"""Interpolation machinery."""
from abc import ABC, abstractmethod
import geomstats.backend as gs
[docs]
class Interpolator(ABC):
"""Abstract class for interpolator."""
def __call__(self, t):
"""Interpolate data.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
Returns
-------
point : array-like, shape=[..., n_time, *point_shape]
"""
return self.interpolate(t)
[docs]
@abstractmethod
def interpolate(self, t):
"""Interpolate data.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
Returns
-------
point : array-like, shape=[..., n_time, *point_shape]
"""
class _LinearInterpolator1D(Interpolator, ABC):
def __init__(self, data, point_ndim=1):
self.data = data
self.point_ndim = point_ndim
time_axis = -(point_ndim + 1)
self._n_times = self.data.shape[time_axis]
@abstractmethod
def _from_t_to_interval(self, t):
"""Get interval index from time.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
Returns
-------
interval_index : array-like, shape=[n_times]
"""
def _get_ratio(self, t, interval_index, end_index):
"""Get ratio within interval.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
interval_index : array-like, shape=[n_times]
end_index : array-like, shape=[n_times]
Returns
-------
ratio : array-like, shape=[n_time]
Ratio of t within interval.
"""
def interpolate(self, t):
"""Interpolate data.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
Returns
-------
point : array-like, shape=[..., n_time, *point_shape]
"""
if not gs.is_array(t):
t = gs.array([t])
if gs.ndim(t) == 0:
t = gs.expand_dims(t, axis=0)
interval_index = self._from_t_to_interval(t)
max_bound_reached = interval_index == self._n_times - 1
end_index = gs.where(max_bound_reached, interval_index, interval_index + 1)
point_ndim_slc = (slice(None),) * self.point_ndim
initial_point = self.data[..., interval_index, *point_ndim_slc]
end_point = self.data[..., end_index, *point_ndim_slc]
ratio = self._get_ratio(t, interval_index, end_index)
diff = end_point - initial_point
ijk = "ijk"[: self.point_ndim]
return initial_point + gs.einsum(f"t,...t{ijk}->...t{ijk}", ratio, diff)
[docs]
class LinearInterpolator1D(_LinearInterpolator1D):
"""A 1D linear interpolator.
Assumes interpolation occurs in the unit interval.
Parameters
----------
times : array-like, [n_times]
Times. Must be sorted.
data : array-like, [..., *point_shape]
point_ndim : int
Dimension of point.
"""
def __init__(self, times, data, point_ndim=1):
super().__init__(data, point_ndim=point_ndim)
self.times = times
self._delta = self.times[1:] - self.times[:-1]
def _from_t_to_interval(self, t):
"""Get interval index from time.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
Returns
-------
interval_index : array-like, shape=[n_times]
"""
indices = gs.searchsorted(self.times, t) - 1
return gs.where(indices < 0, 0, indices)
def _get_ratio(self, t, interval_index, end_index):
"""Get ratio within interval.
Parameters
----------
t : array-like, shape=[n_time]
Interpolation time.
interval_index : array-like, shape=[n_times]
end_index : array-like, shape=[n_times]
Returns
-------
ratio : array-like, shape=[n_time]
Ratio of t within interval.
"""
delta = self._delta[interval_index]
return (delta - (self.times[end_index] - t)) / delta