atol = 1e-5
output = True
for i in range(4):
#--------------------------------------------------------------------------
# Print divider for readability
divider()
# State Subproblem letter
print("Problem {}:".format(index[i]))
print("fixed_point()")
# Start time
tstart = time.time()
x1, its1 = fixed_point(gfunc[i], x0, maxit, rtol, atol, output)
# Stop time
ttot = time.time() - tstart
# Record solution
print(" final solution = ", x1, ", residual = ", np.abs(gfunc[i](x1)),
", time = ", ttot, ", its = ", its1)
#--------------------------------------------------------------------------
print("aitken_fp()")
# Start time
tstart = time.time()
x2, its2 = aitken_fp(gfunc[i], x0, maxit, rtol, atol, output)
# Stop time
import numpy as np
from fixed_point import *
def f(x):
return np.exp(-x)
x0 = 0.0
xroot, _ = fixed_point(f, x0, verbose=True)
print(xroot)
# interp_representation_error
interp_representation_error = lambda Gfun, x_final: abs(
Gfun(x_final) - x_final)
# run trials
for name in order:
Gfun = fixed_point_functions[name]['method']
x0 = fixed_point_functions[name]['initial guess']
if SHOW_OUTPUT:
logger.info(
"\n\n\tRunning fixed point iterations WITHOUT aitken acceleration on problem %s.\n\n\tFunction %s.\n"
% (name, name))
x_final = fixed_point(Gfun, x0, maxit, rtol, atol, output=SHOW_OUTPUT)
if SHOW_OUTPUT:
# display interp_representation_error
error = interp_representation_error(Gfun, x_final)
logger.info(
"\n\n[Method 2]: \nFinal fixed point target error WITHOUT using acceleration acceleration.\n \
\n\tFunction name: %s, \n\n\t\t |Gfun(x) - x| = %s.\n" % (name, error))
if SHOW_OUTPUT:
logger.info(
"\n\n\tRunning fixed point iterations WITH aitken acceleration on problem %s.\n\n\tFunction %s.\n"
% (name, name))
x_final = aitken_fp(Gfun, x0, maxit, rtol, atol, output=SHOW_OUTPUT)
rtol = 10**(-10)
# interp_representation_error
interp_representation_error = lambda Gfun, x_final: abs(
Gfun(x_final) - x_final)
# run trials
for Gfun_name, Gfun in fixed_point_functions.items():
Gfun = fixed_point_functions[Gfun_name]
x = initial_guesses[Gfun_name]
# find x* using aiken acceleration and method 1
# method 1 - in 'fixed_point.py'
x_target = fixed_point(Gfun, x, maxit, rtol, atol, output=SHOW_OUTPUT)
# display interp_representation_error
error1 = interp_representation_error(Gfun, x)
logger.info(
"\n\n[Method 1]: \nFinal fixed point target error WITHOUT aitken acceleration \nusing newtons method on a newton interpolating polynomial in place of Ffun.\n \
\n\tFunction name: %s, \n\n\t\t |Gfun(x) - x| = %s.\n" %
(Gfun_name, error1))
# aiken acceleration
x_target = aitken_fp(Gfun, x, maxit, rtol, atol, output=SHOW_OUTPUT)
# display interp_representation_error
error2 = interp_representation_error(Gfun, x)
logger.info(
"\n\n[Method 2]: \nFinal fixed point target error using acceleration acceleration.\n \