svd_theta

• full name: tenpy.algorithms.truncation.svd_theta

• parent module: tenpy.algorithms.truncation

• type: function

tenpy.algorithms.truncation.svd_theta(theta, trunc_par, qtotal_LR=[None, None], inner_labels=['vR', 'vL'])

Performs SVD of a matrix theta (= the wavefunction) and truncates it.

Perform a singular value decomposition (SVD) with svd() and truncates with truncate(). The result is an approximation theta ~= tensordot(U.scale_axis(S*renormalization, 1), VH, axes=1)

Parameters

thetaArray, shape (M, N)

The matrix, on which the singular value decomposition (SVD) is performed. Usually, theta represents the wavefunction, such that the SVD is a Schmidt decomposition.

trunc_pardict

truncation parameters as described in truncate().

qtotalLR(charges, charges)

The total charges for the returned U and VH.

inner_labels(string, string)

Labels for the U and VH on the newly-created bond.

Returns

UArray

Matrix with left singular vectors as columns. Shape (M, M) or (M, K) depending on full_matrices.

S1D ndarray

The singluar values of the array. If no cutoff is given, it has lenght min(M, N). Normalized to np.linalg.norm(S)==1.

VHArray

Matrix with right singular vectors as rows. Shape (N, N) or (K, N) depending on full_matrices.

errTruncationError

The truncation error introduced.

renormalizationfloat

Factor, by which S was renormalized.