# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Interpolation utilities."""
import html
from itertools import compress
import numpy as np
import scipy.interpolate
from astropy import units as u
from .compat import COPY_IF_NEEDED
__all__ = [
"interpolate_profile",
"interpolation_scale",
"ScaledRegularGridInterpolator",
]
INTERPOLATION_ORDER = {None: 0, "nearest": 0, "linear": 1, "quadratic": 2, "cubic": 3}
[docs]
class ScaledRegularGridInterpolator:
"""Thin wrapper around `scipy.interpolate.RegularGridInterpolator`.
The values are scaled before the interpolation and back-scaled after the
interpolation.
Dimensions of length 1 are ignored in the interpolation of the data.
Parameters
----------
points : tuple of `~numpy.ndarray` or `~astropy.units.Quantity`
Tuple of points passed to `RegularGridInterpolator`.
values : `~numpy.ndarray`
Values passed to `RegularGridInterpolator`.
points_scale : tuple of str
Interpolation scale used for the points.
values_scale : {'lin', 'log', 'sqrt'}
Interpolation scaling applied to values. If the values vary over many magnitudes
a 'log' scaling is recommended.
axis : int or None
Axis along which to interpolate.
method : {"linear", "nearest"}
Default interpolation method. Can be overwritten when calling the
`ScaledRegularGridInterpolator`.
**kwargs : dict
Keyword arguments passed to `RegularGridInterpolator`.
"""
def __init__(
self,
points,
values,
points_scale=None,
values_scale="lin",
extrapolate=True,
axis=None,
**kwargs,
):
if points_scale is None:
points_scale = ["lin"] * len(points)
self.scale_points = [interpolation_scale(scale) for scale in points_scale]
self.scale = interpolation_scale(values_scale)
self.axis = axis
self._include_dimensions = [len(p) > 1 for p in points]
values_scaled = self.scale(values)
points_scaled = self._scale_points(points=points)
kwargs.setdefault("bounds_error", False)
if extrapolate:
kwargs.setdefault("fill_value", None)
method = kwargs.get("method", None)
if not np.any(self._include_dimensions):
if method != "nearest":
raise ValueError(
"Interpolating scalar values requires using "
"method='nearest' explicitly."
)
if np.any(self._include_dimensions):
values_scaled = np.squeeze(values_scaled)
if axis is None:
self._interpolate = scipy.interpolate.RegularGridInterpolator(
points=points_scaled, values=values_scaled, **kwargs
)
else:
self._interpolate = scipy.interpolate.interp1d(
points_scaled[0], values_scaled, axis=axis
)
def _repr_html_(self):
try:
return self.to_html()
except AttributeError:
return f"<pre>{html.escape(str(self))}</pre>"
def _scale_points(self, points):
points_scaled = [scale(p) for p, scale in zip(points, self.scale_points)]
if np.any(self._include_dimensions):
points_scaled = compress(points_scaled, self._include_dimensions)
return tuple(points_scaled)
[docs]
def __call__(self, points, method=None, clip=True, **kwargs):
"""Interpolate data points.
Parameters
----------
points : tuple of `~numpy.ndarray` or `~astropy.units.Quantity`
Tuple of coordinate arrays of the form (x_1, x_2, x_3, ...). Arrays are
broadcast internally.
method : {None, "linear", "nearest"}
Linear or nearest neighbour interpolation.
Default is None, which is `method` defined on init.
clip : bool
Clip values at zero after interpolation.
"""
points = self._scale_points(points=points)
if self.axis is None:
points = np.broadcast_arrays(*points)
points_interp = np.stack([_.flat for _ in points]).T
values = self._interpolate(points_interp, method, **kwargs)
values = self.scale.inverse(values.reshape(points[0].shape))
else:
values = self._interpolate(points[0])
values = self.scale.inverse(values)
if clip:
values = np.clip(values, 0, np.inf)
return values
[docs]
def interpolation_scale(scale="lin"):
"""Interpolation scaling.
Parameters
----------
scale : {"lin", "log", "sqrt"}
Choose interpolation scaling.
"""
if scale in ["lin", "linear"]:
return LinearScale()
elif scale == "log":
return LogScale()
elif scale == "sqrt":
return SqrtScale()
elif scale == "stat-profile":
return StatProfileScale()
elif isinstance(scale, InterpolationScale):
return scale
else:
raise ValueError(f"Not a valid value scaling mode: '{scale}'.")
class InterpolationScale:
"""Interpolation scale base class."""
def __call__(self, values):
if hasattr(self, "_unit"):
values = u.Quantity(values, copy=COPY_IF_NEEDED).to_value(self._unit)
else:
if isinstance(values, u.Quantity):
self._unit = values.unit
values = values.value
return self._scale(values)
def _repr_html_(self):
try:
return self.to_html()
except AttributeError:
return f"<pre>{html.escape(str(self))}</pre>"
def inverse(self, values):
values = self._inverse(values)
if hasattr(self, "_unit"):
return u.Quantity(values, self._unit, copy=COPY_IF_NEEDED)
else:
return values
class LogScale(InterpolationScale):
"""Logarithmic scaling."""
tiny = np.finfo(np.float32).tiny
def _scale(self, values):
values = np.clip(values, self.tiny, np.inf)
return np.log(values)
@classmethod
def _inverse(cls, values):
output = np.exp(values)
return np.where(abs(output) - cls.tiny <= cls.tiny, 0, output)
class SqrtScale(InterpolationScale):
"""Square root scaling."""
@staticmethod
def _scale(values):
sign = np.sign(values)
return sign * np.sqrt(sign * values)
@classmethod
def _inverse(cls, values):
return np.power(values, 2)
class StatProfileScale(InterpolationScale):
"""Square root profile scaling."""
def __init__(self, axis=0):
self.axis = axis
def _scale(self, values):
values = np.sign(np.gradient(values, axis=self.axis)) * values
sign = np.sign(values)
return sign * np.sqrt(sign * values)
@classmethod
def _inverse(cls, values):
return np.power(values, 2)
class LinearScale(InterpolationScale):
"""Linear scaling."""
@staticmethod
def _scale(values):
return values
@classmethod
def _inverse(cls, values):
return values
[docs]
def interpolate_profile(x, y, interp_scale="sqrt", extrapolate=False):
"""Helper function to interpolate one-dimensional profiles.
Parameters
----------
x : `~numpy.ndarray`
Array of x values.
y : `~numpy.ndarray`
Array of y values.
interp_scale : {"sqrt", "lin"}
Interpolation scale applied to the profile. If the profile is
of parabolic shape, a "sqrt" scaling is recommended. In other cases or
for fine sampled profiles a "lin" can also be used.
Default is "sqrt".
extrapolate : bool
Extrapolate or not if the evaluation value is outside the range of x values.
Default is False.
Returns
-------
interp : `interp1d`
Interpolator.
"""
method_dict = {"sqrt": "quadratic", "lin": "linear"}
kwargs = dict(kind=method_dict[interp_scale])
if extrapolate:
kwargs["bounds_error"] = False
kwargs["fill_value"] = "extrapolate"
return scipy.interpolate.interp1d(x, y, **kwargs)
