Improve performance of linspace

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Shane
Shane 2015-4-21
编辑： Jan 2015-9-29
I am needing to greatly improve the performance of a line of code. I need to run this line of code millions of times. But it currently takes ~.7 second to run it once!
The code is as follows:
ShotBinsX = 0.5*sin(linspace(-1*SlowMirrorPhase,...
(2*pi*NumSlowMirrorPeriods)-SlowMirrorPhase,...
ShotsPerFrame+1)) + 0.5;
Where SlowMirrorPhase will take values from 1:12500, and NumSlowMirrorPeriod will take values from 1:~1000, and ShotsPerFrame will vary, but not exceed 10 million or so, but in many cases be in the millions range or less.
Any ideas on how to make it faster?!

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回答（4 个）

Matt J
Matt J 2015-9-28
编辑：Stephen23 2015-9-29
I'm not sure how you're looping right now, but if you write your loops as follows, you reduce the number of linspace evaluations by a factor of 12500 as compared to doing it for all combinations of all 3 variables.
for ShotsPerFrame=... : 1e7
for NumSlowMirrorPeriods=1:1000
LinspaceTerm = linspace(0, 2*pi*NumSlowMirrorPeriods, ShotsPerFrame+1);
for SlowMirrorPhase=1:12500
ShotBinsX = 0.5*sin(LinspaceTerm-SlowMirrorPhase) + 0.5;
end
end
end
The first term involving linspace can be precomputed
  2 个评论
Matt J
Matt J 2015-9-28
编辑：Stephen23 2015-9-29
You can also vectorize the innermost loop to cut down on some overhead,
SlowMirrorPhase = (1:12500).';
for ShotsPerFrame=... : 1e7
for NumSlowMirrorPeriods=1:1000
LinspaceTerm = linspace(0, 2*pi*NumSlowMirrorPeriods, ShotsPerFrame+1);
sineArg=bsxfun(@minus,LinspaceTerm,SlowMirrorPhase);
ShotBinsX = 0.5*sin(sineArg) + 0.5;
end
end
Matt J
Matt J 2015-9-29
Here's an even better version. Now you're only calling linspace once per value of ShotsPerFrame.
SlowMirrorPhase = (1:12500).';
for ShotsPerFrame=... : 1e7
LinspaceTerm = linspace(0, 2*pi, ShotsPerFrame+1);
for NumSlowMirrorPeriods=1:1000
sineArg=bsxfun(@minus,LinspaceTerm*NumSlowMirrorPeriods,...
SlowMirrorPhase);
ShotBinsX = 0.5*sin(sineArg) + 0.5;
end
end

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pfb
pfb 2015-4-21
are you sure that it is a matter of linspace? Did you try profiling your code?
I'd say the "problem" is in the sin function, which I expect to be much slower than linspace itself.
Maybe you can tweak your grid a little bit in order to take advantage of the periodicity of the sin function.
Jeff Lentz
Jeff Lentz 2015-9-28
I agree with pfb that sin could be a bigger problem than linspace.
But I have observed slow performance in linspace before. I wrote my own linspace function that is about 4 times faster than the built-in MATLAB linspace (tested in 2012a but not very thoroughly.) However, it WILL have small amounts of rounding error when compared to the original.
function y = linspace(a, b, n)
y = (b-a)/(n-1)*(0:n-1) + a;
end
Jan
Jan 2015-9-29
编辑：Jan 2015-9-29
What about inlining linspace?
d1 = -SlowMirrorPhase; % Faster than -1 * ...
d2 = (2*pi*NumSlowMirrorPeriods) - SlowMirrorPhase;
n = ShotsPerFrame + 1;
k = 2*pi*NumSlowMirrorPeriods; % Move bevor the loop
% X = [d1 + (0:n-2) .* (d2 - d1)/n1, d2]
X = [-SlowMirrorPhase :k: ((n-2)*k) - SlowMirrorPhase) ./ ShotsPerFrame , d2];
ShotBinsX = sin(X) / 2 + 0.5;

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