Display precision vs actual precision

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Mario Trevino
Mario Trevino 2014-7-30
评论： Seth Wagenman 2014-9-3
Hi everyone We are running some simulations in MATLAB and storing the results afterwards. Yet, we are concerned that the actual precision of the number format used to solve the equations might be huge with respect to what we actually need. For instance, one of the output variables of the program is voltage, which is bound to -120<=V<=40 and we require a max resolution of about 0.01, no more than that....my guess is that the number precision provided by MATLAB is exceeding our needs and this is costing us computing time.....
any comments on this?
thanks!
mario
  2 个评论
Sara
Sara 2014-7-30
It's preferable to do all your calculations with higher precision than needed and only round the results. You may use single variables instead of the default (double) but I'm not sure you'll have any speed up. You could build a toy problem and check it out.
Seth Wagenman
Seth Wagenman 2014-9-3
Do the toy problems below convince you that speed will increase if you use single variables vs. doubles?

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采纳的回答

Image Analyst
Image Analyst 2014-8-2
编辑：Image Analyst 2014-8-2
Your only choices are to cast your variables to single or double. The calculations will take the same amount of time no matter if you use "format long" or "format short" - the number of decimal places upon output do not have any effect on what's being used in the mathematical operations. Using single will cut your memory usage down by half.
Using single will make the calculations faster. See this demo:
m1 = rand(12345,12345);
m2 = rand(size(m1));
tic;
for expt = 1 : 10
m3 = m1 .* m2;
end
toc;
m1 = single(m1);
m2 = single(m2);
tic;
for expt = 1 : 10
m4 = m1 .* m2;
end
toc;
The results:
Elapsed time is 2.756050 seconds.
Elapsed time is 1.518655 seconds.
  2 个评论
Seth Wagenman
Seth Wagenman 2014-9-3
编辑：Seth Wagenman 2014-9-3
I do not know what "expt" and the loop was for (and my computer froze when I tried the script above) so I tried this and got similar results:
m1 = rand(999,999);
m2 = rand(size(m1));
tic
m3 = m1 .* m2;
toc
m1 = single(m1);
m2 = single(m2);
tic
m4 = m1 .* m2;
toc
Elapsed time is 0.011342 seconds.
Elapsed time is 0.007512 seconds.

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更多回答（1 个）

Andrew Reibold
Andrew Reibold 2014-7-30
编辑：Andrew Reibold 2014-7-30
To round to the hundredths place
X_rounded_to_hundredth = round(X*100)/100
Matlab still stores '0's after though. Not sure if you can increase computing time.
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Image Analyst
Image Analyst 2014-8-2
I've heard that (because modern CPUs are so highly optimized that it doesn't matter), so that's why I wrote my code - to test it. Surprisingly I found, at least for that one example, that the single calculations took about half as long, though perhaps it might be dues to a memory thrashing issue due to larger arrays rather than purely due to the multiplication times. I should test that.
Seth Wagenman
Seth Wagenman 2014-9-3
One problem with single variables...if they are ever part of any future calculation, all products become single variables as well, even if a double were part of the calculation.

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