, 1) .* N2(:, 3)), ...
         (N1(:, 1) .* N2(:, 2) - N1(:, 2) .* N2(:, 1))];
Angle   = atan2(sqrt(sum(N1xN2 .* N1xN2, 1)), N1dotN2);
Related Question