import matplotlib.pyplot as plt
from matplotlib import interactive
from numpy import pi,log10
interactive(True)
N = int(input("N terms = "))

#       prepare plot frame and description
plt.figure(figsize=(6,5))
plt.xlabel('log$_{10}$ N',fontsize=14)
plt.ylabel('log$_{10}$ |$x-\pi$|',fontsize=14)
plt.title('Accelerated convergence of Leibniz ser. for $\pi$',fontsize=14)
plt.axis([0.,log10(N*4), -16.,0.])
plt.grid(True,color=(.8,.9,.97))

'''
    Series x = 4/1 -4/3 +4/5 -4/7 +...+(+-1)/(odd N) due to Leibniz
    is accelerated by repeated averaging of neighboring terms.
    This is done with almost zero storage and one series summation
'''
x = x_1 = a = b = c = const = 4. 
i = 1
while(i < N):    # c is the number of people/obj.
    i += 2
    const = -const
    a_1 = a
    b_1 = b
    c_1 = c
    x_2 = x_1
    x_1 = x
    x = x + const/i
    a = (x+x_1)*0.5
    b = (a+a_1)*0.5
    c = (b+b_1)*0.5
    d = (c+c_1)*0.5

    if(i<700 or (i>200 and (i-1)%8==0)):
        i0 = log10(i)
        y0 = log10(max(abs(x-pi),1e-20))
        e1 = log10(max(abs(a-pi),1e-20))
        e2 = log10(max(abs(b-pi),1e-20))
        e3 = log10(max(abs(c-pi),1e-20))
        e4 = log10(max(abs(d-pi),1e-20))
# plot singe point   
        plt.scatter(i0,y0,s=5,color=(.3,0.,.8),linewidth=2)
        plt.scatter(i0,e1,s=5,color=(.7,1.,.2),linewidth=2)
        plt.scatter(i0,e2,s=4,color=(0.,1.,0.),linewidth=2) 
        plt.scatter(i0,e3,s=4,color=(.2,.4,1.),linewidth=2)
        plt.scatter(i0,e4,s=5,color=(.9,.3,.0),linewidth=2)

plt.text(i0+.1,y0,"Leibniz") 
plt.text(i0+.1,e1,"1av")
plt.text(i0+.1,e2,"2av")
plt.text(i0+.1,e3,"3av")
plt.text(i0+.1,-15.3,"4av")

ans = input("ok?")