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‎analysis/Compression_Analysis/PSNR.py‎

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‎analysis/Compression_Analysis/compressed_image.png‎

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‎analysis/Compression_Analysis/example_image.jpg‎

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‎analysis/Compression_Analysis/orignal_image.png‎

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‎arithmetic_analysis/bisection.py‎

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

‎arithmetic_analysis/intersection.py‎

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

‎arithmetic_analysis/lu_decomposition.py‎

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

‎arithmetic_analysis/newton_method.py‎

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

‎arithmetic_analysis/newton_raphson_method.py‎

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

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