Function Loading#

The SeeMPS library provides several methods to load univariate and multivariate functions in MPS and MPO structures. In the following, the most important are listed.

Tensorized operations#

These methods are useful to construct MPS corresponding to domain discretizations, and compose them using tensor products and sums to construct multivariate domains.

`RegularInterval`	Equispaced discretization between start and stop with size points.
`ChebyshevInterval`	Irregular discretization between start and stop given by the zeros or extrema of a Chebyshev polynomial of order size or size-1 respectively.
`mps_interval`(interval)	Returns an MPS corresponding to a specific type of interval.
`mps_tensor_product`(mps_list[, mps_order, ...])	Returns the tensor product of a list of MPS, with the sites arranged according to the specified MPS order.
`mps_tensor_sum`(mps_list[, mps_order, ...])	Returns the tensor sum of a list of MPS, with the sites arranged according to the specified MPS order.

Tensor cross-interpolation (TCI)#

These methods are useful to compose MPS or MPO representations of black-box functions using tensor cross-interpolation (TCI). See Tensor cross-interpolation (TCI).

Polynomial expansions#

These methods are useful to compose univariate function on generic initial MPS or MPO and compute MPS approximations of functions. See Polynomial expansions.

Multiscale interpolative constructions#

These methods are useful to construct polynomial interpolants of low-dimensional functions in MPS using the Chebyshev-Lagrange interpolation framework. See Multiscale interpolative constructions.

Sketching methods#

These methods are useful to construct high-dimensional densities or other black-box non-normalized functions from a collection of samples defining the region of interest. See Sketching constructions.

Computation-tree methods#

These methods are useful to construct procedurally defined functions and functions with sharp features, where polynomial expansions and tensor cross interpolation may suffer from slow convergence or Gibbs-type artifacts. See Computation-tree constructions.