svd¶
full name: tenpy.linalg.np_conserved.svd
parent module:
tenpy.linalg.np_conserved
type: function

tenpy.linalg.np_conserved.
svd
(a, full_matrices=False, compute_uv=True, cutoff=None, qtotal_LR=[None, None], inner_labels=[None, None], inner_qconj=1)[source]¶ Singualar value decomposition of an Array a.
Factorizes
U, S, VH = svd(a)
, such thata = U*diag(S)*VH
(where*
stands for atensordot()
and diag creates an correctly shaped Array with S on the diagonal). For a nonzero cutoff this holds only approximately.There is a gauge freedom regarding the charges, see also
Array.gauge_total_charge()
. We ensure contractibility by settingU.legs[1] = VH.legs[0].conj()
. Further, we gauge the LegCharge such that U and V have the desired qtotal_LR. Parameters
a (
Array
, shape(M, N)
) – The matrix to be decomposed.full_matrices (bool) – If
False
(default), U and V have shapes(M, K)
and(K, N)
, whereK=len(S)
. IfTrue
, U and V are full square unitary matrices with shapes(M, M)
and(N, N)
. Note that the arrays are not directly contractible in that case;diag(S)
would need to be a rectangluar(M, N)
matrix.compute_uv (bool) – Whether to compute and return U and V.
cutoff (
None
 float) – Keep only singular values which are (strictly) greater than cutoff. (Then the factorization holds only approximately). IfNone
(default), ignored.qtotal_LR ([{chargesNone}, {chargesNone}]) – The desired qtotal for U and VH, respectively.
[None, None]
(Default) is equivalent to[None, a.qtotal]
. A single None entry is replaced the unique charge satisfying the requirementU.qtotal + VH.qtotal = a.qtotal (modulo qmod)
.inner_labels_LR ([{strNone}, {strNone}]) – The first label corresponds to
U.legs[1]
, the second toVH.legs[0]
.inner_qconj ({+1, 1}) – Direction of the charges for the new leg. Default +1. The new LegCharge is constructed such that
VH.legs[0].qconj = qconj
.
 Returns
U (
Array
) – Matrix with left singular vectors as columns. Shape(M, M)
or(M, K)
depending on full_matrices.S (1D ndarray) – The singluar values of the array. If no cutoff is given, it has lenght
min(M, N)
.VH (
Array
) – Matrix with right singular vectors as rows. Shape(N, N)
or(K, N)
depending on full_matrices.