increase compute speed compute angle between 2 vectors

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franck lepapaix
franck lepapaix 2016-2-17
评论： Rena Berman 2017-1-24
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
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franck lepapaix
franck lepapaix 2016-2-17
it was my first idea to reduce the time. but I can't do that , in fact I make computation of many objects in space and for position compution (orbit) I compute many point each 10 minutes during one year, and for that I can't increase blocks, my vectors are tri-dimensionnal !(thk mister Kepler)

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Jan
Jan 2016-2-17
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);
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franck lepapaix
franck lepapaix 2016-2-19
编辑：franck lepapaix 2016-2-19
thx for your help, my vectors are [222651 x 3] size !! that's why I use n in my post ! I have no idea about the use of vectorization in matlab, I think this is the next step for me to optimize the speed..
Jan
Jan 2016-2-19
编辑：Jan 2016-2-19
And you provide this [222651 x 3] matrix as input, or do you call the function in a loop for each [1 x 3] vector? The command norm(u) in your code seems to imply, that you call it for vectors. The code in my answer can process the complete matrix in one call, which should be substantially faster. Even a fast C-Mex function, which avoids the creation of large temporary arrays, would suffer from beeing called hundret thousands of times due to the calling overhead.

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