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‎csaps/__init__.py‎

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MultivariateDataType,
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NdGridDataType,
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)
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from csaps._shortcut import csaps, SmoothingResult
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__all__ = [
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# Shortcut
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'csaps',
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'SmoothingResult',
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# Classes
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'SplinePPFormBase',
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'ISmoothingSpline',
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'SplinePPForm',

‎csaps/_shortcut.py‎

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# -*- coding: utf-8 -*-
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"""
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The module provised `csaps` shortcut function for smoothing data
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"""
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from collections import abc as c_abc
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from typing import Optional, Union, Sequence, NamedTuple
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import numpy as np
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from csaps._base import ISmoothingSpline
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from csaps._sspumv import UnivariateCubicSmoothingSpline
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from csaps._sspndg import ndgrid_prepare_data_sites, NdGridCubicSmoothingSpline
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from csaps._types import (
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UnivariateDataType,
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UnivariateVectorizedDataType,
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NdGridDataType,
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)
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_XDataType = Union[UnivariateDataType, NdGridDataType]
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_YDataType = Union[UnivariateVectorizedDataType, np.ndarray]
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_XiDataType = Optional[Union[UnivariateDataType, NdGridDataType]]
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_WeightsDataType = Optional[Union[UnivariateDataType, NdGridDataType]]
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_SmoothDataType = Optional[Union[float, Sequence[Optional[float]]]]
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SmoothingResult = NamedTuple('SmoothingResult', [
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('values', _YDataType),
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('smooth', _SmoothDataType),
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])
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_ReturnType = Union[
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_YDataType,
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SmoothingResult,
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ISmoothingSpline,
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]
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def csaps(xdata: _XDataType,
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ydata: _YDataType,
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xidata: _XiDataType = None,
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weights: _WeightsDataType = None,
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smooth: _SmoothDataType = None,
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axis: Optional[int] = None) -> _ReturnType:
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"""Smooths the univariate/multivariate/gridded data or computes the corresponding splines
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This function might be used in procedural code.
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Parameters
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----------
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xdata : np.ndarray, array-like
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[required] The data sites ``x1 < x2 < ... < xN``:
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- 1-D data vector/sequence (array-like) for univariate/multivariate ydata case
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- The sequence of 1-D data vectors for nd-gridded ydata case
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ydata : np.ndarray, array-like
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[required] The data values:
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- 1-D data vector/sequence (array-like) for univariate data case
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- N-D array/array-like for multivariate data case
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- N-D array for nd-gridded data case
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xidata : np.ndarray, array-like, sequence[array-like]
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[optional] The data sites for output smoothed data:
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- 1-D data vector/sequence (array-like) for univariate/multivariate ydata case
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- The sequence of 1-D data vectors for nd-gridded ydata case
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If this argument was not set, the function will return computed spline for given data
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in `ISmoothingSpline` object.
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weights : np.ndarray, array-like, sequence[array-like]
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[optional] The weights data vectors:
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- 1-D data vector/sequence (array-like) for univariate/multivariate ydata case
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- The sequence of 1-D data vectors for nd-gridded ydata case
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smooth : float, sequence[float]
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[optional] The smoothing factor value(s):
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- float value in the range ``[0, 1]`` for univariate/multivariate ydata case
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- the sequence of float in the range ``[0, 1]`` or None for nd-gridded ydata case
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If this argument was not set or None or sequence with None-items, the function will return
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named tuple `SmoothingResult` with computed smoothed data values and smoothing factor value(s).
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axis : int
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[optional] The ydata axis. Axis along which "ydata" is assumed to be varying.
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If this argument was not set the last axis will be used.
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Currently, `axis` will be ignored for nd-gridded ydata case.
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Returns
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-------
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yidata : np.ndarray
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Smoothed data values if `xidata` and `smooth` were set.
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smoothed_data : SmoothingResult
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The named tuple with two fileds:
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- 'values' -- smoothed data values
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- 'smooth' -- computed smoothing factor
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This result will be returned if `xidata` was set and `smooth` was not set.
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sspobj : ISmoothingSpline
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Smoothing spline object if `xidata` was not set:
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- `UnivariateCubicSmoothingSpline` instance for univariate/multivariate data
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- `NdGridCubicSmoothingSpline` instance for nd-gridded data
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Examples
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--------
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Univariate data smoothing
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.. code-block:: python
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import numpy as np
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from csaps import csaps
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x = np.linspace(-5., 5., 25)
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y = np.exp(-(x/2.5)**2) + (np.random.rand(25) - 0.2) * 0.3
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xi = np.linspace(-5., 5., 150)
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# Smooth data with smoothing factor 0.85
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yi = csaps(x, y, xi, smooth=0.85)
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# Smooth data and compute smoothing factor automatically
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yi, smooth = csaps(x, y, xi)
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# Do not evaluate the spline, only compute it
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sp = csaps(x, y, smooth=0.98)
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See Also
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--------
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`UnivariateCubicSmoothingSpline`
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`NdGridCubicSmoothingSpline`
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"""
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if isinstance(xdata, c_abc.Sequence):
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try:
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ndgrid_prepare_data_sites(xdata, 'xdata')
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except ValueError:
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umv = True
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else:
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umv = False
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else:
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umv = True
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if umv:
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axis = -1 if axis is None else axis
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sp = UnivariateCubicSmoothingSpline(xdata, ydata, weights, smooth, axis)
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else:
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sp = NdGridCubicSmoothingSpline(xdata, ydata, weights, smooth)
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if xidata is None:
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return sp
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yidata = sp(xidata)
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auto_smooth = smooth is None
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if isinstance(smooth, Sequence):
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auto_smooth = any(sm is None for sm in smooth)
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if auto_smooth:
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return SmoothingResult(yidata, sp.smooth)
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else:
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return yidata

‎csaps/_sspndg.py‎

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from csaps._sspumv import SplinePPForm, UnivariateCubicSmoothingSpline
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def ndgrid_prepare_data_sites(data, name) -> ty.Tuple[np.ndarray, ...]:
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if not isinstance(data, c_abc.Sequence):
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raise TypeError("'{}' must be a sequence of the vectors.".format(name))
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data = list(data)
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for i, di in enumerate(data):
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di = np.array(di, dtype=np.float64)
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if di.ndim > 1:
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raise ValueError("All '{}' elements must be a vector.".format(name))
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if di.size < 2:
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raise ValueError(
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"'{}' must contain at least 2 data points.".format(name))
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data[i] = di
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return tuple(data)
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class NdGridSplinePPForm(SplinePPFormBase[ty.Sequence[np.ndarray], ty.Tuple[int, ...]]):
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"""N-D grid spline representation in PP-form
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"""
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return self._spline
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@staticmethod
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def _prepare_grid_vectors(data, name) -> ty.Tuple[np.ndarray, ...]:
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if not isinstance(data, c_abc.Sequence):
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raise TypeError('{} must be sequence of vectors'.format(name))
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data = list(data)
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for i, di in enumerate(data):
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di = np.array(di, dtype=np.float64)
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if di.ndim > 1:
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raise ValueError('All {} elements must be vector'.format(name))
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if di.size < 2:
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raise ValueError(
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'{} must contain at least 2 data points'.format(name))
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data[i] = di
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return tuple(data)
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@classmethod
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def _prepare_data(cls, xdata, ydata, weights, smooth):
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xdata = cls._prepare_grid_vectors(xdata, 'xdata')
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xdata = ndgrid_prepare_data_sites(xdata, 'xdata')
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data_ndim = len(xdata)
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if ydata.ndim != data_ndim:
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if not weights:
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weights = [None] * data_ndim
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else:
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weights = cls._prepare_grid_vectors(weights, 'weights')
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weights = ndgrid_prepare_data_sites(weights, 'weights')
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if len(weights) != data_ndim:
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raise ValueError(
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return xdata, ydata, weights, smooth
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def __call__(self, xi: NdGridDataType) -> np.ndarray:
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xi = self._prepare_grid_vectors(xi, 'xi')
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xi = ndgrid_prepare_data_sites(xi, 'xi')
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if len(xi) != self._ndim:
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raise ValueError(

‎tests/test_shortcut.py‎

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# -*- coding: utf-8 -*-
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import pytest
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import numpy as np
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from csaps import csaps, SmoothingResult, UnivariateCubicSmoothingSpline, NdGridCubicSmoothingSpline
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@pytest.fixture(scope='module')
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def curve():
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np.random.seed(12345)
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x = np.linspace(-5., 5., 25)
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y = np.exp(-(x / 2.5) ** 2) + (np.random.rand(25) - 0.2) * 0.3
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return x, y
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@pytest.fixture(scope='module')
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def surface():
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np.random.seed(12345)
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x = [np.linspace(-3, 3, 61), np.linspace(-3.5, 3.5, 51)]
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i, j = np.meshgrid(*x, indexing='ij')
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y = (3 * (1 - j) ** 2. * np.exp(-(j ** 2) - (i + 1) ** 2)
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- 10 * (j / 5 - j ** 3 - i ** 5) * np.exp(-j ** 2 - i ** 2)
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- 1 / 3 * np.exp(-(j + 1) ** 2 - i ** 2))
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y += np.random.randn(*y.shape) * 0.75
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return x, y
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@pytest.fixture
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def data(curve, surface, request):
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if request.param == 'univariate':
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x, y = curve
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xi = np.linspace(x[0], x[-1], 150)
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return x, y, xi, 0.85, UnivariateCubicSmoothingSpline
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elif request.param == 'ndgrid':
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x, y = surface
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return x, y, x, [0.85, 0.85], NdGridCubicSmoothingSpline
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@pytest.mark.parametrize('data', [
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'univariate',
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'ndgrid',
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], indirect=True)
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def test_shortcut_output(data):
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x, y, xi, smooth, sp_cls = data
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yi = csaps(x, y, xi, smooth=smooth)
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assert isinstance(yi, np.ndarray)
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smoothed_data = csaps(x, y, xi)
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assert isinstance(smoothed_data, SmoothingResult)
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sp = csaps(x, y)
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assert isinstance(sp, sp_cls)
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@pytest.mark.parametrize('smooth, cls', [
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(0.85, np.ndarray),
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([0.85, 0.85], np.ndarray),
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(None, SmoothingResult),
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([None, 0.85], SmoothingResult),
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([0.85, None], SmoothingResult),
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([None, None], SmoothingResult),
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])
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def test_shortcut_ndgrid_smooth_output(surface, smooth, cls):
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x, y = surface
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output = csaps(x, y, x, smooth=smooth)
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assert isinstance(output, cls)

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