# -*- coding: utf-8 -*-
from warnings import warn
import numpy as np
import pandas as pd
import scipy.interpolate
from ..misc import NeuroKitWarning
[docs]
def signal_interpolate(
x_values, y_values=None, x_new=None, method="quadratic", fill_value=None
):
"""**Interpolate a signal**
Interpolate a signal using different methods.
Parameters
----------
x_values : Union[list, np.array, pd.Series]
The samples corresponding to the values to be interpolated.
y_values : Union[list, np.array, pd.Series]
The values to be interpolated. If not provided, any NaNs in the x_values
will be interpolated with :func:`_signal_interpolate_nan`,
considering the x_values as equally spaced.
x_new : Union[list, np.array, pd.Series] or int
The samples at which to interpolate the y_values. Samples before the first value in x_values
or after the last value in x_values will be extrapolated. If an integer is passed, nex_x
will be considered as the desired length of the interpolated signal between the first and
the last values of x_values. No extrapolation will be done for values before or after the
first and the last values of x_values.
method : str
Method of interpolation. Can be ``"linear"``, ``"nearest"``, ``"zero"``, ``"slinear"``,
``"quadratic"``, ``"cubic"``, ``"previous"``, ``"next"``, ``"monotone_cubic"``, or ``"akima"``.
The methods ``"zero"``, ``"slinear"``, ``"quadratic"`` and ``"cubic"`` refer to a spline
interpolation of zeroth, first, second or third order; whereas ``"previous"`` and
``"next"`` simply return the previous or next value of the point. An integer specifying the
order of the spline interpolator to use.
See `monotone cubic method <https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.
PchipInterpolator.html>`_ for details on the ``"monotone_cubic"`` method.
See `akima method <https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.
Akima1DInterpolator.html>`_ for details on the ``"akima"`` method.
fill_value : float or tuple or str
If a ndarray (or float), this value will be used to fill in for
requested points outside of the data range.
If a two-element tuple, then the first element is used as a fill value
for x_new < x[0] and the second element is used for x_new > x[-1].
If "extrapolate", then points outside the data range will be extrapolated.
If not provided, then the default is ([y_values[0]], [y_values[-1]]).
Returns
-------
array
Vector of interpolated samples.
See Also
--------
signal_resample
Examples
--------
.. ipython:: python
import numpy as np
import neurokit2 as nk
import matplotlib.pyplot as plt
# Generate Simulated Signal
signal = nk.signal_simulate(duration=2, sampling_rate=10)
# We want to interpolate to 2000 samples
x_values = np.linspace(0, 2000, num=len(signal), endpoint=False)
x_new = np.linspace(0, 2000, num=2000, endpoint=False)
# Visualize all interpolation methods
@savefig p_signal_interpolate1.png scale=100%
nk.signal_plot([
nk.signal_interpolate(x_values, signal, x_new=x_new, method="zero"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="linear"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="quadratic"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="cubic"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="previous"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="next"),
nk.signal_interpolate(x_values, signal, x_new=x_new, method="monotone_cubic")
], labels = ["Zero", "Linear", "Quadratic", "Cubic", "Previous", "Next", "Monotone Cubic"])
# Add original data points
plt.scatter(x_values, signal, label="original datapoints", zorder=3)
@suppress
plt.close()
"""
# Sanity checks
if x_values is None:
raise ValueError(
"NeuroKit error: signal_interpolate(): x_values must be provided."
)
if y_values is None:
# for interpolating NaNs
return _signal_interpolate_nan(x_values, method=method, fill_value=fill_value)
if isinstance(x_values, pd.Series):
x_values = np.squeeze(x_values.values)
if isinstance(x_new, pd.Series):
x_new = np.squeeze(x_new.values)
if len(x_values) != len(y_values):
raise ValueError("x_values and y_values must be of the same length.")
if isinstance(x_new, int):
if len(x_values) == x_new:
return y_values
x_new = np.linspace(x_values[0], x_values[-1], x_new)
else:
# if x_values is identical to x_new, no need for interpolation
if np.array_equal(x_values, x_new):
return y_values
elif np.any(x_values[1:] == x_values[:-1]):
warn(
"Duplicate x values detected. Averaging their corresponding y values.",
category=NeuroKitWarning,
)
x_values, y_values = _signal_interpolate_average_duplicates(
x_values, y_values
)
# If only one value, return a constant signal
if len(x_values) == 1:
return np.ones(len(x_new)) * y_values[0]
if method == "monotone_cubic":
interpolation_function = scipy.interpolate.PchipInterpolator(
x_values, y_values, extrapolate=True
)
elif method == "akima":
interpolation_function = scipy.interpolate.Akima1DInterpolator(
x_values, y_values
)
else:
if fill_value is None:
fill_value = ([y_values[0]], [y_values[-1]])
interpolation_function = scipy.interpolate.interp1d(
x_values,
y_values,
kind=method,
bounds_error=False,
fill_value=fill_value,
)
interpolated = interpolation_function(x_new)
if method == "monotone_cubic" and fill_value != "extrapolate":
# Find the index of the new x value that is closest to the first original x value
first_index = np.argmin(np.abs(x_new - x_values[0]))
# Find the index of the new x value that is closest to the last original x value
last_index = np.argmin(np.abs(x_new - x_values[-1]))
if fill_value is None:
# Swap out the cubic extrapolation of out-of-bounds segments generated by
# scipy.interpolate.PchipInterpolator for constant extrapolation akin to the behavior of
# scipy.interpolate.interp1d with fill_value=([y_values[0]], [y_values[-1]].
fill_value = ([interpolated[first_index]], [interpolated[last_index]])
elif isinstance(fill_value, float) or isinstance(fill_value, int):
# if only a single integer or float is provided as a fill value, format as a tuple
fill_value = ([fill_value], [fill_value])
interpolated[:first_index] = fill_value[0]
interpolated[last_index + 1 :] = fill_value[1]
return interpolated
def _signal_interpolate_nan(values, method="quadratic", fill_value=None):
if np.any(np.isnan(values)):
# assume that values are evenly spaced
# x_new corresponds to the indices of all values, including missing
x_new = np.arange(len(values))
not_missing = np.where(np.invert(np.isnan(values)))[0]
# remove the missing values
y_values = values[not_missing]
# x_values corresponds to the indices of only non-missing values
x_values = x_new[not_missing]
# interpolate to get the values at the indices where they are missing
return signal_interpolate(
x_values=x_values,
y_values=y_values,
x_new=x_new,
method=method,
fill_value=fill_value,
)
else:
# if there are no missing values, return original values
return values
def _signal_interpolate_average_duplicates(x_values, y_values):
unique_x, indices = np.unique(x_values, return_inverse=True)
mean_y = np.bincount(indices, weights=y_values) / np.bincount(indices)
return unique_x, mean_y
