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spharpy.spatial#

Functions:

greens_function_plane_wave(source_points, ...)

The matrix describing the propagation of a plane wave from a direction of arrival defined by the azimuth and elevation angles of the source points to the receiver points.

greens_function_point_source(sources, ...[, ...])

Green's function for point sources in free space in matrix form.
spharpy.spatial.greens_function_plane_wave(source_points, receiver_points, wave_number, gradient=False)[source]#

The matrix describing the propagation of a plane wave from a direction of arrival defined by the azimuth and elevation angles of the source points to the receiver points. The phase sign convention reflects a direction of arrival from the source position.

Parameters:

  • source_points (spharpy.samplings.Coordinates, pf.Coordinates) – The source points defining the direction of incidence for the plane wave. Note that the radius on which the source is positioned has no relevance.

  • receiver_points (spharpy.samplings.Coordinates, pf.Coordinates) – The receiver points.

  • wave_number (double) – The wave number of the wave

  • speed_of_sound (double) – The speed of sound

  • gradient (bool) – If True, the gradient will be returned as well

Returns:

M – The plane wave propagation matrix

Return type:

ndarray, complex, shape(n_receiver, n_sources)

spharpy.spatial.greens_function_point_source(sources, receivers, k, gradient=False)[source]#

Green’s function for point sources in free space in matrix form. The phase sign convention corresponds to a direction of propagation away from the source at position $r_s$.

\[\begin{split}G(k) = \\frac{e^{- k\\|\\mathbf{r_s} - \\mathbf{r_r}\\|}} {4 \\pi \\|\\mathbf{r_s} - \\mathbf{r_r}\\|}\end{split}\]
Parameters:
Returns:

G – Green’s function

Return type:

ndarray, double

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