mhauru/abeliantensors

A library for Abelian symmetry preserving tensors in Python 3

abeliantensors's Issues

Evenly keep eigenvalues among different sector for abeliantensor

Hi Markus, the current matrix_eig method in abeliantensor.py keep the first several largest eigenvalues among all eigenvalues. For example, if we truncate a leg with bound dimension 30 to 20 for Z2 symmetric tensor, and let's say the initial shape is [15,15], the truncation could end up like [9,11]. However, sometimes, we may wish the truncation is evenly distributed among two sectors to be [10,10], so is it possible to support this "evenly truncation feature" for the eigenvalue decomposition for the abeliantensor?

I think the key is in line 1978 of the abeliantensor.py in matrix_eig method

 # Figure out what bond dimension to truncate to, how this bond
 # dimension is distributed over the different sectors, and what the
 # truncation error is.
        chi, dims, rel_err = type(self)._find_trunc_dim(
            all_eigs,
            eigdecomps,
            minusabs_next_eigs,
            dims,
            chis=chis,
            eps=eps,
            break_degenerate=break_degenerate,
            degeneracy_eps=degeneracy_eps,
            trunc_err_func=trunc_err_func,
            norm_sq=norm_sq,
        )

Current what I do is to add something like this after, just design for Z2-symmetric tensors

if evenTrunc:
            # This piece of codes is only designed
            # with Z2 symmetry tensor in mind
            errmeg = "The matrix should have two sectors (0,0) and (1,1)."
            assert len(dims) == 2, errmeg
            if chiSpec % 2 == 0:
                dims[(0, 0)] = int(chiSpec / 2)
                dims[(1, 1)] = int(chiSpec / 2)
            else:
                dims[(0, 0)] = int((chiSpec + 1) / 2)
                dims[(1, 1)] = int((chiSpec - 1) / 2)

where evenTrunc is a boolean variable specifying whether we want to evenly truncate among sectors or not. However, I think there must be a better way to do it.

Xinliang

The unitary condition of SVD of an U1 symmetric tensor can not be satisfied

Dear Markus,
I try to exploit your package to do a SVD for an U1 symmetric real tensor A = USV. However, I found that U*U^T wasn't identity. Please help me to solve this issue, thanks!
My test code is attached as follows:
D = 10
T0 = np.random.rand(D,D)
T0 = (T0 + T0.T)/2.

d0 = int(D/3)
d1 = int((D-d0)/2)
dimv = [d1,d0,d1]
qimv = [-1,0,1]
dims = tuple([dimv]*2)
qims = tuple([qimv]*2)
dirs = [1,-1]
A = TensorU1.from_ndarray(T0, shape=dims, qhape=qims, dirs=dirs)

U, S, V = A.svd([0], [1])
#S, U = A.eig([0], [1])

U1 = np.transpose(U, [1,0])
print( 'U.dot(U1)= ', U.dot(U1.flip_dir(0),([1], [0])) )

compatibility with pytorch and opt_einsum?