How to choose an element from a vector with not equal probabilities?

I'm working with Monte Carlo simulations of polymers and I need to choose elements from a vector which have a probability to be chosen proportional to the value of the element. For example if I have the following vector:

A=[10 70 30 100];

The probability of every element to be chosen is the following:

P=[1/20 7/20 3/20 1/2]; %P(i)=A(i)/sum(A)

I wanted to know if there is any command in MATLAB or optimized method to choose an specific element, given the probability vector P. I'm using a function made by myself that works well but is quite slow and in high numbers of particles it's insuming a lot of time. The function I'm using is following:

function [sel] = randp(A,upp) %Here upp=sum(A)

r=floor(rand()*upp)+1; %I choose a random point between the extended array
f=0;
f2=A(1);
for i=1:length(A)
    if f<r && r<=f2
        sel=i;
        break
    else
        f=f2;
        f2=f2+A(i+1);
    end

end

Thank you in advance for any help. I hope I made myself clear. And sorry for any grammar mistakes, my english is a bit rusty

Answer 1

[Torsten]

A=[10 70 30 100];
P=[0,cumsum(A)/sum(A)]

P = 1×5

0 0.0476 0.3810 0.5238 1.0000

R = rand(10,1)

R = 10×1

0.5094 0.6495 0.5746 0.8497 0.0329 0.9060 0.5132 0.0183 0.3107 0.9432

Y = discretize(R,P)

Y = 10×1

3 4 4 4 1 4 3 1 2 4

Rand = A(Y)

Rand = 1×10

30 100 100 100 10 100 30 10 70 100

[Tomás Romero Pietrafesa]

This is great, thank you!

Answer 2

[Walter Roberson]

https://www.mathworks.com/help/stats/randsample.html using the w parameter.

If you do not have that toolbox then there are ways to vectorize the approach you are taking.