Eliminate a for loop to increase speed

I have a code snippet below which uses a for loop that I am trying to eliminate as I need to scale up to larger values of N and L.

clc; clearvars;

N = 2; L = 2; T = 1; 

a = [1 1i; -1i -1];         

nplq = int8(de2bi((0:2^(N*L)-1),'left-msb')); % [0 0 0 0; 0 0 0 1; 0 0 1 0; ... ; 1 1 1 1]

a_nl = zeros(2^(N*L),1);

for i = 1:2^(N*L)
    a_nl(i) = a(nplq(i,1)+1,nplq(i,3)+1);
end

% wish i could do something like a_nl = a(nplq(:,1),nplq(:,3))

Any suggestions would be appreciated.

Answer 1

[Jan]

N = 2; L = 2; T = 1; 
a = [1 1i; -1i -1];         
nplq = int8(de2bi((0:2^(N*L)-1),'left-msb')); % [0 0 0 0; 0 0 0 1; 0 0 1 0; ... ; 1 1 1 1]
a_nl = zeros(2^(N*L),1);
for i = 1:2^(N*L)
    a_nl(i) = a(nplq(i,1) + 1, nplq(i,3) + 1);
end

% Without a loop:
a_nl2 = a(sub2ind(size(a), nplq(:,1) + 1, nplq(:,3) + 1));

isequal(a_nl, a_nl2)  % Same result?

ans = logical
   1

Do you really need the complete nplq matrix or are the 2 columns enough?

N = 2; L = 2;
M     = 2^(N*L - 1)
v     = uint8(1:2).';
nplq1 = repelem(v, M, 1);
c     = 3 - 1;  % 3rd column
nplq3 = repmat(repelem(v, M / 2^c, 1), 2^c, 1);

[Howard Wilton]

Yes, need nlpq as everything is cross multiplied.

Thanks for,

a(sub2ind(size(a), nplq(:,1) + 1, nplq(:,3) + 1))

That's awesome.

Also, there was an error in my original code; the number of rows isn't , it is .

[Jan]

The creation of nplq can be expensive, if it exhausts the free memory: It is created as double at first, which needs 8 times the RAM of the needed UINT8 array. If this is a problem, you can try the C-mex function: FEX: VChoseKRO:

VChooseKRO_M(uint8([0,1]), N*L)

[Howard Wilton]

Thank you very much!