c++ - Different eigenvector and eigenvalues in Eigen and Matlab could generate errors? -

like it's explained here , here orde of eigenvalues (and relative eigenvectors , sign too) library dependent , (according first linked question) shouldn't problem. in addition, eigenvectors relative almost-zero eigenvalues can considered garbage. far good.

now, consider matlab code below want rewrite in c++ using eigen library:

%supposing k 3x3 matrix [v_k,d_k] = eig(k); d_k = diag(d_k); ind_k = find(d_k > 1e-8); d_k(ind_k) = d_k(ind_k).^(-1/2); k_half = v_k*diag(d_k)*v_k'; 

and c++ implementation:

eigensolver<matrix3f> es (k,true); auto v = es.eigenvalues(); //set 0 if eigenvalues smal, otherwise v^(-1/2) v = (v.array().real() > 1e-8).select(v.cwisesqrt().cwiseinverse(), 0); auto khalf = es.eigenvectors()*v.asdiagonal()*es.eigenvectors().inverse(); 

the problem k_half values different khafl, can see printed result:

matlab:

v_k =      0.5774    0.8428   -0.0415     0.5774   -0.3806   -0.7468     0.5774   -0.3806    0.6638   d_k =     17.0000         0         0          0    2.0000         0          0         0   -0.0000  k_half =      0.5831   -0.1460   -0.1460    -0.1460    0.1833    0.1833    -0.1460    0.1833    0.1833  eigenvalues=  (2,0) (17,0)  (0,0) eigenvectors= (-0.842777,0)   (0.57735,0) (-0.041487,0)  (0.380609,0)   (0.57735,0) (-0.746766,0)  (0.380609,0)   (0.57735,0)  (0.663792,0)  khalf= (0.0754555,-3.9918e-310)  (0.0764066,1.9959e-310)  (0.0906734,1.9959e-310)            (-0.144533,0)             (0.186401,0)             (0.200668,0)            (-0.144533,0)             (0.186401,0)             (0.200668,0) 

the problem don't know if difference going difference rest of algorithm or not (which post @ end of question completeness). understand there no way guarantee eigenvectors same 2 libraries (since there exists multiple eigenvectors , costant-invariant). have worry this? eventually, how can solve it?

the rest of matlab algorithm:

% p , b int parameters , w , h returned %create indices t random points each hash bit %then form weight matrix = 1:b     rp = randperm(p);     i_s(i,:) = rp(1:t);     e_s = zeros(p,1);     e_s(i_s(i,:)) = 1;     w(:,i) = sqrt((p-1)/t)*k_half*e_s; end h = (k*w)>0; w = real(w); 

thanks both answer's comments figured out problem:

eigen::matrixxcf khalf = es.eigenvectors()*v.asdiagonal()*es.eigenvectors().transpose(); 

(using transpose() , eigen::matrixxcf made trick)