random number generation for known sum

i what do generate some 15 random numbers that sum for each separate value of say, 60 , 70, 40, 65. How would i go abouts this?

sum = [60 70 40 65];
n=15;
b = [ ];
for i = 1:1:n,
a = randi([1,??]);
b = [b a];
end

Answer 1

[Azzi Abdelmalek]

n=60;
m=1:n;
a=m(sort(randperm(60,15)));
b=diff(a);
b(end+1)=60-sum(b)
sum(b)

[harley]

thanks Azzi, i get an error

Error in ==> Untitled at 3
a=m(sort(randperm(60,15)));

[Walter Roberson]

You must be using an older MATLAB that does not have that enhancement to randperm(). Try

t = randperm(n);
a=m(sort(t(1:15));

[harley]

thanks

[Arnab Pal]

I want to generate the same, but I need Non-integer numbers. Is it possible?

[Bruno Luong]

@Arnab

sumtarget = 60;
n = 5;

x = diff([0,sort(randperm(sumtarget+n-1,n-1)),sumtarget+n])-1

[Arnab Pal]

Sir, It is generating the integer numbers only.

[Bruno Luong]

Ah sorry some how I read non-negative.

For random non-negative floating numbers, you need using Roger Stafford FEX

[Tejas]

Is there an easy way to control the maximum value each number in 'b' can have? Say, each value in 'b' must be less than or equal to 7, and still the 15 numbers in 'b' should add up to 60.

[Walter Roberson]

Roger's FEX contribution, the a and b parameters are lower bound and upper bound. You can use zeros for the lower bound if that is appropriate for your situation.

[Tejas]

I want the numbers to be integers, as in the original question. Roger's FEX contribution seems to work with real numbers.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/327656-conditional-random-number-generation#answer_257296 has some discussion

[Bruno Luong]

The easiest way is perhaps using Roger FEX function, then do some sort of "integering" the float solution

sumatarget = 60
n = 15;
ub = 7;

x = floor([0; cumsum(randfixedsum(n,1,sumatarget,0,ub))]); 
x(end) = sumatarget; % prevent floating point error
r = diff(x)

The distribution might be not perfectly uniform but possibly close enough and suitable for what ever you want to do with it.

[Tejas]

Integering the solution from Roger's function works very well for me. I do not require the numbers to be perfectly uniform. Thanks!

Answer 2

[Walter Roberson]

http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum