Filters

The Filters class is defined below.

The WaveletFilters class inherits from the previous class and is specific to Daubechies wavelets, where a so-called magic filter has to be defined, in addition to the gradient and laplacian filters.

Both classes are used to define some families of filters:

  • FD2_filters, for the Finite Difference filters of order 2,
  • FD8_filters, for the Finite Difference filters of order 8,
  • Sym8_filters, for a family of Daubechies wavelets filters.

These three families of filters are easily available:

>>> from siegpy import FD2_filters, FD8_filters, Sym8_filters
class siegpy.filters.Filters(grad_filter, laplac_filter)[source]

Bases: object

This class specifies a family of filters that are useful to describe numerical Hamiltonians. It allows the definition of the gradient and Laplacian operators in matrix form by means of filters and a specified number of grid points.

Parameters:
  • grad_filter (numpy array or list) – Gradient filter.
  • laplac_filter (numpy array or list) – Laplacian filter.
grad_filter
Returns:Gradient filter.
Return type:numpy array
laplac_filter
Returns:Laplacian filter.
Return type:numpy array
fill_gradient_matrix(npts)[source]

Fill a gradient matrix of dimension npts.

Parameters:npts (int) – Number of grid points.
Returns:Gradient matrix.
Return type:2D numpy array
fill_laplacian_matrix(npts)[source]

Fill a Laplacian matrix of dimension npts.

Parameters:npts (int) – Number of grid points.
Returns:Laplacian matrix.
Return type:2D numpy array
static _fill_matrix(_filter, npts)[source]

This method creates a matrix operator, given a filter and a number of grid points.

Parameters:
  • _filter (numpy array) – Filter of an operator.
  • npts (int) – Number of grid points.
Returns:

Operator in matrix form, filled thanks to a filter.
Return type:

numpy array
Raises:

ValueError – If the filter is larger than the discretization grid.
class siegpy.filters.WaveletFilters(grad_filter, laplac_filter, magic_filter)[source]

Bases: siegpy.filters.Filters

This class defines the methods specific to the Daubechies wavelets filers.

The main difference with respect to the parent class is the requirement of a so-called magic filter.

Parameters:
  • grad_filter (numpy array or list) – Gradient filter.
  • laplac_filter (numpy array or list) – Laplacian filter.
  • magic_filter (numpy array or list) – Magic filter.
magic_filter
Returns:Magic filter.
Return type:numpy array
fill_magic_matrix(npts)[source]

Fill a magic filter matrix of dimension npts.

Parameters:npts (int) – Number of grid points.
Returns:Magic filter matrix.
Return type:2D numpy array