Speed up Array computation

New to Julia
, ,
1

I have an array of matrices whose columns are used as vectors to do the following calculation in the function E_int

nb=6; #number of columns
dim=120; #number of rows
np=400; #number of matrices in the array
function H0(n::Integer)
half=rand(ComplexF64,dim,dim);	
H0=half+adjoint(half);
	return H0
end
function E_int()
u_list=[rand(ComplexF64,dim,nb-1) for i=1:np];
En=sum(dot(u_list[n][:,i],H0(n)*u_list[n][:,i]) for n=1:length(u_list),i=1:nb-1)/(np^2);
	return En
end

Calculating the sum En scales badly in the computation time and the memory allocation as the dimension increases. For example that is the output of @time

0.806685 seconds (142.97 k allocations: 901.410 MiB, 9.86% gc time, 19.40% compilation time)

Any advice how to efficiently do this kind of computation would be appreciated.

2

@views

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3

I actually did try using @views in the following way

En=@views sum(dot(u_list[n][:,i],H0(n)*u_list[n][:,i]) for n=1:length(u_list),i=1:nb-1)/(np^2)

It didn’t seem to improve the performance however (maybe I’m not using it correctly?)
This was the output of time when using @views

0.821903 seconds (145.36 k allocations: 894.015 MiB, 7.92% gc time, 22.87% compilation time)

Thanks for your reply!

4

These are all non constant global variables. See: Performance Tips · The Julia Language

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5

Note also that you can use the 3-argument dot function here