MaplePrimes - answers and comments on Question, Using random numbers

Are they calculated equally fast?

gkokovidis — Sun, 09 Sep 2012 06:20:18 Z

You can determine the speed difference yourself, to see which is better, based on how many values you need to calculate. I ran both of your code segement twice. The time difference will vary based on machine speed and memory. For small values of i, <100000, the time difference between the two versions is not noticeable.

>	restart:st := time():

>	for i from 1 by 1 to 5000000 do

>	randomize():

>	rand()/(1000000000000.);

end do:

>	time() - st;

(1)

>	restart:with(RandomTools[MersenneTwister]):st := time():

>	for i from 1 by 1 to 5000000 do

>	randomize():

>	GenerateFloat();

end do:

>	time() - st;

(2)

>	restart:st := time():

>	for i from 1 by 1 to 5000000 do

>	randomize():

>	rand()/(1000000000000.);

end do:

>	time() - st;

(3)

>	restart:with(RandomTools[MersenneTwister]):st := time():

>	for i from 1 by 1 to 5000000 do

>	randomize():

>	GenerateFloat();

end do:

>	time() - st;

(4)

Download randtime.mw

Regards,

Georgios Kokovidis

Dräger Medical

speed

acer — Sun, 09 Sep 2012 06:50:56 Z

If you want it fast then you could compute the random values up front, using Statistics:-Sample and then access them one at a time, as you need them, from that resulting Array/Vector.

It will take memory, however, to store all the precomputed values up front. It is also possible to take a middle road -- by precomputing in smaller batches. In recent Maple a float[8] Vector can be (memory efficiently) re-used repeatedly as the container into which one periodically computes batches of the random values.

Another way to precompute a sample of floats from the uniform distribution on [0,1) is with the `rtable` constructor, or more conveniently by accessing that though the LinearAlgebra package's commands `RandomVector` and `RandomMatrix`.

V:=LinearAlgebra:-RandomVector[row](3,generator=0.0..1.0,
                                 outputoptions=[datatype=float[8]]);

       V := [0.223811939491137, 0.585267750979777, 0.340385726666133]

X:=Statistics:-RandomVariable('Uniform'(0,1)):

S:=Statistics:-Sample(X,3);

       S := [0.751267059305653, 0.255095115459269, 0.505957051665142]

Statistics:-Sample(X,S):  # re-using S
S;

          [0.699076722656686, 0.890903252535798, 0.959291425205444]

You can compare with calling GenerateFloat() or rand() repeatedly. Note that `randomize` usually only needs to be called once, upon restart. The following is on 64bit Maple 16.01 for Windows 7.

restart:
randomize():
st := time():
X:=Statistics:-RandomVariable('Uniform'(0,1)):
S:=Statistics:-Sample(X,5000000):
for i from 1 by 1 to 5000000 do
S[i];
end do:
time() - st;

                                    2.792

restart:
randomize():
with(RandomTools[MersenneTwister]):
st := time():
for i from 1 by 1 to 5000000 do
GenerateFloat();
end do:
time() - st;

                                   11.170

restart:
randomize():
st := time():
for i from 1 by 1 to 5000000 do
rand()/(1000000000000.);
end do:
time() - st;

                                   29.063

Statistics:-Sample and the rtable constructors also respect the `randomize()` command.

acer

Time command

erik10 — Sun, 09 Sep 2012 16:13:49 Z

Thanks to both of you. I learned the time command and several new ways to collect random numbers. I am trying to simulate how well the distribution of Karl Pearsons well-known Test Statistics is following the Chi-Square distribution. I will need a high number of samples, so probably I can use some of the techniques you describe.

Erik