# Truncated eigendecomposition¶

linalg.custom_eig.truncated_eig_arnoldi(M, chi, v0=None, dtype=None, device=None, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)[source]
Parameters
• M (torch.Tensor or scipy.sparse.linalg.LinearOperator) – matrix of dimensions $$N \times N$$ or numpy LinearOperator

• chi (int) – desired maximal rank $$\chi$$

• v0 (torch.Tensor) – initial vector

• abs_tol (float) – absolute tolerance on minimal(in magnitude) eigenvalue

• rel_tol (float) – relative tolerance on minimal(in magnitude) eigenvalue

• keep_multiplets (bool) – truncate spectrum down to last complete multiplet

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading $$\chi$$ eigenvalues D and eigenvectors U

Return type

torch.tensor, torch.tensor

Note: depends on scipy

Returns leading $$\chi$$ eigenpairs of a matrix M, where M is a symmetric matrix $$M=M^T$$, by computing the partial symmetric decomposition $$M= UDU^T$$ up to rank $$\chi$$. Returned tensors have dimensions

$dim(D)=(\chi),\ dim(U)=(N,\chi)$

Note

This function does not support autograd.

linalg.custom_eig.truncated_eig_sym(M, chi, abs_tol=1e-14, rel_tol=None, ad_decomp_reg=1e-12, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)[source]
Parameters
• M (torch.tensor) – symmetric matrix of dimensions $$N \times N$$

• chi (int) – desired maximal rank $$\chi$$

• abs_tol (float) – absolute tolerance on minimal(in magnitude) eigenvalue

• rel_tol (float) – relative tolerance on minimal(in magnitude) eigenvalue

• keep_multiplets (bool) – truncate spectrum down to last complete multiplet

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading $$\chi$$ eigenvalues D and eigenvectors U

Return type

torch.tensor, torch.tensor

Returns leading $$\chi$$ eigenpairs of a matrix M, where M is a symmetric matrix $$M=M^T$$, by computing the full symmetric decomposition $$M= UDU^T$$. Returned tensors have dimensions

$dim(D)=(\chi),\ dim(U)=(N,\chi)$
linalg.custom_eig.truncated_eig_symarnoldi(M, chi, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)[source]
Parameters
• M (torch.tensor) – symmetric matrix of dimensions $$N \times N$$

• chi (int) – desired maximal rank $$\chi$$

• abs_tol (float) – absolute tolerance on minimal(in magnitude) eigenvalue

• rel_tol (float) – relative tolerance on minimal(in magnitude) eigenvalue

• keep_multiplets (bool) – truncate spectrum down to last complete multiplet

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading $$\chi$$ eigenvalues D and eigenvectors U

Return type

torch.tensor, torch.tensor

Note: depends on scipy

Returns leading $$\chi$$ eigenpairs of a matrix M, where M is a symmetric matrix $$M=M^T$$, by computing the partial symmetric decomposition $$M= UDU^T$$ up to rank $$\chi$$. Returned tensors have dimensions

$dim(D)=(\chi),\ dim(U)=(N,\chi)$

Note

This function does not support autograd.