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Speeding up loop for finding index in a large vector

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I am trying to speed up the following piece of code. It computes position (i.e., index) of random draws according to the CDF m. In other words, it simulates the initial position of a large number of objects where these objects have CDF m. Is there a way to speed up this loop?
% Cumulative distribution function
m = sim.m;
m_vec = m(:);
m_cum =cumsum(m_vec)';
R = rand(s.N,s.T); % random draws
% Initial distirbution
ind_ini = zeros(s.N,1);
m_cum = [0 m_cum];
for ii=1:s.N
ind_ini(ii,1) = sum(R(ii,1)>m_cum,2);
The issue here is that m_cum is a very large vector (1-by-1e6) and s.N is also large (>100000). I tried using find function but it was slower on my machine. Also tried vectorizing naively but then I hit the limit on the size of the machine...

Accepted Answer

Michal Szkup
Michal Szkup on 3 Apr 2020
Edited: Michal Szkup on 3 Apr 2020
I managed to cut the time by factor of 3 following the method suggested in this answer:
For benefit of others, here is the solution:
for ii=1:s.N
while R(ii,1)>m_cum(ini)
ini= ini+1;
ind_ini(ii,1) = ini;
ini = 1;
This is fast enough for my puropose.

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