random numbers on the half open interval

The function rand generates random numbers on the open interval (0,1). How can I generate random numbers on (0,1]?

Answer 1

[Jan]

The chance to get 1.0 exactly is 1:2^52. It is small, but when you want to be sure, that your code run properly, such details should not be neglected. I have personally seen a function crashing, because it did not catch the case, when the random value is exactly zero.

Although the algorithm for random numbers in [0, 1) is fast due to its simplicity, Matlab's RAND produces (0,1). I did not find an algorithm for this, so I assume, that the 0.0 is simply rejected. It is not trivial to inject it afterwards, but you can emulate the algorithm relative efficiently by obtaining two 32bit integers:

s = RandStream('mt19937ar','Seed',0)
RandStream.setGlobalStream(s);
r1 = randi([0, 4294967295]);
r2 = randi([0, 4294967295]);
r  = (2097152 * r1 + fix(r2 / 2048)) / 9007199254740992;

For 0<=r<=1 you need:

r  = (2097152 * r1 + fix(r2 / 2048)) / 9007199254740991;

For 0<r<=1:

r  = (1 + 2097152 * r1 + fix(r2 / 2048)) / 9007199254740992;

Perhaps this is faster when UINT32 types are used in RANDI, but I cannot test this currently.

Well, I do not think that this is nice. Encapsulating this inside a C-MEX function would faster and perhaps more reliable. I'm working on such a function, because I'm really too confused by the changes in RAND, RNG and RANDSTREAM, when I write software which must be compatible with Matlab 6.5 to 2013a.

NOTE: There have been many bugs in published software for RNGs. Be sure to test this by your own before using it. Set r1 and r2 to 0 and 2^32-1 manually to check if the results really matches the claimed range!

[Cristina]

Thank you for your help!

Answer 2

[Image Analyst]

I think the same way. I mean, what is the possibility that you'll ever get exactly 1.0000000000000000000000000000000000000 anyway? Virtually never.

[Jan]

The chance is small, but not 0. It is more likely, that a program fails by forgetting the 0.0 if the RNG replies 0<x<=1, but even the 1.0 might be important for any reason.

[Image Analyst]

Theoretically, but in practice you'd need to calculate a billion numbers a second for about 20 trillion trillion universe lifetimes to get a 1 if the chance was 1 in 2^52.

c=1e52 % chance to hit exactly 1.0
randNumsPerSecond = 1e9 % a billion numbers per second
secondsToGenerate = c/1e9
secondsPerYear = 60*60*24*365.24
YearsToGenerateAllNumbers = secondsToGenerate / secondsPerYear
universeLifetimes = YearsToGenerateAllNumbers / 15e9

c =
                   1e+52
randNumsPerSecond =
              1000000000
secondsToGenerate =
                   1e+43
secondsPerYear =
  31556736
YearsToGenerateAllNumbers =
    3.16889554103441e+35
universeLifetimes =
    2.11259702735627e+25

So that's why I say it doesn't matter, except in a theoretical sense.

[Jan]

Perhaps the OP was asked to write a function with these specifications and the reliability of the code must be proved by forcing the RNG to reply the extremal values. Then it is not a question of fair probability.

Btw, pi*1e7 is a nice approximation for the number of seconds per year. This is a direct effect of the almost circular trajectory of the earth ;-)

Answer 3

[Azzi Abdelmalek]

tol=0.001;
a=randi(1/tol,2000,1)*tol; %generate 2000 random numbers (0 1]
% check values equal to 1
find(a==1)