how to make a function that generate uniformely distributed random matrix

Hi every one..

I am going to make a function which takes three input arguments limit,a,b in that order. The function returns an a-by-b matrix of uniformly distributed random integers between 1 and limit inclusive. I am not allowed to use randi, but i can use rand. To make sure that my result is indeed uniformly distributed, test the output of the function by using the built-in function hist, which plots a histogram.

to make such function i am using that codes

function rad=rad1(limit,n,m)
mat=zeros(n,m);
for i=1:n
    for j=1:m
        a=rand(1,limit);
        mat(i,j)=floor(a)
    end
end
end

but i getting error every time.Can anybody assist me to make such function...Thanks in advance

Answer 1

[Thorsten]

Define your function as

 function r = myrandi(limit, a, b)
 r = ceil(limit*rand(a,b));

Check with

 a= 10; b = 3000; limit = 12;
 r = myrandi(limit, a, b); 
 hist(r(:), 1:limit)

Answer 2

[Guillaume]

The syntax of rand is completely different from that of randi. The arguments you pass to rand are just the size of the matrix you want, never the bounds, rand always return floating point numbers between 0 and 1.

Thus to create a matrix of size m x n, of numbers (floating point) between x and y, you'd do:

r = rand(m, n) * (y-x) + x;

You can figure out the rest of your function yourself.

[Muhammad Usman Saleem]

thanks #Guillaume for answer..i do not get you about the rand function.How can i create random matrix with out using radomi ,These radom number matrix should be uniformly distributed.I have post my question.If you have another way to make such function share with me..thank in advance

[Guillaume]

You're using rand wrong. It does not work like randi. rand doesn't take a limit. I've linked to the documentation for you in my answer. Look at it.

I've also given you the code to generate a matrix between two numbers using rand. (i.e. multiply the rand output| by the difference between the limits and add the lower limit).

I'm not sure what is hard to understand in any of this.

[Guillaume]

Muhammad comments copied here:

Thanks Guilaume... I am now use that function

function rad=rad1(limit,n,m)
mat=zeros(n,m);
for i=1:n
    for j=1:m
        a=limit*rand(1,1); 
        mat(i,j)=floor(a)
    end
end
rad=mat(i,j)
end

Other comment:

other problem is that these no are not uniformly distributed random integers...

[Guillaume]

Please comment in the right answer (and use the {} Code button to format code)

As stated several times:

a = limit * rand; %no need for (1, 1)

WILL NOT generate numbers between [1, limit], but between [0, limit]. I've given the correct formula in my original answer. Just replace y by limit and x by 1.

Secondly, if you want uniformly distributed integer, using floor like you did is wrong, since it will round numbers between [0, 1[ to 0, [1, 2[ to 1, etc. up to [limit-1, limit[ rounded to limit-1, but just [limit] to limit. Hence the probability of limit appearing is much lower.

Hopefully from this, you can see were you went wrong. You need to generate the correct range of floating point numbers before rounding.

[Brendan Hamm]

Hence P(a = limit) = 0.

Answer 3

[Purushottama Rao]

Replace a=rand(1,limit); with a=limit*rand(1,1); in your code

[Guillaume]

This will not generate a number between [1, limit].

[Purushottama Rao]

Yeah..this is a sort of generating numbers between [0 9] along with floor function. can we look at something like floor(a)+1

[Muhammad Usman Saleem]

Thanks Guilaume... I am now use that function

function rad=rad1(limit,n,m) mat=zeros(n,m); for i=1:n for j=1:m a=limit*rand(1,1); mat(i,j)=floor(a) end end rad=mat(i,j) end

but now i am getting in output

>> rad1(10,2,2)

mat =

     7     0
     0     0

mat =

     7     7
     0     0

mat =

     7     7
     1     0

mat =

     7     7
     1     4

rad =

     4

ans =

     4 
these are repetition of the inner loop..kindly check my new code where i need correction so that i not get repetition of ans

[Purushottama Rao]

put semicolon at

mat(i,j)=floor(a)

[Muhammad Usman Saleem]

other problem is that these no are not uniformly distributed random integers...

[Purushottama Rao]

The problrm is associated with floor function. If we consider real values, it still follows a uniform distribution.

do you need to deal only with integer values?

[Michael Haderlein]

To get a readable copy of your function, I copied and formatted it here:

function rad=rad1(limit,n,m) 
 mat=zeros(n,m); 
 for i=1:n 
  for j=1:m 
   a=limit*rand(1,1); 
   mat(i,j)=floor(a);
  end 
 end 
 rad=mat(i,j);
end

1. There's zero need for any loop here. As this seems to be homework, I don't want to give the correct solution but only tell you to think about vectorization.
2. rand will give something 0<x<1. If you multiply this with 10, for instance, you will get something between 0 and 9. So you'll need to add 1 as Purushottama has mentioned before.
3. You return mat(i,j) only. This is only the very last element (lower right corner of the matrix). I guess you want to return entire mat.

[Guillaume]

@Michael,

It's unfortunately not clear from the official documentation, but I think rand generates numbers in the range [0, 1], not ]0, 1[. For this assignment, it probably does not matter.

[Michael Haderlein]

I agree that it probably does not matter and is rather an academic question (the probability of getting the smallest/largest value of whatever the interval is will be extremely low).

The documentation of R2014a says "rand returns a pseudorandom scalar drawn from the standard uniform distribution on the open interval (0,1)." which clearly cuts 0 and 1 (and made me give the statement in the comment above).

Now, to my surprise I just found the online documentation to only say "rand returns a single uniformly distributed random number between 0 and 1." The fact that somebody at TMW obviously took the effort to change that sentence is a suggests that someone figured out that the older version was wrong and the interval indeed is closed [0,1].

[Guillaume]

Yes, I looked at the 2015 doc and saw that it was not specified, and assumed it was closed from the example on how to generate numbers in a range. That example shows a closed interval.

From this discussion, it looks like rand does use an open interval. I'm not sure why mathworks took the effort to make the documentation less precise.

[Brendan Hamm]

The 2015 doc simply says "generates values between 0 and 1". This is to allow for the possibility of changing the algorithm used to generate random numbers, as each algorithm will have a different period and therefore produce a different interval of values. Unless you change the algorithm you are as close to [0,1] as possible.

While the doc may not mention this, it is clear from Cleve Moler's blog on the Mersenne Twister algorithm. The values generate are actually in the range [2^(-53), 1-2^(-53)]. It is impossible to generate values 1 with this algorithm, but you could generate values of 0, but they will be rejected by the algorithm. This is really irrelevant as this is the machine precision of a double.

eps/2 == 2^(-53)
ans = 

       1

http://blogs.mathworks.com/cleve/2015/04/17/random-number-generator-mersenne-twister/

[Muhammad Usman Saleem]

@Purushottama Rao when i put semi colon against floor(a) i am getting in output ans a variable which is a vector of length 1. I want to show complete matrix in output..

[Purushottama Rao]

@MUS: You can try to use disp function after the last ietration for varaible 'matt'

Answer 4

[Muhammad Usman Saleem]

@Michael Haderlein thanks for contributions... yes i want to print complete matrix but to my knowledge mat(i,j) at last is getting values from the mat(i,j)=floor(a) which is inside the second for loop. mat(i,j) in the second loop has created when the loops completed. then its complier goes to mat(i,j) at the end to show in the output. Kindly correct me if i am wrong. I want to print all matrix in output.Thanks in advance for assistance..

[Michael Haderlein]

No matter where the variable mat is coming from,

 rad=mat(i,j);

will return exactly 1 value (as long as i and j are scalar values). If you want the full array, don't use the indices here

 rad=mat;

If you want a short, vectorized and correct version, see Thorsten's answer. As this still seems to be homework and the learning effect of simply using a given answer is rather low, my advise would be to go through this fully equivalent function step by step:

 function r = myrandi(limit, a, b)
 rand_doubles_0_1=rand(a,b);
 rand_doubles_0_limit=limit*rand_doubles_0_1;
 r=ceil(rand_doubles_0_limit);

Use a limit of 10 and set a,b to maybe 3 or 4 to keep it simple.

[Muhammad Usman Saleem]

thank you so much for assistance.... i am getting my error in previous codes.... @Michael Haderlein ....if you like my effort vote up my question..thanks