Conversion function taking a very long time to run in loop, anyway to improve?

I created a function that does a simple conversion to my data with two coordinates being the input (below)

%%
function [ GazeDirDegrees ] = ConvertGazeDir( GazeDir1,GazeDir2 )
GazeDirDegrees = 180*asin(GazeDir1/sqrt(GazeDir1.^2+GazeDir2.^2))/pi
end

I am running this in a loop over 120 cells, with each cell containing 1000-1700 data points. As you can imagine this means that the function has to be called over 120,000 times. Not only that, but I have to run this loop 4 times for 4 different variables. (below is an example for just one variable))

%%
for i = 1:length(LeftGazeDirX)
    for b = 1:length(FilteredLeftGazeDirX{1,i})
     ConvLeftGazeDirX{b,i} = ConvertGazeDir(FilteredLeftGazeDirX{1,i}(b,1),FilteredLeftGazeDirZ{1,i}(b,1))
    end
end

Not sure if there is anything I can do to make this run more efficiently, as it currently takes about 20 seconds for a single cells worth of data.

Answer 1

[Walter Roberson]

Vectorize your formula by replacing the / with ./ and then you can pass in entire cells (provided the two cells are the same size)

Also you can improve performance slightly by making it 180/pi * .... instead of 180*.../pi so that the division by pi only has to be done once

Also consider using asind without the 180/pi

[JM]

The vectorized solution worked great, thank you!

Answer 2

[Steven Lord]

Call asind on arrays of data instead of on scalars. Use the hypot function if your data is real.

n = 100;
X = rand(n);
Y = rand(n);

tic
Z = asind(X./hypot(X, Y));
toc

tic
Z2 = asind(X./sqrt(X.^2+Y.^2));
toc

differenceBetweenApproaches = norm(Z-Z2)

The difference between the two approaches should be small.