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.