fill a vector (efficiently) with values specified by matrix and multiple vectors

Hi,

I need to run this problem efficiently (because it will run a billion times or more)

There is a fixed 2x2x2 matrix M

Each time the code runs, there are three vectors x,y,z of length N corresponding to the same entitities.

their values are 1 or 2, because the correspond to matrix M. So that each entity is linked to a element of M. I.e. value I want for entity 1: M(x(1),y(1),z(1))

So my goal is to have a vector of length N filled with the values I want BUT

as efficiently as possible (one line?)

I currently do it for only two vectors like this

M=reshape(1:8,2,2,2);N=10;
x=(rand(N,1)>0.5)+1;y=(rand(N,1)>0.1)+1;z=(rand(N,1)>0.1)+1;
tmp=M(x,y,z(1)); %which creates a N by N matrix instead of a vector
    %NOTE: this uses z(1), but I would like to use the whole vector z
OUT=tmp(1:N+1:end); %which extracts the diagonal, which are the values I want

Any suggestions appreciated

PS:

I currently have Corona and can't figure out how I need to replace "1:N+1:end" to deal with a N by N by N matrix, which would work (unlike my brain right now)

BUT

if N~100 that matrix (which I don't need) gets pretty big and probably slows it all down. So would nice to avoid that

Answer 1

[Matt J]

M=reshape(1:8,2,2,2);N=10;
x=(rand(N,1)>0.5)+1;y=(rand(N,1)>0.1)+1;z=(rand(N,1)>0.1)+1;


OUT=M(   sub2ind(size(M),x,y,z)     )

OUT = 10×1

7 7 7 6 7 7 7 8 7 7