Package: qilum
Qilum is a statistical and utility library supplementing existing statistical libraries
including numpy [1] and scipy [2].
We use numba library [3] to speed up some calculations.In this first version, we provide several random number generators. They are based on the
C++ LOPOR library [4]
and the article Canonical local algorithms for spin systems: heat bath
and Hasting methods [5].
We respect the scipy.stats random number generator interface and any of the scipy.stats classes can be used to initialize qilum classes.The main classes are:Dist_reject. Construct an exact generator for any probability functions. This is the fastest method when you do not know how to calculate or inverse the cumulative [5].Dist_sum. Construct a sum of known distributionsDist_scale. Apply scaling for x and y, for any distributions, even negative scaling for xDist_cubicSpline. Create an approximate random number generator for any functions using cubic spline. If you need an exact random number generator, use Dist_reject. TheDist_cubicSplinecan be used instead ofscipy.stats.rv_histogram, if you need a smooth functionDist_walker. Create a very fast random number generator for discrete distributions.In addition, we expose the functionf_walkerwhich calculates the parameters of the Walker algorithm [6]The most up-to-date Qilum documentation can be found athttps://www.qilum.comThe source code can be found athttps://bitbucket.org/daminou_fr/qilumExample: Discrete Walker distribution Dist_walker# Define a discrete distribution with Walker algorithm 
import qilum.stats as qs
walker = qs.Dist_walker(probabilities=[0.2, 0.5, 0.3], values=[0, 10, 2])
# and call the random number generator
rans = walker.rvs(size=100000)Example: Sum of distributions Dist_sum# exponential distributions left and right types
exp_left  = qs.Dist_scale(scipy.stats.expon(),loc_x=-1.000001, scale_x=-1, scale_y=2, name='Exp+')
exp_right = qs.Dist_scale(scipy.stats.expon(),loc_x= -1, scale_x= 1, scale_y=2, name='Exp-')
# sum of the distributions
dist_sum = qs.Dist_sum([exp_left, exp_right]); 
# random numbers
rans = dist_sum.rvs(100)Example: Rejection method distribution Dist_reject# generate a random generator for f_f(x)     
def f_f(xs): return np.where((xs<-5) | (xs>5), 0, 3.*np.exp(-np.power(xs,4)/10.))
# find a step function above f_f(x)
xs = np.linspace(-6,6, 1001)
ys = f_f(xs)
xs_step, ys_step = qs.f_max(xs, ys, 20)    
ys_step *= 1.2 # just to be sure that our step function >= f_f() 
# create a distribution for this step function:
hist_dist = scipy.stats.rv_histogram((ys_step, xs_step))
# scale this diribution
cumulative = qs.f_cumulative(xs_step, ys_step)[-1]
dist_step = qs.Dist_scale(hist_dist, scale_y = cumulative, name='dist_step')
# create dist_reject 
dist_reject = qs.Dist_reject(dist_step, f_f)
# random numbers
rans = dist_reject.rvs(100)References:[1] numpy:https://numpy.org[2] scipyhttps://www.scipy.org/[3] numbahttp://numba.pydata.org[4] C++ LOPOR library:http://www.damienloison.com/finance/LOPOR/index.html[5] Canonical local algorithms for spin systems: heat bath
and Hasting methods:http://www.damienloison.com/articles/reference26.pdf[6] A.J. Walker, ACM Transaction on Mathematical Software 3 (1977) 253