Secant Method 1.5.7.172

import math
import scipy.integrate as integrate

def PROBLEM1_EQ(x):

    i = ((3 * (x**3)) - (5 * (x**2)) - (4 * x) + 4)

    return i

def PROBLEM1_DERIV_EQ(x):

    i = (9 * (x ** 2)) - (10 * x) - 4

    return i

def PROBLEM5_EQ(x):

    i = ((math.exp(x)) - (100 * (x**2)))

    return i

def PROBLEM5_DERIV_EQ(x):

    i = (-200 * x) + (math.exp(x))

    return i

def PROBLEM7_EQ(x):

    i = (x * (math.cosh(100/x))) - x - 15

    return i

def PROBLEM7_EQ_DER(x):

    i = math.cosh(100/x)-((100*math.sinh(100/x))/x)-1

    return i

def PROBLEM7_Integ():

    i = integrate.quad(lambda x: math.sqrt(1+math.pow(math.sinh(x/335.7), 2)), 0, 100)
    print("Length:", i[0] * 2)


def rate_of_convergence(x):

    L = len(x)

    y0 = math.log(abs(x[L-1] - x[L-2]))
    x0 = math.log(abs(x[L-2] - x[L-3]))
    y1 = x0
    x1 = math.log(abs(x[L-3] - x[L-4]))

#    x0 = round(x0, 1)
#    y0 = round(y0, 0)
#    x1 = round(x1, 0)
#    y1 = x0

    slope = ((y1 - y0) / (x1 - x0))

    print("\nRate of convergence: ", slope)

def bisect(fcn,a,b,acc):

    fa = fcn(a)
    #fb = fcn(b)
    count = 1

    print(f'{count:<4} : {a:<20}  {b:<25} ')
    while abs(b - a) > acc:
        m = (a + b) / 2
        fm = fcn(m)
        if fa * fm <= 0:
            b = m
            count = count + 1
            print(f'{count:<4} : {a:<20}  {b:<25} ')
        else:
            a = m
            count = count + 1
            print(f'{count:<4} : {a:<20}  {b:<25} ')

    count = count + 1
    return (a + b) / 2

def secant(fcn, x0, x1, op1, tol):

    count = 2
    outputs.append(x0)
    outputs.append(x1)

    if op1 == 1:
        for x in range(4):
            x_new = x1 - ((fcn(x1) * (x0 - x1)) / (fcn(x0) - fcn(x1)))
            print("x" + str(count),":",x_new)
            outputs.append(x_new)
            count = count + 1
            x0 = x1
            x1 = x_new

    if op1 == 2:
        while(abs(x0 - x1) > tol):
            x_new = x1 - ((fcn(x1) * (x0 - x1)) / (fcn(x0) - fcn(x1)))
            print("x" + str(count),":",x_new)
            outputs.append(x_new)
            count = count + 1
            x0 = x1
            x1 = x_new

def newton(fcn, df, x0, tol, option):
    c = 1

    if option == 0:
        for x in range(4):
            x1 = x0 - ((fcn(x0)) / (df(x0)))
            outputs_comparison.append(x1)
            print("Iteration", x+1,": ", x1)
            x0 = x1
    elif option == 1:
        while True:
            x1 = x0 - ((fcn(x0)) / (df(x0)))
            outputs_comparison.append(x1)
            print("Iteration", c,": ", x1)
            c += 1
            if abs(x0 - x1) <= tol:
                break

            x0 = x1

outputs = []
outputs_comparison = []

print("\n---------")
print("PROBLEM 1")
print("---------\n")
print("SECANT")
print("------\n")
print("x0 :", 0.6)
print("x1 :", 0.7)
secant(PROBLEM1_EQ, 0.4, 0.5, 1, 0)
rate_of_convergence(outputs)
print("\nNEWTON")
print("------\n")
newton(PROBLEM1_EQ, PROBLEM1_DERIV_EQ, 0.4, 10e-6, 0)
rate_of_convergence(outputs_comparison)

outputs = []
outputs_comparison = []
print("\n---------")
print("PROBLEM 5")
print("---------\n")
print("SECANT")
print("------\n")

print("---")
print("(i)")
print("---")
print("x0 :", 0)
print("x1 :", 0.2)
secant(PROBLEM5_EQ, 0, 0.2, 2, 10e-10)
rate_of_convergence(outputs)

outputs = []
outputs_comparison = []
print("----")
print("(ii)")
print("----")
print("x0 :", -0.2)
print("x1 :", 0)
secant(PROBLEM5_EQ, -0.2, 0, 2, 10e-10)
rate_of_convergence(outputs)

outputs = []
outputs_comparison = []
print("-----")
print("(iii)")
print("-----")
print("x0 :", 8)
print("x1 :", 10)
secant(PROBLEM5_EQ, 8, 10, 2, 10e-10)
rate_of_convergence(outputs)

print("\nNEWTON")
print("------\n")

print("---")
print("(i)")
print("---")
newton(PROBLEM5_EQ, PROBLEM5_DERIV_EQ, -0.2, 10e-10, 0)

print("----")
print("(ii)")
print("----")
newton(PROBLEM5_EQ, PROBLEM5_DERIV_EQ, 0.3, 10e-10, 0)

print("-----")
print("(iii)")
print("-----")
newton(PROBLEM5_EQ, PROBLEM5_DERIV_EQ, 8, 10e-10, 0)
outputs = []
outputs_comparison = []
print("\n---------")
print("PROBLEM 7")
print("---------\n")
print("x0 :", 300)
print("x1 :", 400)
secant(PROBLEM7_EQ, 300, 400, 1, 10e-12)
rate_of_convergence(outputs)
newton(PROBLEM7_EQ, PROBLEM7_EQ_DER, 340, 10e-6, 0)
rate_of_convergence(outputs_comparison)
bisect(PROBLEM7_EQ, 300, 400, 10e-2)
outputs = [335.546875, 335.7421875, 335.83984375, 335.791015625]
rate_of_convergence(outputs)
PROBLEM7_Integ()