def problem11():
a,b,dx = (-6, 6, 0.01)
print("The roots for problem 11 are:")
while True:
x1,x2 = rootsearch(f,a,b,dx)
if x1 != None:
a = x2
root = newtonRaphson(f,df11,x1,x2)
if root != None: print(root)
else:
print("Done\n")
break
def problem23():
a,b,dx = (-2, 2, 0.001)
print("Problem 23: The coordinates where the two points of the circle intersect are:")
while True:
x1,x2 = rootsearch(f23,a,b,dx)
if x1 != None:
a = x2
root = newtonRaphson(f23,df23,x1,x2)
if root != None: print(root)
else:
print("Done\n")
break
def problem10():
a,b,dx = (-6, 6, 0.01)
print("The roots for problem 10 are:")
while True:
x1,x2 = rootsearch(f,a,b,dx)
if x1 != None:
a = x2
root = ridder(f,x1,x2)
if root != None: print(root)
else:
print("Done\n")
break
from math import tan
from bisect import *
from rootsearch import *
f = lambda x: x - tan(x)
a, b, dx = (0, 20, 0.01)
print('The roots are:')
while True:
x1, x2 = rootsearch(f, a, b, dx)
if x1 != None:
a = x2
root = bisect(f, x1, x2, 1)
if root != None: print(root)
else:
print('\ndone!')
break
input('Press return to exit')
#!/usr/bin/python
## example4_3
from math import tan
from rootsearch import *
from bisect import *
def f(x):
return x - tan(x)
a, b, dx = (0.0, 20.0, 0.01)
print "The roots are:"
while 1:
x1, x2 = rootsearch(f, a, b, dx)
if x1 != None:
a = x2
root = bisect(f, x1, x2, 1)
if root != None: print root
else:
print "\nDone"
break
raw_input("Press return to exit")
##
## example4_3 (pp. 150-151, Kiusalaas 3rd Ed)
##
from math import tan
from numpy import arange,zeros
from rootsearch import *
from bisection import *
import pylab
def f(x): return x - tan(x)
a,b,dx = (0.0, 20.0, 0.01)
print ("The roots of f(x)= x-tan x on (0,20) using delta x = " + str(dx) + " :")
while 1:
x1,x2 = rootsearch(f,a,b,dx) # What is rootsearch doing here?
if x1 != None:
a = x2
root = bisection(f,x1,x2,1) # switch is set to 1 to avoid
if root != None: print(root) # singularities in f(x)
else: # What epsilon is bisection using?
print ("\nDone")
n=20
xData = arange(0,n,.1,dtype=float)
n2=xData.size
yData = zeros((n2),dtype=float)
for j in range(0,n2):
yData[j]=f(xData[j])
pylab.xlabel("x")
my_title= 'Plot of f(x)=x-tan x'
def main():
low = float(raw_input("low = "))
high = float(raw_input("high = "))
step = float(raw_input("step = "))
root = rootsearch(f, low, high, step)
bisect = bisection(f, low, high)
newton = newtonRaphson(f, df, low, high)
ridders = ridder(f, low, high)
correct = math.pi
print "rootsearch =", root
print "rootsearch error =", max(abs(correct - root[0]), abs(correct - root[1]))
print ""
print "bisection =", bisect
print "bisection error =", abs(correct - bisect)
print ""
print "newtonRaphson =", newton
print "newton error =", abs(correct - newton)
print ""
print "ridder =", ridders
print "ridder error =", abs(correct - ridders)
print ""
print ""
print "Average root =", (((root[0] + root[1]) / 2.0) + bisect + newton + ridders) / 4.0
print "Average root error =", abs(((((root[0] + root[1]) / 2.0) + bisect + newton + ridders) / 4.0) - correct)
print ""
print "Most Accurate root =", min(
min(abs(correct - root[0]), abs(correct - root[1])),
abs(correct - bisect),
abs(correct - newton),
abs(correct - ridders),
)
print "Least Accurate root =", max(
max(abs(correct - root[0]), abs(correct - root[1])),
abs(correct - bisect),
abs(correct - newton),
abs(correct - ridders),
)
gdisplay(title="Root Search")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
f2 = gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[(root[0], f(root[0])), (root[1], f(root[1]))], color=color.green)
gdisplay(title="Bisection")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[bisect, 0], color=color.green)
gdisplay(title="Newton Raphson")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[newton, 0], color=color.green)
gdisplay(title="Ridder")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[ridders, 0], color=color.green)
gdisplay(title="Combination: RootSearch(white), Bisection(yellow), NewtonRaphson(blue), Ridders(green)")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[(root[0], f(root[0])), (root[1], f(root[1]))], color=color.white)
gdots(pos=[bisect, 0], color=color.yellow)
gdots(pos=[newton, 0], color=color.blue)
gdots(pos=[ridders, 0], color=color.green)
#!/usr/bin/python
## example4_1
from rootsearch import *
def f(x):
return x**3 - 10.0 * x**2 + 5.0
x1 = 0.0
x2 = 1.0
for i in range(4):
dx = (x2 - x1) / 10.0
x1, x2 = rootsearch(f, x1, x2, dx)
x = (x1 + x2) / 2.0
print('x =', '{:6.4f}'.format(x))
input("Press return to exit")
def main():
low = float(raw_input("low = "))
high = float(raw_input("high = "))
step = float(raw_input("step = "))
root = rootsearch(f, low, high, step)
bisect = bisection(f, low, high)
newton = newtonRaphson(f, df, low, high)
ridders = ridder(f, low, high)
correct = math.pi
print "rootsearch =", root
print "rootsearch error =", max(abs(correct - root[0]),
abs(correct - root[1]))
print ""
print "bisection =", bisect
print "bisection error =", abs(correct - bisect)
print ""
print "newtonRaphson =", newton
print "newton error =", abs(correct - newton)
print ""
print "ridder =", ridders
print "ridder error =", abs(correct - ridders)
print ""
print ""
print "Average root =", ((
(root[0] + root[1]) / 2.0) + bisect + newton + ridders) / 4.0
print "Average root error =", abs((((
(root[0] + root[1]) / 2.0) + bisect + newton + ridders) / 4.0) -
correct)
print ""
print "Most Accurate root =", min(min(abs(correct - root[0]), abs(correct - root[1])), abs(correct - bisect), \
abs(correct - newton), abs(correct - ridders))
print "Least Accurate root =", max(max(abs(correct - root[0]), abs(correct - root[1])), abs(correct - bisect), \
abs(correct - newton), abs(correct - ridders))
gdisplay(title="Root Search")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
f2 = gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[(root[0], f(root[0])), (root[1], f(root[1]))],
color=color.green)
gdisplay(title="Bisection")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[bisect, 0], color=color.green)
gdisplay(title="Newton Raphson")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[newton, 0], color=color.green)
gdisplay(title="Ridder")
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[ridders, 0], color=color.green)
gdisplay(
title=
"Combination: RootSearch(white), Bisection(yellow), NewtonRaphson(blue), Ridders(green)"
)
f1 = gcurve()
for x in linspace(low - 1, high + 1, 200):
f1.plot(pos=(x, f(x)), color=color.red)
gdots(pos=[low, f(low)], color=color.yellow)
gdots(pos=[high, f(high)], color=color.yellow)
gdots(pos=[(root[0], f(root[0])), (root[1], f(root[1]))],
color=color.white)
gdots(pos=[bisect, 0], color=color.yellow)
gdots(pos=[newton, 0], color=color.blue)
gdots(pos=[ridders, 0], color=color.green)
