File:Population curve of Mesopotamia - Uruk period 1.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'mesopotamia1.csv', delimiter=';')

beginx=-4000 endx=-3000 xnum=20 xnum1=xnum+1 pxlen=100

1. bc;est_pop;pop_lower;pop_upper

origx=np.array(df['Year']) origy=np.array(df['Population'])

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=ydata0/1000000.0

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)

y3a=x y3b=np.add(y3a,4000) y3c=np.multiply(y3a,0.09) y3d=np.exp(y3c) y3e=np.multiply(y3d,38000) y3=np.round(y3e,0)

print (y3)

y2=y*1000000

1. print (y2)

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)*-1 dout1=np.round(dout1,0)*-1

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)
3. plt.plot(thirdx,y2, 'g-.', lw=3,label="Theoretical exponent curve")

plt.plot(thirdx,y3, 'r-.', lw=4, label="Test curve") plt.plot(origx,origy, 'b-', lw=5, label="Data from archaeologists")

plt.xlim(beginx,endx) plt.xlim(-4000,-3000) plt.ylim(0,300000) plt.xticks(fontsize=15) plt.yticks(fontsize=15) plt.xlabel("Years (negative is BC)" , fontsize=15) plt.ylabel("Population of Mesopotamia" , fontsize=15 ) plt.title("Population growth of Mesopotamia" , fontsize=18 )

plt.text(-3950, 200000, annot1, fontsize=17) plt.legend()

plt.grid(True) plt.show()