#16 Bisection method using python

import os
import matplotlib.pyplot as plt
import numpy as np
os.chdir('/home/vg/Downloads/projects/ex16')
os.getcwd()
f = lambda x: np.exp(x)-2
tol=0.1
a,b=-2,2
x=np.linspace(-2.1,2.1,1000)
fig,ax=plt.subplots(1,1,figsize=(12,4)) 
ax.plot(x,f(x),lw=1.5)
ax.axhline(0,ls=':',color='k')
ax.set_xticks([-2,-1,0,1,2])
ax.set_xlabel(r'$x$',fontsize=18)
ax.set_ylabel(r'$f(x)$',fontsize=18)
fa,fb=f(a),f(b)
ax.plot(a,fa,'ko')
ax.plot(b,fb,'ko')
ax.text(a,fa+0.5,r"$a$",ha='center',fontsize=18)
ax.text(b,fb+0.5,r"$b$",ha='center',fontsize=18)
n=1
while b-a > tol:
    m=a+(b-a)/2
    fm=f(m)
    ax.plot(m,fm,'ko')
    ax.text(m,fm-0.5,r"$m_%d$" % n,ha='center')
    n=n+1
    if (np.sign(fa)==np.sign(fm)):
        a,fa=m,fm
    else:
        b,fb=m,fm

ax.plot(m,fm,'r*',markersize=10)
ax.annotate("Root approximately at %.3f" % m,fontsize=12,
    xy=(a,fm),xycoords='data',
    xytext=(-150,+50),textcoords='offset points',
    arrowprops=dict(arrowstyle="->",
    connectionstyle="arc3, rad=-.5"))
ax.set_title("Bisection method")
plt.savefig("example16.png", dpi=100)
plt.show()
plt.close()