Generate point cloud around the specified point with log-normal distribution

genParCloud.py

#!/usr/bin/env python3

import numpy as np
import pandas as pd
import math
import sys

print("Using pandas ver "+pd.__version__)
try:
    if len(sys.argv) != 3:
        raise
    sigma = float(sys.argv[1])
    outf = sys.argv[2]
except:
    print("Please run ./genParCloud.py [sigma] [output.csv]")
    sys.exit(1)

# an example point
x = np.array([ 0.0009825491410708322, 7.598713300486712e-05, 4.224027984344428, 10.3581808483661,
 0.214155408367835, 5.6896492525618285, 0.0004998229601811062, 3.98329388118285,
 3.2188620413130344, 0.0008449489223685573, 0.00033669412739256114, 36.82257415654826,
 0.5313070938965305, 1.97336462453e-05, 6.75165317732e-05, 1.4323111044574848])

l_x = np.log(x)
s_x = [sigma]*x.shape[0]

# generate distribution over every dimension
nsamp = 1000
pgen = pd.DataFrame(np.zeros((nsamp,x.shape[0])))
pdist = +666
it = 0
while pdist > 0.2:
    it += 1
    for i in range(x.shape[0]):
        jj = np.random.lognormal(l_x[i]-s_x[i]**2/2., s_x[i], nsamp)
        pgen[i] = jj
    pdist = np.max( np.abs ( 1 - pgen.apply(np.mean) / x ) )
#print(jj)
print("Found co-distributions after %d iterations" % (it))
print( np.abs ( 1 - pgen.apply(np.mean) / x ) )

# generate point cloud based on generated distributions
nCombs = 100000
parCombs = pd.DataFrame( np.zeros((nCombs,x.shape[0])) )
for i in range(nCombs):
    parCombs.iloc[i,:] = pgen.iloc[ [np.random.randint(0,nsamp) for i in range(x.shape[0])], :].to_numpy().diagonal()
print("Head of combinations table")
print(parCombs.head())

parCombs.to_csv(outf, index=True, na_rep='nan')

Note1: the log-normal distribution is shifted to reproduce mean at the point.
Note2: The cycle for per-dimension distribution is used to be sure that the real statistical properties of the generated sequence is not very far from the designed.