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This commit is contained in:
Alex Brown
2018-10-19 07:48:28 -05:00
parent 718b99ae39
commit 564179a0ec
131 changed files with 16252 additions and 0 deletions

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import math
def bisection(function, a, b): # finds where the function becomes 0 in [a,b] using bolzano
start = a
end = b
if function(a) == 0: # one of the a or b is a root for the function
return a
elif function(b) == 0:
return b
elif function(a) * function(b) > 0: # if none of these are root and they are both positive or negative,
# then his algorithm can't find the root
print("couldn't find root in [a,b]")
return
else:
mid = (start + end) / 2
while abs(start - mid) > 0.0000001: # until we achieve precise equals to 10^-7
if function(mid) == 0:
return mid
elif function(mid) * function(start) < 0:
end = mid
else:
start = mid
mid = (start + end) / 2
return mid
def f(x):
return math.pow(x, 3) - 2*x - 5
print(bisection(f, 1, 1000))

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import math
def intersection(function,x0,x1): #function is the f we want to find its root and x0 and x1 are two random starting points
x_n = x0
x_n1 = x1
while True:
x_n2 = x_n1-(function(x_n1)/((function(x_n1)-function(x_n))/(x_n1-x_n)))
if abs(x_n2 - x_n1)<0.00001 :
return x_n2
x_n=x_n1
x_n1=x_n2
def f(x):
return math.pow(x,3)-2*x-5
print(intersection(f,3,3.5))

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import numpy
def LUDecompose (table):
#table that contains our data
#table has to be a square array so we need to check first
rows,columns=numpy.shape(table)
L=numpy.zeros((rows,columns))
U=numpy.zeros((rows,columns))
if rows!=columns:
return
for i in range (columns):
for j in range(i-1):
sum=0
for k in range (j-1):
sum+=L[i][k]*U[k][j]
L[i][j]=(table[i][j]-sum)/U[j][j]
L[i][i]=1
for j in range(i-1,columns):
sum1=0
for k in range(i-1):
sum1+=L[i][k]*U[k][j]
U[i][j]=table[i][j]-sum1
return L,U
matrix =numpy.array([[2,-2,1],[0,1,2],[5,3,1]])
L,U = LUDecompose(matrix)
print(L)
print(U)

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def newton(function,function1,startingInt): #function is the f(x) and function1 is the f'(x)
x_n=startingInt
while True:
x_n1=x_n-function(x_n)/function1(x_n)
if abs(x_n-x_n1)<0.00001:
return x_n1
x_n=x_n1
def f(x):
return (x**3)-2*x-5
def f1(x):
return 3*(x**2)-2
print(newton(f,f1,3))

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# Implementing Newton Raphson method in Python
# Author: Haseeb
from sympy import diff
from decimal import Decimal
def NewtonRaphson(func, a):
''' Finds root from the point 'a' onwards by Newton-Raphson method '''
while True:
c = Decimal(a) - ( Decimal(eval(func)) / Decimal(eval(str(diff(func)))) )
a = c
# This number dictates the accuracy of the answer
if abs(eval(func)) < 10**-15:
return c
# Let's Execute
if __name__ == '__main__':
# Find root of trigonometric function
# Find value of pi
print ('sin(x) = 0', NewtonRaphson('sin(x)', 2))
# Find root of polynomial
print ('x**2 - 5*x +2 = 0', NewtonRaphson('x**2 - 5*x +2', 0.4))
# Find Square Root of 5
print ('x**2 - 5 = 0', NewtonRaphson('x**2 - 5', 0.1))
# Exponential Roots
print ('exp(x) - 1 = 0', NewtonRaphson('exp(x) - 1', 0))