How to generate a random data vector that follows a constraint

1 次查看(过去 30 天)
I want to generate random data vector where that follows this constrainst. where and is a constant. I would appreciate any help.

采纳的回答

Bruno Luong
Bruno Luong 2019-9-29
编辑:Bruno Luong 2019-9-29
This will generate uniform distribution (within to polytope)
N = 10;
Etotal = 0;
E = -log(rand(N+1,1));
E = E(1:N,:)./sum(E,1);
  2 个评论
Bruno Luong
Bruno Luong 2019-9-29
编辑:Bruno Luong 2019-9-29
Here is a comparison of distribution with the two other methods proposed below to show the issue of non-uniformity if one doesn't pay attention
N = 2;
Etotal = 1;
p = 3e3;
Ebias = rand(1,p) .* randfixedsum(N,p,Etotal,0,Etotal);
E = rand(1,p).^(1/N)*Etotal .* randfixedsum(N,p,1,0,1);
E2 = -log(rand(N+1,p)); E2 = E2(1:N,:)./sum(E2,1);
subplot(2,2,1)
plot(Ebias(1,:),Ebias(2,:),'.');
title('rand * randfixedsum')
axis equal
subplot(2,2,2)
plot(E(1,:),E(2,:),'.');
axis equal
title('sqrt(rand) * randfixedsum')
subplot(2,2,3)
plot(E2(1,:),E2(2,:),'.');
axis equal
title('exponential method')

请先登录,再进行评论。

更多回答(1 个)

Walter Roberson
Walter Roberson 2019-9-29
Look in the File Exchange for Roger's randfixedsum(). Generate a vector with fixed sum . Multiply all of the elements by rand() to implement the <= part. (Though you might want to worry about the difficulty that rand() is never exactly 1, so if you generate a sum exactly equal to and multiply by rand() then the result can never exactly total
  3 个评论
Walter Roberson
Walter Roberson 2019-9-29
I was thinking of
rand() * randfixedsum(N,1,Etotal,0,Etotal)
but your comment might still apply.
Bruno Luong
Bruno Luong 2019-9-29
编辑:Bruno Luong 2019-9-29
Both give the same non-uniform pdf
The "correct" one is
E = rand()^(1/N)*Etotal * randfixedsum(N,1,1,0,1);

请先登录,再进行评论。

类别

Help CenterFile Exchange 中查找有关 Solver Outputs and Iterative Display 的更多信息

产品


版本

R2019b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by