API Reference

Summary

csaps	Smooths the univariate/multivariate/gridded data or computes the corresponding splines
AutoSmoothingResult	The result for auto smoothing for csaps function
ISmoothingSpline	The interface class for smooting splines
CubicSmoothingSpline	Cubic smoothing spline
NdGridCubicSmoothingSpline	N-D grid cubic smoothing spline
ISplinePPForm	The interface class for spline representation in PP-form
SplinePPForm	The base class for univariate/multivariate spline in piecewise polynomial form
NdGridSplinePPForm	N-D grid spline representation in PP-form

Main API

csaps.csaps(xdata: Union[ndarray, Sequence[Number]], ydata: Union[ndarray, Sequence], *, weights: Optional[Union[ndarray, Sequence[Number]]] = None, smooth: Optional[float] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → ISmoothingSpline

csaps.csaps(xdata: Union[ndarray, Sequence[Number]], ydata: Union[ndarray, Sequence], xidata: Union[ndarray, Sequence[Number]], *, weights: Optional[Union[ndarray, Sequence[Number]]] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → AutoSmoothingResult

csaps.csaps(xdata: Union[ndarray, Sequence[Number]], ydata: Union[ndarray, Sequence], xidata: Union[ndarray, Sequence[Number]], *, smooth: float, weights: Optional[Union[ndarray, Sequence[Number]]] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → Union[ndarray, Sequence]

csaps.csaps(xdata: Sequence[Union[ndarray, Sequence[Number]]], ydata: Union[ndarray, Sequence], *, weights: Optional[Sequence[Union[ndarray, Sequence[Number]]]] = None, smooth: Optional[Sequence[float]] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → ISmoothingSpline

csaps.csaps(xdata: Sequence[Union[ndarray, Sequence[Number]]], ydata: Union[ndarray, Sequence], xidata: Sequence[Union[ndarray, Sequence[Number]]], *, weights: Optional[Sequence[Union[ndarray, Sequence[Number]]]] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → AutoSmoothingResult

csaps.csaps(xdata: Sequence[Union[ndarray, Sequence[Number]]], ydata: Union[ndarray, Sequence], xidata: Sequence[Union[ndarray, Sequence[Number]]], *, smooth: Sequence[float], weights: Optional[Sequence[Union[ndarray, Sequence[Number]]]] = None, axis: Optional[int] = None, normalizedsmooth: bool = False) → Union[ndarray, Sequence]

Smooths the univariate/multivariate/gridded data or computes the corresponding splines

This function might be used as the main API for smoothing any data.

Parameters:

xdatanp.ndarray, array-like

The data sites x1 < x2 < ... < xN:

• 1-D data vector/sequence (array-like) for univariate/multivariate ydata case

• The sequence of 1-D data vectors for nd-gridded ydata case

ydatanp.ndarray, array-like

The data values:

• 1-D data vector/sequence (array-like) for univariate data case

• N-D array/array-like for multivariate data case

• N-D array for nd-gridded data case

xidata[Optional] np.ndarray, array-like, Sequence[array-like]

The data sites for output smoothed data:

• 1-D data vector/sequence (array-like) for univariate/multivariate ydata case

• The sequence of 1-D data vectors for nd-gridded ydata case

If this argument was not set, the function will return computed spline for given data in ISmoothingSpline object.

weights[Optional] np.ndarray, array-like, Sequence[array-like]

The weights data vectors:

• 1-D data vector/sequence (array-like) for univariate/multivariate ydata case

• The sequence of 1-D data vectors for nd-gridded ydata case

smooth[Optional] float, Sequence[float]

The smoothing factor value(s):

• float value in the range [0, 1] for univariate/multivariate ydata case

• the sequence of float in the range [0, 1] or None for nd-gridded ydata case

If this argument was not set or None or sequence with None-items, the function will return named tuple AutoSmoothingResult with computed smoothed data values and smoothing factor value(s).

axis[Optional] int

The ydata axis. Axis along which ydata is assumed to be varying. If this argument was not set the last axis will be used (axis == -1).

Note

Currently, axis will be ignored for nd-gridded ydata case.

normalizedsmooth[Optional] bool

If True, the smooth parameter is normalized such that results are invariant to xdata range and less sensitive to nonuniformity of weights and xdata clumping

New in version 1.1.0.

Returns:

yidatanp.ndarray

Smoothed data values if xidata and smooth were set.

autosmoothing_resultAutoSmoothingResult

The named tuple object with two fileds:

• ‘values’ – smoothed data values

• ‘smooth’ – computed smoothing factor

This result will be returned if xidata was set and smooth was not set.

ssp_objISmoothingSpline

Smoothing spline object if xidata was not set:

• CubicSmoothingSpline instance for univariate/multivariate data

• NdGridCubicSmoothingSpline instance for nd-gridded data

See also

CubicSmoothingSpline

NdGridCubicSmoothingSpline

Examples

Univariate data smoothing

import numpy as np
from csaps import csaps

x = np.linspace(-5., 5., 25)
y = np.exp(-(x/2.5)**2) + (np.random.rand(25) - 0.2) * 0.3
xi = np.linspace(-5., 5., 150)

# Smooth data with smoothing factor 0.85
yi = csaps(x, y, xi, smooth=0.85)

# Smooth data and compute smoothing factor automatically
yi, smooth = csaps(x, y, xi)

# Do not evaluate the spline, only compute it
sp = csaps(x, y, smooth=0.98)

---

class csaps.AutoSmoothingResult(values: Union[ndarray, Sequence], smooth: Union[float, Sequence[Optional[float]]])

Bases: tuple

The result for auto smoothing for csaps function

property values

Smoothed data values

property smooth

The calculated smoothing parameter

Object-Oriented API

class csaps.CubicSmoothingSpline(xdata: Union[ndarray, Sequence[Number]], ydata: Union[ndarray, Sequence], weights: Optional[Union[ndarray, Sequence[Number]]] = None, smooth: Optional[float] = None, axis: int = -1, normalizedsmooth: bool = False)

Bases: ISmoothingSpline[SplinePPForm, float, Union[ndarray, Sequence[Number]], int, Union[bool, str]]

Cubic smoothing spline

The cubic spline implementation for univariate/multivariate data.

Parameters:

xdatanp.ndarray, sequence, vector-like

X input 1-D data vector (data sites: x1 < x2 < ... < xN)

ydatanp.ndarray, vector-like, sequence[vector-like]

Y input 1-D data vector or ND-array with shape[axis] equal of xdata size)

weights[Optional] np.ndarray, list

Weights 1-D vector with size equal of xdata size

smooth[Optional] float

Smoothing parameter in range [0, 1] where:

• 0: The smoothing spline is the least-squares straight line fit

• 1: The cubic spline interpolant with natural condition

axis[Optional] int

Axis along which ydata is assumed to be varying. Meaning that for x[i] the corresponding values are np.take(ydata, i, axis=axis). By default is -1 (the last axis).

normalizedsmooth[Optional] bool

If True, the smooth parameter is normalized such that results are invariant to xdata range and less sensitive to nonuniformity of weights and xdata clumping

New in version 1.1.0.

__call__(x: Union[ndarray, Sequence[Number]], nu: Optional[int] = None, extrapolate: Optional[Union[bool, str]] = None) → ndarray

Evaluate the spline for given data

Parameters:

x1-d array-like

Points to evaluate the spline at.

nu[Optional] int

Order of derivative to evaluate. Must be non-negative.

extrapolate[Optional] bool or ‘periodic’

If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. If ‘periodic’, periodic extrapolation is used. Default is True.

Notes

Derivatives are evaluated piecewise for each polynomial segment, even if the polynomial is not differentiable at the breakpoints. The polynomial intervals are considered half-open, [a, b), except for the last interval which is closed [a, b].

property smooth: float

Returns the smoothing factor

Returns:

smoothfloat

Smoothing factor in the range [0, 1]

property spline: SplinePPForm

Returns the spline description in SplinePPForm instance

Returns:

splineSplinePPForm

The spline representation in SplinePPForm instance

---

class csaps.NdGridCubicSmoothingSpline(xdata: Sequence[Union[ndarray, Sequence[Number]]], ydata: ndarray, weights: Optional[Union[ndarray, Sequence[Number], Sequence[Union[ndarray, Sequence[Number]]]]] = None, smooth: Optional[Union[float, Sequence[Optional[float]]]] = None, normalizedsmooth: bool = False)

Bases: ISmoothingSpline[NdGridSplinePPForm, Tuple[float, …], Sequence[Union[ndarray, Sequence[Number]]], Tuple[int, …], bool]

N-D grid cubic smoothing spline

Class implements N-D grid data smoothing (piecewise tensor product polynomial).

Parameters:

xdatalist, tuple, Sequence[vector-like]

X data site vectors for each dimensions. These vectors determine ND-grid. For example:

# 2D grid
x = [
    np.linspace(0, 5, 21),
    np.linspace(0, 6, 25),
]

ydatanp.ndarray

Y data ND-array with shape equal xdata vector sizes

weights[Optional] list, tuple, Sequence[vector-like]

Weights data vector(s) for all dimensions or each dimension with size(s) equal to xdata sizes

smooth[Optional] float, Sequence[float]

The smoothing parameter (or a sequence of parameters for each dimension) in range [0, 1] where:

• 0: The smoothing spline is the least-squares straight line fit

• 1: The cubic spline interpolant with natural condition

normalizedsmooth[Optional] bool

If True, the smooth parameter is normalized such that results are invariant to xdata range and less sensitive to nonuniformity of weights and xdata clumping

New in version 1.1.0.

__call__(x: Union[Sequence[Union[ndarray, Sequence[Number]]], Sequence[Number]], nu: Optional[Tuple[int, ...]] = None, extrapolate: Optional[bool] = None) → ndarray

Evaluate the spline for given data

Parameters:

xtuple of 1-d array-like

The tuple of point values for each dimension to evaluate the spline at.

nu[Optional] tuple of int

Orders of derivatives to evaluate. Each must be non-negative.

extrapolate[Optional] bool

Whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs.

Returns:

yarray-like

Interpolated values. Shape is determined by replacing the interpolation axis in the original array with the shape of x.

property smooth: Tuple[float, ...]

Returns a tuple of smoothing parameters for each axis

Returns:

smoothTuple[float, …]

The smoothing parameter in the range [0, 1] for each axis

property spline: NdGridSplinePPForm

Returns the spline description in ‘NdGridSplinePPForm’ instance

Returns:

splineNdGridSplinePPForm

The spline description in NdGridSplinePPForm instance

---

class csaps.SplinePPForm(c, x, extrapolate=None, axis=0)

Bases: ISplinePPForm[ndarray, int], PPoly

The base class for univariate/multivariate spline in piecewise polynomial form

Piecewise polynomial in terms of coefficients and breakpoints.

Notes

Inherited from scipy.interpolate.PPoly

property breaks: ndarray

Returns the breaks for the spline

Returns:

breaksUnion[np.ndarray, ty.Tuple[np.ndarray, …]]

Breaks data

property coeffs: ndarray

Returns the spline coefficients

Returns:

coeffsnp.ndarray

Coefficients n-d array

property ndim: int

Returns the number of spline dimensions

The number of dimensions is product of shape without shape[self.axis].

property order: int

Returns the spline order

Returns:

orderty.Union[int, ty.Tuple[int, …]]

The spline order

property pieces: int

Returns the spline pieces data

Returns:

piecesty.Union[int, ty.Tuple[int, …]]

The spline pieces data

property shape: Tuple[int]

Returns the source data shape

---

class csaps.NdGridSplinePPForm(c, x, extrapolate=None)

Bases: ISplinePPForm[Tuple[ndarray, …], Tuple[int, …]], NdPPoly

N-D grid spline representation in PP-form

N-D grid spline is represented in piecewise tensor product polynomial form.

Notes

Inherited from scipy.interpolate.NdPPoly

property breaks: Tuple[ndarray, ...]

Returns the breaks for the spline

Returns:

breaksUnion[np.ndarray, ty.Tuple[np.ndarray, …]]

Breaks data

property coeffs: ndarray

Returns the spline coefficients

Returns:

coeffsnp.ndarray

Coefficients n-d array

property ndim: int

Returns the spline dimension count

Returns:

ndimint

The spline dimension count

property order: Tuple[int, ...]

Returns the spline order

Returns:

orderty.Union[int, ty.Tuple[int, …]]

The spline order

property pieces: Tuple[int, ...]

Returns the spline pieces data

Returns:

piecesty.Union[int, ty.Tuple[int, …]]

The spline pieces data

property shape: Tuple[int, ...]

Returns the source data shape

Returns:

shapetuple of int

The source data shape

Interfaces

class csaps.ISmoothingSpline(*args, **kwds)

Bases: ABC, Generic[TSpline, TSmooth, TXi, TNu, TExtrapolate]

The interface class for smooting splines

abstract __call__(xi: TXi, nu: Optional[TNu] = None, extrapolate: Optional[TExtrapolate] = None) → ndarray

Evaluates spline on the data sites

abstract property smooth: TSmooth

Returns smoothing factor(s)

abstract property spline: TSpline

Returns spline representation in PP-form

---

class csaps.ISplinePPForm(*args, **kwds)

Bases: ABC, Generic[TData, TProps]

The interface class for spline representation in PP-form

abstract property breaks: TData

Returns the breaks for the spline

Returns:

breaksUnion[np.ndarray, ty.Tuple[np.ndarray, …]]

Breaks data

abstract property coeffs: ndarray

Returns the spline coefficients

Returns:

coeffsnp.ndarray

Coefficients n-d array

abstract property ndim: int

Returns the spline dimension count

Returns:

ndimint

The spline dimension count

abstract property order: TProps

Returns the spline order

Returns:

orderty.Union[int, ty.Tuple[int, …]]

The spline order

abstract property pieces: TProps

Returns the spline pieces data

Returns:

piecesty.Union[int, ty.Tuple[int, …]]

The spline pieces data

abstract property shape: Tuple[int]

Returns the source data shape

Returns:

shapetuple of int

The source data shape