meyers hw 3.ipynb

Kernel: Python 3 (Anaconda)

import scipy.optimize as optimize
import numpy as np

def f1a(x):
    return x**3-x-2
def f1b(x):
    return -1*np.exp(x)+7
def f1c(x):
    return e^x+sin(x)-4+x
print('1(a) = ',optimize.fixed_point(f1a,0, xtol=1e-8))
print('1(b) = ',optimize.fixed_point(f1b,0))
print('1(c) = ',optimize.fixed_point(f1c,0))

def f2a(x):
    return -x**5+1
def f2b(x):
    return np.e**(x**2+3)
def f2c(x):
    return np.sqrt(-np.log(x) + 3)
print('2(a) = ',optimize.fixed_point(f2a,0, xtol=1e-8))
print('2(b) = ',optimize.fixed_point(f2b,0))
print('2(c) = ',optimize.fixed_point(f2c,0, maxiter=10000))

#Due to Python's precise nature, this code causes an overflow error for some choices of f(x). 

1(a) =  1.7692923542386314
1(b) =  1.6728216986289064

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-2-1cfd69b5dec4> in <module>()
     10 print('1(a) = ',optimize.fixed_point(f1a,0, xtol=1e-8))
     11 print('1(b) = ',optimize.fixed_point(f1b,0))
---> 12 print('1(c) = ',optimize.fixed_point(f1c,0))
     13 
     14 def f2a(x):
/ext/anaconda3/lib/python3.5/site-packages/scipy/optimize/minpack.py in fixed_point(func, x0, args, xtol, maxiter, method)
    891     use_accel = {'del2': True, 'iteration': False}[method]
    892     x0 = _asarray_validated(x0, as_inexact=True)
--> 893     return _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel)

/ext/anaconda3/lib/python3.5/site-packages/scipy/optimize/minpack.py in _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel)
    833     p0 = x0
    834     for i in range(maxiter):
--> 835         p1 = func(p0, *args)
    836         if use_accel:
    837             p2 = func(p1, *args)
<ipython-input-2-1cfd69b5dec4> in f1c(x)
      7     return -1*np.exp(x)+7
      8 def f1c(x):
----> 9     return e^x+sin(x)-4+x
     10 print('1(a) = ',optimize.fixed_point(f1a,0, xtol=1e-8))
     11 print('1(b) = ',optimize.fixed_point(f1b,0))
NameError: name 'e' is not defined

def sqrt(x):
    list = [x]
    last = list[-1]
    next = 0
    while (np.abs(next-last)>.5):
        next = (last + x/last)/2
        list.append(next)
        last = list[-1]
        print(next)
sqrt(3)

def dx(f, x):
    return abs(0-f(x))
 
def newtons_method(f, df, x0, e):
    delta = dx(f, x0)
    while delta > e:
        x0 = x0 - f(x0)/df(x0)
        delta = dx(f, x0)
    print ('Root is at: ', x0)
    print ('f(x) at root is: ', f(x0))
n