a matlab code of getting a value uniformly at random from a the set {-1,1}

I need to get a value uniformly at random from a the set {-1,1}

Answer 1

[Massimo Zanetti]

If you look for a real number in the interval [-1,1], here is it

n = 2*rand-1

If you look for an integer either 1 or -1, here is it

n = 2*randi(2)-3

[James Tursa]

Neither of these produce results from the set {-1,1} as requested.

[Massimo Zanetti]

The first one returns a random REAL number in the interval [-1,1]. That is why it doesn't return only -1 or 1.

The second one, I have fixed it. Now it returns a random integer among {-1,1}.

Answer 2

[Matthew Eicholtz]

To generate values uniformly from the set {-1,1}, use:

N = 100;
x = 2*(rand(N,1)>0.5)-1;

where N is the number of values you want.

Answer 3

[Walter Roberson]

>> N=10000000;
>> timeit(@() 2*(rand(N,1)>0.5)-1, 0)
ans =
    0.1797
>> timeit(@() 2*randi(2,N,1)-3, 0)
ans =
    0.1467
>> timeit(@() 2*round(rand(N,1))-1, 0)
ans =
    0.1269

[Walter Roberson]

Using

N=10000000;
clear x;tic;x=2*round(rand(N,1))-1;toc   %"round"
clear x;tic;x=2*(rand(N,1)>0.5)-1;toc    %"rand>"
clear x;tic;x=2*randi(2,N,1)-3;toc       %"randi"

and taking the lowest of several timings for each of the three, I record

same Virtual machine with Windows 10 (host is Mac)

• R2011b: round 0.169, rand> 0.187, randi 0.218
• R2012b: round 0.165, rand> 0.191, randi 0.220
• R2013b: round 0.172, rand> 0.193, randi 0.220
• R2015a: round 0.179, rand> 0.180, randi 0.169
• R2015b: round 0.176, rand> 0.184, randi 0.155
• R2016a: round 0.166, rand> 0.178, randi 0.156
• R2016b: round 0.165, rand> 0.176, randi 0.150

So round did not change much; rand> got slightly faster; and randi improved a fair bit

Native on host (OS-X El Capitan)

• R2014b: round 0.141, rand> 0.214, randi 0.144 %but randi was faster on average
• R2015a: round 0.140, rand> 0.238, randi 0.148 %but randi was faster on average
• R2015b: round 0.127, rand> 0.169, randi 0.143
• R2016a: round 0.105, rand> 0.144, randi 0.122
• R2016b: round 0.093, rand> 0.165, randi 0.117

so the three all got faster, but not all at the same time

The times to process rand> were sometimes worse on native OS-X than on emulated Windows 10, but the final times are pretty comparable; it might even be the case that if I were to boot into Windows 10 that the times for rand> might be better than running it in OS-X .

The final processing times for round are much better on OS-X

randi appears to have gotten faster on OS-X as of R2016a.

I note that the timing of randi getting faster differs between operating systems.

Answer 4

[kortas manel]

thank you for your answerers

Answer 5

[James Tursa]

Yet another way (although Matthew's Answer is faster so I voted for it):

N = number of values
R = 2*randi(2,N,1) - 3;

[Massimo Zanetti]

Matthew's way is NOT faster:

N=10000000;
tic;
x = 2*(rand(N,1)>0.5)-1;
toc
Elapsed time is 0.187635 seconds.

tic;
y = 2*randi(2,N,1)-3;
toc
Elapsed time is 0.140225 seconds.

Try several times to convince yourself. The reason is simple: Matthew's method other than generating random numbers, also have to threshold a big vector.

[James Tursa]

It is on my computer. Tested several times with large N. Results can obviously vary with machine & OS & MATLAB version. Timing can also vary depending on what is most recently in the cache, etc.

[Walter Roberson]

Could you show the timings for the 3 versions I show?

[James Tursa]

When I get to my other computer in the morning.

[James Tursa]

I happened to be using PCWIN 32-bit R2011b for the testing, which doesn't have timeit. However, here are the manual timing results:

>> version
ans =
7.13.0.564 (R2011b)
>> 
>> N=10000000;
>> 
>> clear x;tic;x=2*(rand(N,1)>0.5)-1;toc
Elapsed time is 0.206160 seconds.
>> clear x;tic;x=2*(rand(N,1)>0.5)-1;toc
Elapsed time is 0.181466 seconds.
>> clear x;tic;x=2*(rand(N,1)>0.5)-1;toc
Elapsed time is 0.182702 seconds.
>> 
>> 
>> clear x;tic;x=2*randi(2,N,1)-3;toc
Elapsed time is 0.259775 seconds.
>> clear x;tic;x=2*randi(2,N,1)-3;toc
Elapsed time is 0.244608 seconds.
>> clear x;tic;x=2*randi(2,N,1)-3;toc
Elapsed time is 0.251186 seconds.
>> 
>> 
>> clear x;tic;x=2*round(rand(N,1))-1;toc
Elapsed time is 0.151603 seconds.
>> clear x;tic;x=2*round(rand(N,1))-1;toc
Elapsed time is 0.164555 seconds.
>> clear x;tic;x=2*round(rand(N,1))-1;toc
Elapsed time is 0.150253 seconds.

So, the rand beats randi for my particular setup, but your round method is better yet. I'll have to remember that one! (and give you a vote)

[Walter Roberson]

timeit is also in the File Exchange; https://www.mathworks.com/matlabcentral/fileexchange/18798-timeit-benchmarking-function