As of #2445 eigenvalue calculation seems to work correctly. Yet, sometimes there is a problem with eigenvector computation. Consider the following examples.
let A = [[1, 2, 3], [2, 4, 0], [3, 0, 1]];
let cnt = 0.1;
let Ath = math.multiply( math.exp(math.multiply(math.complex(0,1), -cnt)), AA );
let Hth = math.divide(math.add(Ath, math.ctranspose(Ath)), 2);
math.eigs(Hth)
This code works correctly and produces correct eigenvalues. But if I change
let Hth = math.divide(math.add(Ath, math.transpose(Ath)), 2);
math.eigs(Hth)
I get the following error
Uncaught Error: Failed to find eigenvectors for the following eigenvalues: -2.32076242897952 + 0.2328529372998936i, 2.7657291798020682 - 0.27749853033260213i, 5.525058240845601 - 0.5543549068482564i
at complexEigs.js:461:19
at complexEigs.js:49:17
at j (eigs.js:100:12)
at Function.Array (eigs.js:51:14)
at Object.eigs (typed-function.js:1085:85)
at <anonymous>:1:6
The expected output would be
julia> A = [1 2 3; 2 4 0; 3 0 1];
julia> cnt = 0.1;
julia> Ath = exp(-1im*cnt)*A;
julia> Hth = (Ath + transpose(Ath))/2;
julia> eigen(Hth)
Eigen{ComplexF64, ComplexF64, Matrix{ComplexF64}, Vector{ComplexF64}}
values:
3-element Vector{ComplexF64}:
-2.320762428979524 + 0.23285293729989398im
2.7657291798020984 - 0.27749853033260563im
5.525058240845574 - 0.5543549068482575im
vectors:
3×3 Matrix{ComplexF64}:
0.723537+0.0im 0.391404+4.34166e-17im 0.568592-7.08711e-17im
-0.228519-3.1175e-17im -0.641444-1.01409e-16im 0.732345+0.0im
-0.651363-4.64016e-17im 0.659812+0.0im 0.374665+1.22787e-16imThe eigenvalues look correct, there is some problem with eigenvectors only. I tried some other examples and it seemed to work in that case. These were:
let A = [[3, -2], [math.complex(4, 2), -1]];
let Ah = math.ctranspose(A);
console.log(math.eigs(math.add(A, Ah)));
console.log(math.eigs(A));
console.log(math.eigs(Ah));
In this case there are no errors and the results are correct. I tried a handful of other Hermitian matrices and the error did not occur.
As of #2445 eigenvalue calculation seems to work correctly. Yet, sometimes there is a problem with eigenvector computation. Consider the following examples.
This code works correctly and produces correct eigenvalues. But if I change
I get the following error
The expected output would be
The eigenvalues look correct, there is some problem with eigenvectors only. I tried some other examples and it seemed to work in that case. These were:
In this case there are no errors and the results are correct. I tried a handful of other Hermitian matrices and the error did not occur.