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# Copyright (c) 2017,2019 Weitian LI <wt@liwt.net>
# MIT License
"""
Utilities to help analyze the simulation results.
"""
import logging
import numpy as np
logger = logging.getLogger(__name__)
def inverse_cumsum(x):
"""
Do cumulative sum reversely.
Credit: https://stackoverflow.com/a/28617608/4856091
"""
x = np.asarray(x)
return x[::-1].cumsum()[::-1]
def countdist(x, nbin, log=True, xmin=None, xmax=None):
"""
Calculate the counts distribution, i.e., a histogram.
Parameters
----------
x : list[float]
Array of quantities of every object/source.
nbin : int
Number of bins to calculate the counts distribution.
log : bool, optional
Whether to take logarithm on the ``x`` quantities to determine
the bin edges?
Default: True
xmin, xmax : float, optional
The lower and upper boundaries within which to calculate the
counts distribution. They are default to the minimum and
maximum of the given ``x``.
Returns
-------
counts : 1D `~numpy.ndarray`
The counts in each bin, of length ``nbin``.
bins : 1D `~numpy.ndarray`
The central positions of every bin, of length ``nbin``.
binedges : 1D `~numpy.ndarray`
The edge positions of every bin, of length ``nbin+1``.
"""
x = np.asarray(x)
if xmin is None:
xmin = x.min()
if xmax is None:
xmax = x.max()
x = x[(x >= xmin) & (x <= xmax)]
if log is True:
if xmin <= 0:
raise ValueError("log=True but x have elements <= 0")
x = np.log(x)
xmin, xmax = np.log([xmin, xmax])
binedges = np.linspace(xmin, xmax, num=nbin+1)
bins = (binedges[1:] + binedges[:-1]) / 2
counts, __ = np.histogram(x, bins=binedges)
if log is True:
bins = np.exp(bins)
binedges = np.exp(binedges)
return counts, bins, binedges
def countdist_integrated(x, nbin, log=True, xmin=None, xmax=None):
"""
Calculate the integrated counts distribution (e.g., luminosity
function, mass function), representing the counts with a greater
value, e.g., N(>flux), N(>mass).
"""
counts, bins, binedges = countdist(x=x, nbin=nbin, log=log,
xmin=xmin, xmax=xmax)
counts = inverse_cumsum(counts)
return counts, bins, binedges
def logfit(x, y):
"""
Fit the data points with: y = a * x^b
Parameters
----------
x, y : list[float]
The data points.
Returns
-------
coef : (a, b)
The fitted coefficients.
fp : function
The function with fitted coefficients to calculate the fitted
values: fp(x).
"""
logx = np.log(x)
logy = np.log(y)
fit = np.polyfit(logx, logy, deg=1)
coef = (np.exp(fit[1]), fit[0])
fp = lambda x: np.exp(np.polyval(fit, np.log(x)))
return coef, fp
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