smooth.lowess

smooth.lowess(x, y=None, f=0.6666666666666666, iter=3, delta=None)

LOWESS smoother that exactly matches R’s stats::lowess function.

Performs locally weighted polynomial regression using Cleveland’s LOWESS algorithm. This implementation produces results identical to R’s stats::lowess function.

Parameters:

  • x (array-like) – The x values for the data. Can also be a 2D array or list with two elements, in which case the first column/element is used as x and second as y.

  • y (array-like, optional) – The y values for the data. If None, x must contain both x and y values as a 2D array or a list/tuple of two arrays.

  • f (float, default=2/3) – The smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness.

  • iter (int, default=3) – The number of robustifying iterations which should be performed. Using smaller values of iter will make lowess run faster.

  • delta (float, optional) – Values within delta of each other are treated as being at the same point. If None (default), uses 0.01 * (max(x) - min(x)), matching R’s default.

Returns:

A dictionary with two keys matching R’s lowess output: - ‘x’: The sorted x values - ‘y’: The smoothed y values corresponding to the sorted x values

Return type:

dict

Notes

This function is a direct port of R’s stats::lowess, which implements Cleveland’s (1979) LOWESS algorithm. The algorithm uses locally weighted polynomial regression with a tricube weight function and iterative reweighting for robustness to outliers.

The function returns results in the same format as R’s lowess: a list/dict with ‘x’ and ‘y’ components, where x is sorted and y contains the corresponding smoothed values.

References

Cleveland, W.S. (1979) “Robust Locally Weighted Regression and Smoothing Scatterplots”. Journal of the American Statistical Association 74(368): 829-836.

See also

smooth.adam_general.lowess_cpp

Direct C++ lowess function (unsorted output)

smooth.adam_general.core.utils.utils.lowess_r

Pure Python implementation

Examples

Basic usage with separate x and y arrays:

>>> import numpy as np
>>> from smooth import lowess
>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
>>> y = np.array([1.1, 2.0, 2.9, 4.2, 4.8, 6.1, 7.0, 7.9, 9.2, 9.8])
>>> result = lowess(x, y)
>>> result['x']  # Sorted x values
array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
>>> result['y']  # Smoothed y values
array([...])

With custom smoother span:

>>> result = lowess(x, y, f=0.5)

Using a 2D array input (like R’s behavior):

>>> xy = np.column_stack([x, y])
>>> result = lowess(xy)