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secantmethod.py
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secantmethod.py
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from sympy import symbols, lambdify, diff
import math
def secantMethod():
print("\n")
x = symbols('x')
functionString = str(input("Enter the function in the form \'x**3 - 5*x - 9\': "))
expression = lambdify(x, functionString, "math")
maxIterations = int(input("Enter maximum number of iterations: "))
accuracy = float(input("Enter the desired tolerance: "))
x0 = float(input("Enter the first point x0: "))
x1 = float(input("Enter the second point x1: "))
if x1 == x0:
print("The two points must not be the same! Press enter to continue...")
delay = input()
return False
elif x1 > x0:
x0, x1 = x1, x0
count = 0
fxi = 0.0
xi = 0.0
print("\nS. No.\tx_i-1\t\tx_i-2\t\tx_i\t\tfx_i")
while True:
fx0 = expression(x0)
fx1 = expression(x1)
xi = ((x0 * fx1) - (x1 * fx0)) / (fx1 - fx0)
fxi = expression(xi)
print("{0}\t{1:.8f}\t{2:.8f}\t{3:.8f}\t{4:.8f}".format(count+1, x1, x0, xi, fxi))
x0 = x1
x1 = xi
count += 1
if (abs(fxi) < accuracy) or (count >= maxIterations):
break
print("\nAfter {0} iterations, the root of the given equation is\n x = {1}\nf(x) = {2}\n\n".format(count, xi, fxi))
return True