spharapy.spharafilter: SPHARA Filter

SPHARA filter

This module provides a class to perform a spatial filtering using a SPHARA basis. The class is derived from spharapy.spharabasis.SpharaBasis. It provides methodes to design different types of filters and to apply this filters to spatially irregularly sampled data.

class spharapy.spharafilter.SpharaFilter(triangsamples=None, mode='fem', specification=0)

Bases: spharapy.spharabasis.SpharaBasis

SPHARA filter class

This class is used to design different types of filters and to apply this filters to spatially irregularly sampled data.

Parameters

triangsamplestrimesh object

A trimesh object from the package spharapy in which the triangulation of the spatial arrangement of the sampling points is stored. The SPHARA basic functions are determined for this triangulation of the sample points.

mode{‘unit’, ‘inv_euclidean’, ‘fem’}, optional

The discretisation method used to estimate the Laplace-Beltrami operator. Using the option ‘unit’ all edges of the mesh are weighted by unit weighting function. The option ‘inv_euclidean’ results in edge weights corresponding to the inverse Euclidean distance of the edge lengths. The option ‘fem’ uses a FEM discretisation. The default weighting function is ‘fem’.

specificationinteger or array, shape (1, n_points)

If an integer value for specification is passed to the constructor, it must be within the interval (-n_points, n_points), where n_points is the number of spatial sample points. If a positive integer value is passed, a spatial low-pass filter with the corresponding number of SPHARA basis functions is created, if a negative integer value is passed, a spatial low-pass filter is created. If a vector is passed, then all SPHARA basis functions corresponding to nonzero elements of the vector are used to create the filter. The default value of specification is 0, it means a neutral all-pass filter is designed and applied.

filter(data)

Perform the SPHARA filtering

This method performs the spatial SPHARA filtering for data defined at spatially distributed sampling points described by a triangular mesh. The filtering is performed by matrix multiplication of the data matrix and a precalculated filter matrix.

Parameters

dataarray, shape(m, n_points)

A matrix with data to be filtered by spatial SPHARA filter. The number of vertices of the triangular mesh is n_points. The order of the spatial sample points must correspond to that in the vertex list used to determine the SPHARA basis functions.

Returns

data_filteredarray, shape (m, n_points)

A matrix containing the filtered data.

Examples

>>> import numpy as np
>>> from spharapy import trimesh as tm
>>> from spharapy import spharafilter as sf
>>> # define the simple test mesh
>>> testtrimesh = tm.TriMesh([[0, 1, 2]], [[1., 0., 0.], [0., 2., 0.],
...                                        [0., 0., 3.]])
>>> # create a spatial lowpass filter, FEM discretisation
>>> sf_fem = sf.SpharaFilter(testtrimesh, mode='fem',
...                          specification=[1., 1., 0.])
>>> # create some test data
>>> data = np.concatenate([[[0., 0., 0.], [1., 1., 1.]],
...                          np.transpose(sf_fem.basis()[0])])
>>> data
array([[ 0.        ,  0.        ,  0.        ],
       [ 1.        ,  1.        ,  1.        ],
       [ 0.53452248,  0.53452248,  0.53452248],
       [-0.49487166, -0.98974332,  1.48461498],
       [ 1.42857143, -1.14285714, -0.28571429]])
>>> # filter the test data
>>> data_filtered = sf_fem.filter(data)
>>> data_filtered
array([[  0.00000000e+00,   0.00000000e+00,   0.00000000e+00],
       [  1.00000000e+00,   1.00000000e+00,   1.00000000e+00],
       [  5.34522484e-01,   5.34522484e-01,   5.34522484e-01],
       [ -4.94871659e-01,  -9.89743319e-01,   1.48461498e+00],
       [ -1.69271249e-16,  -2.75762028e-16,   3.10220481e-16]])

property specification

Get or set the specification of the filter.

The parameter specification has to be an integer or a vector. Setting the specification will simultaneously apply a plausibility check.