How to speed up function evaluation by vectorization

4 次查看（过去 30 天）
Frederik Lohof
Frederik Lohof 2015-10-7
编辑： Frederik Lohof 2015-10-7
Is there a way to speed up this code significantly? Maybe by more vectorization?
It is the evaluation of a Hesse matrix. The first loop is a "dot product" between basis elements in the form of 16x16 matrices (Lambda) and corresponding coefficients (T). The second (double-) loop is the evaluation of the Hesse matrix itself.
This is a more generic version of the code:
Hesse=eye(256,256);
B=rand(1296,256);
T=rand(256,1);
Lambda=rand(16,16,256);
f=rand(1296,1);
P_int=B*T;
rho_int=zeros(16);
%Loop 1
for j=1:256
rho_int=rho_int+T(j,1)*Lambda(:,:,j)/2^4;
end
rho_int_inv=inv(rho_int);
%Loop 2
for k=2:256
for l=2:256
Hesse(k,l)=dot(f, (B(:,k).*B(:,l))./(P_int.^2))+trace(rho_int_inv*Lambda(:,:,k)*rho_int_inv*Lambda(:,:,l)/4^4);
end
end
  2 个评论
Frederik Lohof
Frederik Lohof 2015-10-7
编辑：Frederik Lohof 2015-10-7
In my setting P_int is a vector of probabilities that is used in the calculation of the Hesse matrix. The original function to the Hesse matrix is a likelihood function which is obtained in the context of quantum state tomography (quantum state estimation). The likelihood function is a measure for the likelihood of a certain quantum state (parametrized by T) given the frequencies f of certain measurement outcomes. These are obtained (in my case simulated) by measuring n identical copies of the same (unknown) quantum state in different measurement bases. P_int is a vector of probabilities of measuring a certain outcome given a certain state (B is a matrix yielding the connection between the parametrization T and the expected probabilities P_int).
Edit: And I made a typo in the initialization: It is P_int=B*T :)

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Kirby Fears
Kirby Fears 2015-10-7
编辑：Kirby Fears 2015-10-7
The second loop seems fine. Vectorization of loop 1 below.
% rho_int=zeros(16);
% Loop 1 replaced by vector operation
rho_int=sum(repmat(reshape(T,1,1,numel(T)),...
size(Lambda,1),size(Lambda,2)).*Lambda,3)/2^4;
rho_int_inv=inv(rho_int);
You could speed up the second loop with the parallel computing toolbox.
Hope this helps.

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Quantum Mechanics 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by