File:Population curve of Uruk 2.svg

1. 1. uruk population Python 3 code
2. ver 2

import matplotlib import matplotlib.pyplot as plt import numpy as np import pandas as pd from scipy.interpolate import interp1d from scipy.optimize import curve_fit import math as math

1. 1. sigmoid

def sigmoid(x, L ,x0, k, b):

   y = L / (1 + np.exp(-k*(x-x0)))+b
   return (y)

1. 1. exp

def func(x, a, c, d):

   return a*np.exp(-c*x)+d

df = pd.read_csv(r'uruk3.csv', delimiter=';')

beginx=4200 endx=2800 xnum=20 xnum1=xnum+1 pxlen=100

1. bc;est_pop;pop_lower;pop_upper

origx=np.array(df['bc']) origy=np.array(df['est_pop'])

sekondx=np.linspace(beginx, endx,xnum1) xdata0=np.linspace(0, xnum,xnum1)

interp1 = interp1d(origx,origy, kind='cubic')

ydata0 = interp1(sekondx)

1. print (sekondx)
2. rint (xdata0)
3. print (ydata0)

xdata1=xdata0 ydata1=ydata0/100000.0

1. print(ydata1)

1. p0 = [max(ydata1), np.median(xdata1),1,min(ydata1)] # this is an mandatory initial guess
2. popt, pcov = curve_fit(sigmoid, xdata1, ydata1,p0, method='dogbox')

popt, pcov = curve_fit(func, xdata1, ydata1, p0=(1, 1e-6, 1))

print ("Popt") print (popt)

1. print (pcov)

x=np.linspace(0, xnum,pxlen) thirdx=np.linspace(beginx,endx,pxlen)

1. y = sigmoid(x, *popt)

y = func(x, *popt)

y2=y*100000

lok1=0 lok2=pxlen-1

rx1=thirdx[lok1] ry1=y2[lok1] rx2=thirdx[lok2] ry2=y2[lok2]

dx1=rx1-rx2 ## years bc dy1=ry2-ry1

gr1=math.log(ry2/ry1)/dx1

gp1=gr1*100 dout1=math.log(2.0)/gr1

gp1=np.round(gp1,2) dout1=np.round(dout1,0)

annot1="Population growth rate "+str(gp1)+ "%,\n doubling time "+str(dout1)+ " years"

1. print(rx1,rx2, ry1,ry2)
2. print(dx1,dy1)

print("Growth rate %", gp1)

1. print(gp1)

print(" Doubling time yr",dout1)

1. plt.plot(x,y, label='fit')
2. plt.plot(xdata1,ydata1)

plt.plot(thirdx,y2, 'g-.', lw=3,label="Theoretical exponent curve") plt.plot(origx,origy, 'b-', lw=5, label="Data from archaeologists") plt.xlim(beginx,endx) plt.xticks(fontsize=15) plt.yticks(fontsize=15) plt.xlabel("Years BC" , fontsize=15) plt.ylabel("Population of Uruk" , fontsize=15 ) plt.title("Population growth of Uruk" , fontsize=18 )

plt.text(4000, 50000, annot1, fontsize=17) plt.legend()

plt.grid(True) plt.show()