Source code for pyretis.analysis.histogram

# -*- coding: utf-8 -*-
# Copyright (c) 2015, PyRETIS Development Team.
# Distributed under the LGPLv2.1+ License. See LICENSE for more info.
"""Histogram functions for data analysis.

This module defines some simple functions for histograms.

Important methods defined here

histogram (:py:func:`.histogram`)
    Create a histogram from given data.

match_all_histograms (:py:func:`.match_all_histograms`)
    Function to match histograms, for instance from an umbrella
    sampling simulation.

histogram_and_avg (:py:func:`.histogram_and_avg`)
    Create histogram an return bins, midpoints and simple statistics.

import numpy as np

__all__ = ['histogram', 'match_all_histograms', 'histogram_and_avg']

[docs]def histogram(data, bins=10, limits=(-1, 1), density=False, weights=None): """Create a histogram of the given data. Parameters ---------- data : numpy.array The data for making the histogram. bins : int, The number of bins to divide the data into. limits : tuple/list The max/min values to consider. density : boolean If True the histogram will be normalised. weights : numpy.array Weighting factors for data. Returns ------- hist : numpy.array The binned counts. bins : numpy.array The edges of the bins. bin_mid : numpy.array The midpoint of the bins. Examples -------- >>> import numpy as np >>> from pyretis.analysis.histogram import histogram >>> data = np.random.randn(50000) >>> hist, bins, bin_mid = histogram(data, bins=30, limits=(-5, 5)) For plotting the histogram: >>> from matplotlib import pyplot as plt >>> plt.plot(bin_mid, hist, '-o', lw=3, alpha=0.8, ms=9) >>> """ hist, bins = np.histogram(data, bins=bins, range=limits, density=density, weights=weights) bin_mid = 0.5 * (bins[1:] + bins[:-1]) return hist, bins, bin_mid
[docs]def histogram_and_avg(data, bins, density=True): """Create histogram an return bins, midpoints and simple statistics. The simple statistics includes the mean value and the standard deviation. The return structure is useful for plotting routines. The midpoints returned are the midpoints of the bins. Parameters ---------- data : 1D numpy.array This is the data to create the histogram from. bins : int The number of bins to use for the histogram. density : boolean, optional If `density` is true, the histogram will be normalised. Returns ------- out[0] : numpy.array The histogram (frequency) values. out[1] : numpy.array The mid points for the bins. out[2] : tuple of floats These are some simple statistics, `out[2][0]` is the average `out[2][1]` is the standard deviation. See Also -------- histogram Examples -------- >>> import numpy as np >>> from pyretis.analysis.histogram import histogram_and_avg >>> data = np.random.randn(50000) >>> hist_data = histogram_and_avg(data, bins=30) Print out the average and standard deviation: >>> print(hist_data[2]) For plotting with matplotlib: >>> from matplotlib import pyplot as plt >>> plt.plot(hist_data[1], hist_data[0], '-o', lw=3, alpha=0.8, ms=9) >>> """ hist, _, bin_mid = histogram(data, bins=bins, limits=(data.min(), data.max()), density=density) return hist, bin_mid, (data.mean(), data.std())
def _match_histograms(histo1, histo2, bin_x, overlap): """Match two histograms given an overlapping region. The matching is done so that the integral of the overlapping regions of the two histograms are equal. Parameters ---------- histo1 : numpy.array The first histogram. histo2 : numpy.array The second histogram, this is the histogram that will be scaled. bin_x : numpy.array This is the bin mid-points of the histograms. Note that we assume here that `histo1` and `histo2` are obtained using the same number of bins and limits. overlap : object like list, tuple or numpy.array This is the overlapping region. Returns ------- out[0] : numpy.array A scaled version of second input histogram `histo2`. out[1] : float The calculated scale factor. """ int1, int2 = 0.0, 0.0 for histi, histj, bin_xi in zip(histo1, histo2, bin_x): if overlap[0] <= bin_xi < overlap[1]: int1 += histi int2 += histj if int2 == 0.0: scale_factor = 1.0 else: scale_factor = int1 / int2 return histo2 * scale_factor, scale_factor
[docs]def match_all_histograms(histograms, umbrellas): """Match several histograms from an umbrella sampling. Parameters ---------- histograms : list of numpy.arrays The histograms to match. umbrellas : list of lists The umbrella windows used in the computation. Returns ------- histograms_s : list of numpy.arrays The scaled histograms. scale_factor : list of floats The scale factors. matched_count : numpy.array Count for overall matched histogram - a "averaged" histogram. """ histograms_s, scale_factor = [histograms[0][0]], [1.0] bin_x = histograms[0][2] for i in range(len(umbrellas) - 1): limits = (umbrellas[i+1][0], umbrellas[i][1]) matched, scale = _match_histograms(histograms_s[-1], histograms[i+1][0], bin_x, limits) histograms_s.append(matched) scale_factor.append(scale) # merge histograms: matched_count = [] for i, bin_xi in enumerate(bin_x): hist = 0.0 # histogram value at bin_xi norm = 0.0 for k, umb in enumerate(umbrellas): if umb[0] <= bin_xi < umb[1]: hist += histograms_s[k][i] norm += 1.0 if norm > 0.0: hist /= norm matched_count.append(hist) return histograms_s, scale_factor, np.array(matched_count)