def iqdht(k: np.ndarray, f: np.ndarray, order: int = 0) -> Tuple[np.ndarray, np.ndarray]:
"""Perform a inverse quasi-discrete Hankel transform of the function ``f`` (sampled at points
``k``) and return the transformed function and its sample points in radial space.
If you have the transform on a frequency axis (as opposed to a :math:`k`-axis), the
:math:`k`-axis can be calculated using :math:`k = 2\\pi{}f`.
.. warning::
This method is a convenience wrapper for :meth:`.HankelTransform.iqdht`, but incurs a
significant overhead in calculating the :class:`.HankelTransform` object. If you
are performing multiple transforms on the same grid, it will be much quicker to
construct a single :class:`.HankelTransform` object and call
:meth:`.HankelTransform.iqdht` multiple times.
:param k: The :math:`k` coordinates at which the function is sampled
:type k: :class:`numpy.ndarray`
:param f: The value of the function to be transformed.
:type f: :class:`numpy.ndarray`
:param order: The order of the Hankel Transform to perform. Defaults to 0.
:return: A tuple containing the radial coordinates of the transformed function and its values
:rtype: (:class:`numpy.ndarray`, :class:`numpy.ndarray`)
"""
transformer = HankelTransform(order=order, k_grid=k)
f_transform = transformer.to_transform_k(f)
ht = transformer.iqdht(f_transform)
return transformer.r, ht
def test_round_trip_k_interpolation(radius: np.ndarray, order: int, shape: Callable):
k_grid = radius/10
transformer = HankelTransform(order=order, k_grid=k_grid)
# the function must be smoothish for interpolation
# to work. Random every point doesn't work
func = shape(k_grid)
transform_func = transformer.to_transform_k(func)
reconstructed_func = transformer.to_original_k(transform_func)
assert np.allclose(func, reconstructed_func, rtol=1e-4)
def test_round_trip_k_interpolation_2d(radius: np.ndarray, order: int,
shape: Callable, axis: int):
k_grid = radius / 10
transformer = HankelTransform(order=order, k_grid=k_grid)
# the function must be smoothish for interpolation
# to work. Random every point doesn't work
dims_amplitude = np.ones(2, np.int)
dims_amplitude[1 - axis] = 10
amplitude = np.random.random(dims_amplitude)
dims_k = np.ones(2, np.int)
dims_k[axis] = len(radius)
func = np.reshape(shape(k_grid), dims_k) * np.reshape(
amplitude, dims_amplitude)
transform_func = transformer.to_transform_k(func, axis=axis)
reconstructed_func = transformer.to_original_k(transform_func, axis=axis)
assert np.allclose(func, reconstructed_func, rtol=1e-4)