Python before 16-9-18

BISECTION

import math
import random

def f(x):
    return math.exp(-x) - x

while(1):
    a = random.random()
    b = random.random()
    if f(a)*f(b) < 0:
        break
x = []
y = []
i = 0
n = 20
c = (a+b)/2
while(i < n):

    if f(c) == 0:
        break
    if f(c)*f(a) > 0:
        a = c
    if f(c)*f(b) > 0:
        b = c
    temp = c
    c = (a+b)/2
    #Difference of current c and previous c
    #Error approximation
    y.append(abs((c-temp)/c)*100)
    i+=1

print c, f(c)

import matplotlib.pyplot as plt
plt.plot(range(1,n+1),y,marker = 'o')
plt.show()



POWER


# -*- coding: wtf-8 -*-
"""
Created on Tue Sep  4 14:06:16 2018

@author: CSE CARNIVAL 2017
"""

import math
def ePower(x,tol):
   val=1
   i=0
   while True:
       temp=val
       i+=1;
       val+=(x**i)/math.factorial(i)
       if (val-temp)/val<=tol:
           break

   return val,i

print ePower(5,0.01)
print math.exp(0.5)

EXPONENTIAL

# -*- coding: utf-8 -*-
"""
Created on Sun Sep  9 14:24:32 2018

@author: CSE CARNIVAL 2017
"""

"""
e^x - exponential
"""

#Loop until a fixed tolerance of error
import numpy as np
import math
def myexp(x, tol):
    s = 1.
    i = 1
    while(1):
        s_p = s
        s += (x**i)/math.factorial(i)
        err = (s-s_p)/s*100

        if(err < tol):
            break
        i+=1
    return s,i

#Loop until a fixed number of iterations
def myexp2(x, n):
    s = 1.
    i = 1
    while(1):
        s_p = s
        s += (x**i)/math.factorial(i)
        err = (s-s_p)/s*100

        if(i >= n):
            break
        i+=1
    return s

print myexp(0.5,0.0000001)
print myexp2(0.5,10)
print math.exp(0.5)

true_val = math.exp(0.5)
y = []
x = range(10)
y= []
for i in x:
    approx_val = myexp2(0.5,i)
    true_err = (true_val - approx_val)/true_val*100
    y.append(true_err)

#Same shit using list comprehension
#y = [(true_val - myexp2(0.5,i))/true_val*100 for i in x]

import matplotlib.pyplot as plt
plt.plot(x,y,marker='o')
plt.show()


FALSE POSITION

# -*- coding: utf-8 -*-
"""
Created on Tue Sep 11 14:12:56 2018

@author: CSE CARNIVAL 2017
"""
import math
import random

def f(x):
    return math.exp(-x)-x

while(True):
    x_l=random.random()
    x_u=random.random()
    if f(x_l)*f(x_u)<0:
        break

#x_l=0
#x_u =1
i=0
x_r=x_u-(f(x_u)*(x_l-x_u))/(f(x_l)-f(x_u))
err=[]
while(i<20):


    if f(x_r)==0:
        break
    if f(x_r)*f(x_l)>0:
        x_l=x_r
    if f(x_r)*f(x_u)>0:
        x_u=x_r
    old=x_r
    x_r=x_u-(f(x_u)*(x_l-x_u))/(f(x_l)-f(x_u))
    i+=1
    #sign is not important for error
    #error is high for 1st iteration
    err.append(abs((x_r-old)/x_r)*100)
print(x_r,i)

import matplotlib.pyplot as plt
plt.plot(range(i),err,marker='o')
plt.show()


GIVEN

# -*- coding: utf-8 -*-
"""
Created on Tue Sep  4 14:36:49 2018

@author: CSE CARNIVAL 2017
"""

import math
def ePower(x,tol):
   val=1
   i=0
   while True:
       temp=val
       i+=1;
       val+=(x**i)/math.factorial(i)
       if (val-temp)/val<=tol:
           break

   return val,i

def ePower2(x,n):
   val=1
   i=0
   while True:
       i+=1;
       val+=(x**i)/math.factorial(i)
       if i==n:
           break

   return val,i
print ePower(0.5,5)
print ePower2(0.5,5)
print math.exp(0.5)
x,_=ePower(0.5,0.01)
y=math.exp(0.5)
print ((y-x)/y*100)



MIXED

# -*- coding: utf-8 -*-
"""
Created on Tue Aug 14 14:40:39 2018

@author: CSE CARNIVAL 2017
"""

import matplotlib.pyplot as plt
import math
import numpy as np
x=np.linspace(0,3*math.pi,100)
y=[]
#for v in x:
    #y.append(math.sin(v))
y=[math.cos(v)*1000 for v in x]
y1=[math.sin(v)*1000 for v in x]
y2=[math.exp(v) for v in x]

plt.plot(x,y,color="blue")
plt.plot(x,y1,color="red")
plt.plot(x,y2,color="black")
plt.show()


NEWTON RAFSON

# -*- coding: utf-8 -*-
"""
Created on Tue Sep 11 15:08:41 2018

@author: CSE CARNIVAL 2017
"""

import math
import random

def f(x):
    return math.exp(-x)-x
def ff(x):
    return -math.exp(-x)-1

x_i=random.random()
print x_i
i=0
x_r=x_i-f(x_i)/ff(x_i)
err=[]
while(True):

    x_r=x_i-f(x_i)/ff(x_i)
    err.append(abs((x_r-x_i)/x_r)*100)
    i+=1
    if f(x_r)==0:
        break
    x_i=x_r


print(x_r,i)
import matplotlib.pyplot as plt
plt.plot(range(i),err,marker='o')
plt.show()


SIN
# -*- coding: utf-8 -*-
"""
Created on Tue Aug 14 14:18:47 2018

@author: CSE CARNIVAL 2017
"""

import matplotlib.pyplot as plt
import math
import numpy as np
x=np.linspace(0,2*math.pi,100)
y=[]
#for v in x:
    #y.append(math.sin(v))
y=[math.sin(v) for v in x]

plt.plot(x,y,marker='.')
plt.show()


UNTITLED

# -*- coding: utf-8 -*-
"""
Created on Tue Sep 11 15:37:29 2018

@author: CSE CARNIVAL 2017
"""

# -*- coding: utf-8 -*-
"""
Created on Tue Sep 11 15:08:41 2018

@author: CSE CARNIVAL 2017
"""

import math
import random

def f(x):
    return math.exp(-x)-x
def ff(x):
    return -math.exp(-x)-1

while(True):
    x_l=random.random()
    x_u=random.random()
    if f(x_l)*f(x_u)<0:
        break

#x_l=0
#x_u =1
i=0
x_r=x_u-(f(x_u)*(x_l-x_u))/(f(x_l)-f(x_u))
y=[]

while(i<20):


    if f(x_r)==0:
        break
    if f(x_r)*f(x_l)>0:
        x_l=x_r
    if f(x_r)*f(x_u)>0:
        x_u=x_r
    old=x_r
    x_r=x_u-(f(x_u)*(x_l-x_u))/(f(x_l)-f(x_u))
    i+=1


    y.append(abs((x_r-old)/x_r)*100)
print(x_r,i)

import matplotlib.pyplot as plt
plt.plot(range(i),y,marker='*',label='FP')


x_i=random.random()
print x_i
i=0
x_r=x_i-f(x_i)/ff(x_i)
err=[]
while(True):

    x_r=x_i-f(x_i)/ff(x_i)
    err.append(abs((x_r-x_i)/x_r)*100)
    i+=1
    if f(x_r)==0:
        break
    x_i=x_r


print(x_r,i)

plt.plot(range(i),err,marker='o',label='NR')
plt.legend()
plt.show()