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rootfindingmethods.py
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rootfindingmethods.py
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from tkinter import *
import numpy as np
import pandas as pd
import math as m
import matplotlib.pyplot as plt
from IPython.core.display import HTML
from sympy import Symbol, Derivative
from scipy.misc import derivative
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
window = Tk()
window.title("Welcome to Root Finding Methods")
window.geometry('650x650')
window.resizable(width=False, height=False)
bg_image = PhotoImage(file ="bg.png")
x = Label (image = bg_image)
x.grid(row = 0, column = 0)
selected = DoubleVar()
RF=0
NR=0
SC=0
BM=0
def func( x ):
return ((x**2)+(2*x)-10);
def derivFunc( x ):
h=(derivative(func,x))
return h
def f(x):
f = func(x)
return f;
def newtonRaphson( x ,E, n):
print("----------Newton Rephson-------------")
global NR
newtonCount=0;
mylist=[]
h = func(x) / derivFunc(x)
while abs(h) >= E:
if(derivFunc(x)==0):
print("Not Possible")
break;
else:
h = func(x)/derivFunc(x)
mylist.append(h)
x = x - h
newtonCount=newtonCount+1;
if(newtonCount>n):
break
if(newtonCount>n):
print("Could Not Found Solution even in ",n, "iterations")
NR=0
else:
NR=newtonCount
print("The value of the root By Newton rephson method is : ", "%.4f"% x)
print("Counts : ",newtonCount)
plt.plot(mylist, color='g')
plt.xlabel('No. of iteration')
plt.ylabel('Tolerence')
plt.title('Graph - NewtonRephson')
plt.show()
return
def bisection(a,b,E, n):
print("----------Bisection-------------")
global BM
bisectionCount=0;
mylist=[]
if (func(a) * func(b) >= 0):
print("Here f(a)>0 and f(b)>0 So, Solution is not possible. Try Again...")
return
c = a
while ((b-a) >= E):
mylist.append((b-a))
c = (a+b)/2
if (func(c) == 0.0):
break
if (func(c)*func(a) < 0):
b = c
else:
a = c
bisectionCount=bisectionCount+1
if(bisectionCount>n):
break;
if(bisectionCount>n):
BM=0
print("Could Not Found Solution even in ",n, "iterations")
else:
BM=bisectionCount
print("The value of root is : ","%.4f"%c)
print("Counts : ",bisectionCount)
plt.plot(mylist, color='g')
plt.xlabel('No. of iteration')
plt.ylabel('Tolerence')
plt.title('Graph - Bisection')
plt.show()
return
def regulaFalsi(a,b,TOL,N):
print("----------Regula Falsi-------------")
global RF
mylist=[]
i = 1
FA = f(a)
if(f(a)*f(b)<0):
while True:
p = (a*f(b)-b*f(a))/(f(b) - f(a))
FP = f(p)
if(FP == 0 or np.abs(f(p)) < TOL):
break
mylist.append(np.abs(f(p)))
i = i + 1
if(FA*FP > 0):
a = p
else:
b = p
if(i>N):
break
if(i>N):
print("Could Not Found Solution even in ",nn, "iterations")
RF=0
else:
print("The value of root is : " , '%.4f'%a)
print("Count : ",i)
RF=i;
else:
print("Here f(a)>0 and f(b)>0 So, Solution is not possible. Try Again...")
plt.plot(mylist, color='g')
plt.xlabel('No. of iteration')
plt.ylabel('Tolerence')
plt.title('Graph - Regula Falsi')
plt.show()
return
def secant(x1, x2, E, nn):
print("----------Secant-------------")
global SC
n = 0; xm = 0; x0 = 0; c = 0;
mylist=[]
if(f(x1)*f(x2)<0):
while True:
x0 = ((x1 * f(x2) - x2 * f(x1)) /
(f(x2) - f(x1)));
c = f(x1) * f(x0);
x1 = x2;
x2 = x0;
n += 1;
if(n>nn):
break;
if (c == 0):
break;
xm = ((x1 * f(x2) - x2 * f(x1)) /
(f(x2) - f(x1)));
if(abs(xm - x0) < E):
break;
mylist.append(abs(xm - x0))
SC=n
if(n>nn):
print("Could Not Found Solution even in ",nn, "iterations")
SC=0
else:
print("Root of the given equation =",
round(x0, 4));
print("No. of iterations = ", n);
else:
print("Here f(a)>0 and f(b)>0 So, Solution is not possible. Try Again...")
plt.plot(mylist, color='g')
plt.xlabel('No. of iteration')
plt.ylabel('Tolerence')
plt.title('Graph - Secant')
plt.show()
return
def draw_Graph():
MethodName = ['Bisection Method','Regula Falsi','Newton Rephson','Secant Method']
Count = [BM,RF,NR, SC]
plt.plot(MethodName, Count, color='g')
plt.xlabel('Method Name')
plt.ylabel('No. of iteration')
plt.title('Comparision of root finding Methods')
plt.show()
return
def draw_Bar_Graph():
s = pd.Series(
[BM,RF,NR, SC],
index = ['Bisection Method','Regula Falsi','Newton Rephson','Secant Method']
)
plt.title("Comparision of Root Finding Methods")
plt.ylabel('No of Iteration')
plt.xlabel('Mathod Name')
ax = plt.gca()
ax.tick_params(axis='x', colors='blue')
ax.tick_params(axis='y', colors='red')
my_colors = 'Black'
s.plot(
kind='bar',
color=my_colors,
)
plt.show()
return
def a():
a=txt2.get()
b=txt3.get()
E=selected.get()
N=txt1.get()
bisection(float(a),float(b),E,int(N))
def b():
a=txt2.get()
b=txt3.get()
E=selected.get()
N=txt1.get()
newtonRaphson(float(a),E,int(N))
def c():
a=txt2.get()
b=txt3.get()
E=selected.get()
N=txt1.get()
regulaFalsi(float(a),float(b),E,int(N))
def d():
a=txt2.get()
b=txt3.get()
E=selected.get()
N=txt1.get()
secant(float(a),float(b),E,int(N))
def allF():
a=txt2.get()
b=txt3.get()
E=selected.get()
N=txt1.get()
print(" ")
print(" --- ")
print(" ")
bisection(float(a),float(b),E,int(N))
newtonRaphson(float(a),E,int(N))
regulaFalsi(float(a),float(b),E,int(N))
secant(float(a),float(b),E,int(N))
draw_Bar_Graph()
draw_Graph()
lbl = Label(window, text="Max Iterations")
lbl.place(x=15,y=70)
lbl.config(bg="white")
txt1 =Entry(window,bd=5,width="30")
txt1.place(x=115,y=70)
lbl = Label(window, text="Enter a")
lbl.place(x=15,y=115)
lbl.config(bg="white")
txt2 =Entry(window,bd=5,width="30")
txt2.place(x=115,y=115)
lbl = Label(window, text="Enter b")
lbl.place(x=15,y=160)
lbl.config(bg="white")
txt3 =Entry(window,bd=5,width="30")
txt3.place(x=115,y=160)
lbl = Label(window, text="Select Tolerance")
lbl.place(x=15,y=250)
lbl.config(bg="white")
rad1 = Radiobutton(window,text='0.1', value=0.1, variable=selected)
rad2 = Radiobutton(window,text='0.01', value=0.01, variable=selected)
rad3 = Radiobutton(window,text='0.001', value=0.001, variable=selected)
rad4 = Radiobutton(window,text='0.0001', value=0.0001, variable=selected)
rad5 = Radiobutton(window,text='0.00001', value=0.00001, variable=selected)
rad6 = Radiobutton(window,text='0.000001', value=0.000001, variable=selected)
rad1.place(x=115, y=250)
rad1.config(bg="white")
rad2.place(x=185, y=250)
rad2.config(bg="white")
rad3.place(x=255, y=250)
rad3.config(bg="white")
rad4.place(x=325, y=250)
rad4.config(bg="white")
rad5.place(x=395, y=250)
rad5.config(bg="white")
rad6.place(x=465, y=250)
rad6.config(bg="white")
btn = Button(window, text="Bisection", height="2", width="20", command=a)
btn.place(x=100,y=300)
btn = Button(window, text="Newton Rephson", height="2", width="20", command=b)
btn.place(x=100,y=350)
btn = Button(window, text="Regula", height="2", width="20", command=c)
btn.place(x=100,y=400)
btn = Button(window, text="Secant", height="2", width="20", command=d)
btn.place(x=100,y=450)
btn = Button(window, text="Compare All", height="2", width="20", command=allF)
btn.place(x=100,y=500)
window.mainloop()