SVD drivers

linalg.custom_svd.truncated_svd_arnoldi(M, chi, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)

Parameters

• M (torch.tensor) – square matrix of dimensions \(N \times N\)

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

• abs_tol (float) – absolute tolerance on minimal singular value

• rel_tol (float) – relative tolerance on minimal singular value

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

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading \(\chi\) left singular vectors U, right singular vectors V, and singular values S

Return type

torch.tensor, torch.tensor, torch.tensor

Note: depends on scipy

Returns leading \(\chi\)-singular triples of a matrix M, by computing the partial symmetric decomposition of \(H=M^TM\) as \(H= UDU^T\) up to rank \(\chi\). Returned tensors have dimensions

\[dim(U)=(N,\chi),\ dim(S)=(\chi,\chi),\ \textrm{and}\ dim(V)=(N,\chi)\]

linalg.custom_svd.truncated_svd_gesdd(M, chi, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)

Parameters

• M (torch.tensor) – matrix of dimensions \(N \times L\)

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

• abs_tol (float) – absolute tolerance on minimal singular value

• rel_tol (float) – relative tolerance on minimal singular value

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

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading \(\chi\) left singular vectors U, right singular vectors V, and singular values S

Return type

torch.tensor, torch.tensor, torch.tensor

Returns leading \(\chi\)-singular triples of a matrix M by computing the full SVD \(M= USV^T\). Returned tensors have dimensions

\[dim(U)=(N,\chi),\ dim(S)=(\chi,\chi),\ \textrm{and}\ dim(V)=(L,\chi)\]

linalg.custom_svd.truncated_svd_symarnoldi(M, chi, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)

Parameters

• M (torch.tensor) – square matrix of dimensions \(N \times N\)

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

• abs_tol (float) – absolute tolerance on minimal singular value

• rel_tol (float) – relative tolerance on minimal singular value

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

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading \(\chi\) left singular vectors U, right singular vectors V, and singular values S

Return type

torch.tensor, torch.tensor, torch.tensor

Note: depends on scipy

Returns leading \(\chi\)-singular triples 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

\[dim(U)=(N,\chi),\ dim(S)=(\chi,\chi),\ \textrm{and}\ dim(V)=(N,\chi)\]

linalg.custom_svd.truncated_svd_symeig(M, chi, abs_tol=1e-14, rel_tol=None, keep_multiplets=False, eps_multiplet=1e-12, verbosity=0)

Parameters

• M (torch.tensor) – square matrix of dimensions \(N \times N\)

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

• abs_tol (float) – absolute tolerance on minimal singular value

• rel_tol (float) – relative tolerance on minimal singular value

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

• eps_multiplet (float) – allowed splitting within multiplet

• verbosity (int) – logging verbosity

Returns

leading \(\chi\) left singular vectors U, right singular vectors V, and singular values S

Return type

torch.tensor, torch.tensor, torch.tensor

Returns leading \(\chi\)-singular triples 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

\[dim(U)=(N,\chi),\ dim(S)=(\chi,\chi),\ \textrm{and}\ dim(V)=(N,\chi)\]