Fixed more bugs in distributions.py
Per.Andreas.Brodtkorb
11 years ago
parent
6b88f2d4cc
commit
0bfe623f5c
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from __future__ import division, print_function, absolute_import
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import warnings
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import numpy as np
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from scipy.lib.six import callable
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def binned_statistic(x, values, statistic='mean',
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bins=10, range=None):
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"""
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Compute a binned statistic for a set of data.
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This is a generalization of a histogram function. A histogram divides
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the space into bins, and returns the count of the number of points in
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each bin. This function allows the computation of the sum, mean, median,
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or other statistic of the values within each bin.
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.. versionadded:: 0.11.0
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Parameters
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----------
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x : array_like
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A sequence of values to be binned.
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values : array_like
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The values on which the statistic will be computed. This must be
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the same shape as `x`.
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statistic : string or callable, optional
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The statistic to compute (default is 'mean').
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The following statistics are available:
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* 'mean' : compute the mean of values for points within each bin.
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Empty bins will be represented by NaN.
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* 'median' : compute the median of values for points within each
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bin. Empty bins will be represented by NaN.
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* 'count' : compute the count of points within each bin. This is
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identical to an unweighted histogram. `values` array is not
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referenced.
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* 'sum' : compute the sum of values for points within each bin.
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This is identical to a weighted histogram.
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* function : a user-defined function which takes a 1D array of
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values, and outputs a single numerical statistic. This function
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will be called on the values in each bin. Empty bins will be
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represented by function([]), or NaN if this returns an error.
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bins : int or sequence of scalars, optional
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If `bins` is an int, it defines the number of equal-width
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bins in the given range (10, by default). If `bins` is a sequence,
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it defines the bin edges, including the rightmost edge, allowing
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for non-uniform bin widths.
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range : (float, float) or [(float, float)], optional
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The lower and upper range of the bins. If not provided, range
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is simply ``(x.min(), x.max())``. Values outside the range are
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ignored.
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Returns
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-------
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statistic : array
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The values of the selected statistic in each bin.
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bin_edges : array of dtype float
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Return the bin edges ``(length(statistic)+1)``.
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binnumber : 1-D ndarray of ints
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This assigns to each observation an integer that represents the bin
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in which this observation falls. Array has the same length as values.
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See Also
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--------
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numpy.histogram, binned_statistic_2d, binned_statistic_dd
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Notes
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-----
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All but the last (righthand-most) bin is half-open. In other words, if
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`bins` is::
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[1, 2, 3, 4]
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then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the
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second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes*
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4.
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Examples
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--------
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>>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
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... bins=3)
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(array([ 1., 2., 4.]), array([ 1., 2., 3., 4.]), array([1, 2, 1, 2, 3]))
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>>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean', bins=3)
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(array([ 1., 2., 4.]), array([ 1., 2., 3., 4.]), array([1, 2, 1, 2, 3]))
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"""
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try:
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N = len(bins)
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except TypeError:
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N = 1
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if N != 1:
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bins = [np.asarray(bins, float)]
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if range is not None:
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if len(range) == 2:
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range = [range]
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medians, edges, xy = binned_statistic_dd([x], values, statistic,
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bins, range)
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return medians, edges[0], xy
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def binned_statistic_2d(x, y, values, statistic='mean',
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bins=10, range=None):
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"""
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Compute a bidimensional binned statistic for a set of data.
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This is a generalization of a histogram2d function. A histogram divides
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the space into bins, and returns the count of the number of points in
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each bin. This function allows the computation of the sum, mean, median,
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or other statistic of the values within each bin.
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.. versionadded:: 0.11.0
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Parameters
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----------
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x : (N,) array_like
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A sequence of values to be binned along the first dimension.
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y : (M,) array_like
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A sequence of values to be binned along the second dimension.
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values : (N,) array_like
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The values on which the statistic will be computed. This must be
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the same shape as `x`.
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statistic : string or callable, optional
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The statistic to compute (default is 'mean').
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The following statistics are available:
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* 'mean' : compute the mean of values for points within each bin.
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Empty bins will be represented by NaN.
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* 'median' : compute the median of values for points within each
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bin. Empty bins will be represented by NaN.
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* 'count' : compute the count of points within each bin. This is
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identical to an unweighted histogram. `values` array is not
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referenced.
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* 'sum' : compute the sum of values for points within each bin.
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This is identical to a weighted histogram.
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* function : a user-defined function which takes a 1D array of
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values, and outputs a single numerical statistic. This function
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will be called on the values in each bin. Empty bins will be
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represented by function([]), or NaN if this returns an error.
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bins : int or [int, int] or array-like or [array, array], optional
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The bin specification:
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* the number of bins for the two dimensions (nx=ny=bins),
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* the number of bins in each dimension (nx, ny = bins),
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* the bin edges for the two dimensions (x_edges = y_edges = bins),
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* the bin edges in each dimension (x_edges, y_edges = bins).
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range : (2,2) array_like, optional
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The leftmost and rightmost edges of the bins along each dimension
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(if not specified explicitly in the `bins` parameters):
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[[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
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considered outliers and not tallied in the histogram.
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Returns
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-------
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statistic : (nx, ny) ndarray
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The values of the selected statistic in each two-dimensional bin
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xedges : (nx + 1) ndarray
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The bin edges along the first dimension.
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yedges : (ny + 1) ndarray
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The bin edges along the second dimension.
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binnumber : 1-D ndarray of ints
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This assigns to each observation an integer that represents the bin
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in which this observation falls. Array has the same length as `values`.
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See Also
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--------
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numpy.histogram2d, binned_statistic, binned_statistic_dd
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"""
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# This code is based on np.histogram2d
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try:
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N = len(bins)
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except TypeError:
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N = 1
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if N != 1 and N != 2:
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xedges = yedges = np.asarray(bins, float)
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bins = [xedges, yedges]
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medians, edges, xy = binned_statistic_dd([x, y], values, statistic,
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bins, range)
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return medians, edges[0], edges[1], xy
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def binned_statistic_dd(sample, values, statistic='mean',
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bins=10, range=None):
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"""
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Compute a multidimensional binned statistic for a set of data.
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This is a generalization of a histogramdd function. A histogram divides
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the space into bins, and returns the count of the number of points in
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each bin. This function allows the computation of the sum, mean, median,
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or other statistic of the values within each bin.
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.. versionadded:: 0.11.0
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Parameters
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----------
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sample : array_like
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Data to histogram passed as a sequence of D arrays of length N, or
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as an (N,D) array.
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values : array_like
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The values on which the statistic will be computed. This must be
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the same shape as x.
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statistic : string or callable, optional
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The statistic to compute (default is 'mean').
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The following statistics are available:
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* 'mean' : compute the mean of values for points within each bin.
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Empty bins will be represented by NaN.
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* 'median' : compute the median of values for points within each
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bin. Empty bins will be represented by NaN.
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* 'count' : compute the count of points within each bin. This is
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identical to an unweighted histogram. `values` array is not
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referenced.
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* 'sum' : compute the sum of values for points within each bin.
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This is identical to a weighted histogram.
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* function : a user-defined function which takes a 1D array of
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values, and outputs a single numerical statistic. This function
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will be called on the values in each bin. Empty bins will be
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represented by function([]), or NaN if this returns an error.
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bins : sequence or int, optional
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The bin specification:
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* A sequence of arrays describing the bin edges along each dimension.
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* The number of bins for each dimension (nx, ny, ... =bins)
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* The number of bins for all dimensions (nx=ny=...=bins).
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range : sequence, optional
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A sequence of lower and upper bin edges to be used if the edges are
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not given explicitely in `bins`. Defaults to the minimum and maximum
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values along each dimension.
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Returns
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-------
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statistic : ndarray, shape(nx1, nx2, nx3,...)
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The values of the selected statistic in each two-dimensional bin
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edges : list of ndarrays
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A list of D arrays describing the (nxi + 1) bin edges for each
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dimension
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binnumber : 1-D ndarray of ints
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This assigns to each observation an integer that represents the bin
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in which this observation falls. Array has the same length as values.
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See Also
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--------
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np.histogramdd, binned_statistic, binned_statistic_2d
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"""
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if type(statistic) == str:
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if statistic not in ['mean', 'median', 'count', 'sum', 'std']:
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raise ValueError('unrecognized statistic "%s"' % statistic)
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elif callable(statistic):
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pass
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else:
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raise ValueError("statistic not understood")
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# This code is based on np.histogramdd
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try:
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# Sample is an ND-array.
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N, D = sample.shape
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except (AttributeError, ValueError):
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# Sample is a sequence of 1D arrays.
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sample = np.atleast_2d(sample).T
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N, D = sample.shape
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nbin = np.empty(D, int)
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edges = D * [None]
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dedges = D * [None]
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try:
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M = len(bins)
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if M != D:
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raise AttributeError('The dimension of bins must be equal '
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'to the dimension of the sample x.')
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except TypeError:
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bins = D * [bins]
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# Select range for each dimension
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# Used only if number of bins is given.
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if range is None:
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smin = np.atleast_1d(np.array(sample.min(0), float))
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smax = np.atleast_1d(np.array(sample.max(0), float))
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else:
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smin = np.zeros(D)
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smax = np.zeros(D)
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for i in np.arange(D):
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smin[i], smax[i] = range[i]
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# Make sure the bins have a finite width.
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for i in np.arange(len(smin)):
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if smin[i] == smax[i]:
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smin[i] = smin[i] - .5
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smax[i] = smax[i] + .5
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# Create edge arrays
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for i in np.arange(D):
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if np.isscalar(bins[i]):
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nbin[i] = bins[i] + 2 # +2 for outlier bins
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edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1)
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else:
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edges[i] = np.asarray(bins[i], float)
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nbin[i] = len(edges[i]) + 1 # +1 for outlier bins
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dedges[i] = np.diff(edges[i])
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nbin = np.asarray(nbin)
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# Compute the bin number each sample falls into.
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Ncount = {}
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for i in np.arange(D):
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Ncount[i] = np.digitize(sample[:, i], edges[i])
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# Using digitize, values that fall on an edge are put in the right bin.
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# For the rightmost bin, we want values equal to the right
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# edge to be counted in the last bin, and not as an outlier.
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for i in np.arange(D):
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# Rounding precision
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decimal = int(-np.log10(dedges[i].min())) + 6
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# Find which points are on the rightmost edge.
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on_edge = np.where(np.around(sample[:, i], decimal)
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== np.around(edges[i][-1], decimal))[0]
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# Shift these points one bin to the left.
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Ncount[i][on_edge] -= 1
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# Compute the sample indices in the flattened statistic matrix.
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ni = nbin.argsort()
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xy = np.zeros(N, int)
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for i in np.arange(0, D - 1):
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xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod()
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xy += Ncount[ni[-1]]
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result = np.empty(nbin.prod(), float)
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if statistic == 'mean':
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result.fill(np.nan)
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flatcount = np.bincount(xy, None)
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flatsum = np.bincount(xy, values)
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a = flatcount.nonzero()
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result[a] = flatsum[a] / flatcount[a]
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elif statistic == 'std':
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result.fill(0)
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flatcount = np.bincount(xy, None)
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flatsum = np.bincount(xy, values)
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flatsum2 = np.bincount(xy, values ** 2)
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a = flatcount.nonzero()
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result[a] = np.sqrt(flatsum2[a] / flatcount[a]
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- (flatsum[a] / flatcount[a]) ** 2)
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elif statistic == 'count':
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result.fill(0)
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flatcount = np.bincount(xy, None)
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a = np.arange(len(flatcount))
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result[a] = flatcount
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elif statistic == 'sum':
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result.fill(0)
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flatsum = np.bincount(xy, values)
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a = np.arange(len(flatsum))
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result[a] = flatsum
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elif statistic == 'median':
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result.fill(np.nan)
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for i in np.unique(xy):
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result[i] = np.median(values[xy == i])
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elif callable(statistic):
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with warnings.catch_warnings():
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# Numpy generates a warnings for mean/std/... with empty list
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warnings.filterwarnings('ignore', category=RuntimeWarning)
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old = np.seterr(invalid='ignore')
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try:
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null = statistic([])
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except:
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null = np.nan
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np.seterr(**old)
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result.fill(null)
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for i in np.unique(xy):
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result[i] = statistic(values[xy == i])
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# Shape into a proper matrix
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result = result.reshape(np.sort(nbin))
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for i in np.arange(nbin.size):
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j = ni.argsort()[i]
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result = result.swapaxes(i, j)
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ni[i], ni[j] = ni[j], ni[i]
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# Remove outliers (indices 0 and -1 for each dimension).
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core = D * [slice(1, -1)]
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result = result[core]
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if (result.shape != nbin - 2).any():
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raise RuntimeError('Internal Shape Error')
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return result, edges, xy
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@ -0,0 +1,24 @@
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"""
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Statistics-related constants.
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"""
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from __future__ import division, print_function, absolute_import
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import numpy as np
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# The smallest representable positive number such that 1.0 + _EPS != 1.0.
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_EPS = np.finfo(float).eps
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# The largest [in magnitude] usable floating value.
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_XMAX = np.finfo(float).machar.xmax
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# The smallest [in magnitude] usable floating value.
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_XMIN = np.finfo(float).machar.xmin
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# -special.psi(1)
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_EULER = 0.577215664901532860606512090082402431042
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# special.zeta(3, 1) Apery's constant
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_ZETA3 = 1.202056903159594285399738161511449990765
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File diff suppressed because it is too large
Load Diff
@ -0,0 +1,15 @@
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# -*- coding: utf-8 -*-
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"""
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Created on Tue Dec 06 16:02:47 2011
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@author: pab
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"""
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import numpy as np
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import wafo.kdetools as wk
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n = 100
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x = np.sort(5*np.random.rand(1,n)-2.5, axis=-1).ravel()
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y = (np.cos(x)>2*np.random.rand(n, 1)-1).ravel()
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kreg = wk.KRegression(x,y)
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f = kreg(output='plotobj', title='Kernel regression', plotflag=1)
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f.plot()
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