def root_solve_bisection_intervals(function, a, b, divisions, tol):
start_time = time.time()#
solutions = []
step_size = (b-a)/divisions
i=a
while i < b:
solution = root_solve_bisection(function, i, i+step_size, tol)
if (solution != None):
solutions.append(solution)
i += step_size
return solutions
def root_solve_newton_hybrid(function, function_prime, a, b, tol, maxiter):
c = root_solve_bisection(function, a, b, tol, 4)
if c == None:
return None
solution = root_solve_newton(function, function_prime, c, tol, maxiter)
return solution
#def function(x):
# return x * math.cosh(x) + pow(x, 3) - math.pi
#def function_prime(x):
# return math.cosh(x) + x * math.sinh(x) + 3 * pow(x, 2)
#print(root_solve_newton_hybrid(function, function_prime, 0, 2, 0.000001,20))
def root_solve_secant_hybrid(function, a, b, tol, maxiter):
c = root_solve_bisection(function, a, b, tol, 4)
if c == None:
return None
#Find another point close to c, appropriate to the scale of a and b
if abs(c - a) < abs(c - b): #If c is closer to a
d = c + ((b - a) / 10.0)
else:
d = c - ((b - a) / 10.0)
solution = root_solve_secant(function, c, d, tol, maxiter)
return solution
#def function(x):
# return x * math.cosh(x) + pow(x, 3) - math.pi
#print(root_solve_secant_hybrid(function, 0, 2, 0.000001,20))
def function_prime(x):
return math.cosh(x) + x * math.sinh(x) + 3 * pow(x, 2)
print("The true root to the equation x * cosh(x)+ x^3 - pi is 1.0963278")
try:
solution, maxiter = root_solve_fixed_point(function, 1, 0.000001, 1000,
True)
except:
solution, maxiter = "N/A", "N/A"
print(
f"Using the fixed point iteration, the solution was {solution}, which took {maxiter} iterations."
)
solution, maxiter = root_solve_bisection(function,
0,
2,
0.000001,
getIterCount=True)
print(
f"Using the bisection iteration, the solution was {solution}, which took {maxiter} iterations."
)
solution, maxiter = root_solve_newton(function, function_prime, 1, 0.000001,
30, True)
print(
f"Using the newton iteration, the solution was {solution}, which took {maxiter} iterations."
)
solution, maxiter = root_solve_secant(function, 1.0, 1.2, 0.000001, 30, True)
print(
f"Using the secant iteration, the solution was {solution}, which took {maxiter} iterations."
)
'''
coding language: Python 3.7.0
written by: Jonah Merrell
date written: September 18 2019
written for: Homework2 Task9
course: Math 4610
purpose: For this ask, compare the results of the functional iteration and Bisection iteration on
the problem x cosh(x) + x<sup>3</sup> = pi
'''
import sys, os
sys.path.append(os.path.abspath('../../mylibrary'))
from _mymodules import root_solve_bisection, root_solve_fixed_point
import math
def function(x):
return x * math.cosh(x) + pow(x, 3) - math.pi
print("Attempting to solve equation with root_solve_fixed_point:")
try:
print(root_solve_fixed_point(function, 1, 0.0001, 1000))
except OverflowError:
print("An OverflowError occured")
print("")
print("Attempting to solve equation with root_solve_bisection:")
print(root_solve_bisection(function, 0, 2, 0.0001))