MATLAB Central Newsreader - Random matrix with zeros and ones and twos

Random matrix with zeros and ones and twos

Tim Smith — Mon, 10 Nov 2008 18:41:03 -0500

Hey,

I need to create a 100 x 100 matrix filled 80% with zeros, 10% with ones and 10% twos. The distribution should be random.

Could please someone help me?

cheers,

Tim Smith

Re: Random matrix with zeros and ones and twos

David — Mon, 10 Nov 2008 19:26:02 -0500

Re: Random matrix with zeros and ones and twos

Walter Roberson — Mon, 10 Nov 2008 19:57:51 -0500

Tim Smith wrote:
> I need to create a 100 x 100 matrix filled 80% with zeros, 10% with ones and 10% twos.
> The distribution should be random.

Should it be -exactly- 10% ones and -exactly- 10% twos? Or are those the means
and there is a probability distribution for how they occur? For example, is the
rule that for any given location, the content of the location is a uniform
random distribution, 0.8 zero, 0.1 one, 0.l two? That's a quite different
situation than saying that 10% of the 100 x 100 should be ones.

Here is what you asked for:

TheMatrix = zeros(100,100);
Nel = numel(TheMatrix);
Rindices = randperm(Nel);
N10 = floor(Nel/10);
TheMatrix(Rindices(1:N10)) = 1;
TheMatrix(Rindices(N10+1:N10+N10)) = 2;

(Yes, there are more efficient ways, but the above is easily vectorized.
In particular, you don't need to generate as many random numbers as there are
elements in the full vector -- but you do want to ensure that they are -unique-
element subscripts that you generate, and selection without replacement
implemented as "selection with replacement and reject duplicates" has an
indefinite wait time.)

--
.signature note: I am now avoiding replying to unclear or ambiguous postings.
Please review questions before posting them. Be specific. Use examples of what you mean,
of what you don't mean. Specify boundary conditions, and data classes and value
relationships -- what if we scrambled your data or used -Inf, NaN, or complex(rand,rand)?

Re: Random matrix with zeros and ones and twos

Tim Smith — Mon, 10 Nov 2008 20:22:24 -0500

Hey,

Thanks for the reply

I need to create a 100 x 100 matrix filled a% with zeros, b% with ones and c% twos a+b+c=100%. The distribution should be random.

Tim Smith

Re: Random matrix with zeros and ones and twos

Walter Roberson — Mon, 10 Nov 2008 20:51:16 -0500

Tim Smith wrote:

> Thanks for the reply

> I need to create a 100 x 100 matrix filled a% with zeros, b% with ones and c%
> twos a+b+c=100%. The distribution should be random.

In that case, use the code I gave before. If it comes out too slow, then you can
speed it up afterwards.

However, I do caution you that "the distribution should be random" is insufficiently
precise. When you speak of randomness, you need to speak of particular probability
distributions.

Consider, for example, golfers hitting onto a green. They might hit and have the
ball roll into the hole (a 0); they might need one more stroke to get into the
cup (a 1), or they might need two [or more] strokes to get into the cup (a 2).
In each case, the -exact- location their ball first touches down on the
green is "random" (e.g., affected by micro-gusts of wind), and first touching
down at any particular place does not guarantee a 0, 1, or 2 -- but the
-probability- (over the long term, over sufficient shots by decent golfers)
over the long term of the "result" being 0, 1, or 2 is not evenly distributed
across the green. You -might- land far from the cup and have the ball roll directly
in anyhow, and you -might- land a fraction of an inch from the cup and have a bad
bounce and need 2 shots to get it in. You can have a probability distribution which
is not symmetric or not smooth, and yet the distribution would still be "random".

--
.signature note: I am now avoiding replying to unclear or ambiguous postings.
Please review questions before posting them. Be specific. Use examples of what you mean,
of what you don't mean. Specify boundary conditions, and data classes and value
relationships -- what if we scrambled your data or used -Inf, NaN, or complex(rand,rand)?

Re: Random matrix with zeros and ones and twos

Jos — Mon, 10 Nov 2008 20:53:02 -0500

Tim Smith <imaccormick@gmail.com> wrote in message <7946648.1226342494201.JavaMail.jakarta@nitrogen.mathforum.org>...
> Hey,
>
> I need to create a 100 x 100 matrix filled 80% with zeros, 10% with ones and 10% twos. The distribution should be random.
>
> Could please someone help me?
>
> cheers,
>
> Tim Smith

Take a look at RANDP on the File Exchange:
http://www.mathworks.com/matlabcentral/fileexchange/8891

R = randp([.8 .1 .1],100,100)-1 ;

or if exactly 8,000 of the 10,000 values should be 0 then you might consider:
R = reshape([zeros(8000,1) ; ones(1000,1) ; 2 * ones(1000,1)],100,100) ;
R(:) = R(randperm(numel(R))) ;

hth
Jos