CODEWITHSUNDEEP
matlabrandomnumbers
Abdul Rehman
Abdul Rehman

Reputation: 2334

Creating Random Number row Vector within range ans sum should be equal to M

I am very confused with simple MATLAB random number generation problem. I know it looks silly and basic level some how but I have tried google before but could not find any useful solution.

I have bounds like this

  Lb = [150,100,150]; %in MW
  Ub = [600,400,200]; %in MW
  Pd = 850;   %in MW

I want to create a random guess which sum will be equal to Pd and which should be within limits of Lower and Upper Bounds.

I am able to generate row vector within limits like this 

        `u0=Lb+(Ub-Lb).*rand(1,d);`

and I know that to generate random number which sum would be equal to Pd can be obtained like this 

u0=rand(1,d);
u0=u0/sum(u0);
u0=u0*Pd;

How to combine both effect in single random number generation. thanks

Upvotes: 2

Views: 158

Answers (1)

BillBokeey
BillBokeey

Reputation: 3476

This is not as easy as it looks, as the bound will put some extra constraints on the problem :

1) Your current solution :

Your corrected code (As stated by @il_raffa in the comments) would look like :

Lb = [150,100,150]; %in MW
Ub = [600,400,200]; %in MW
Pd = 850;   %in MW
d=3;

u0=Lb+(Ub-Lb).*rand(1,d) % Output before normalization

u0=(u0/sum(u0))*Pd % Output after normalization

Outputs :

u0 =

  516.6257  371.7376  156.3493 % Before Normalization

u0 =

  420.3374  302.4535  127.2091 % After Normalization

As you can see, the sum of the elements of u0 was quite bigger than Pd, and the third value in u0 was pretty close from the lower bound. Thus after Normalization the third value in u0 is lower than the corresponding lower bound.

A similar problem will happen with the solution @CarlWitthoft presents in the comments. It is possible that after generating n-1 random numbers, the n-th number making the sum be equal to Pd would not lie within the bound range.

2) Conclusion :

The only way to do it in my opinion is to iterate until you find a solution, so it would be something along the lines of :

Lb = [150,100,150]; %in MW
Ub = [600,400,200]; %in MW
Pd = 850;   %in MW
d=3;

u0=[Inf Inf Inf];

while(~all((u0>Lb).*(u0<Ub))) 

u0=Lb+(Ub-Lb).*rand(1,d);

u0=(u0/sum(u0))*Pd;

end

Output :

u0 =

533.9384  134.6124  181.4492

Upvotes: 2

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