def runTest(self):
# n, m = 2, 2
x0 = np.array([-1.2, 1.0])
np.random.seed(0)
soln = dfbgn.solve(rosenbrock, x0)
print(soln)
print(rosenbrock_jacobian(soln.x))
self.assertTrue(
array_compare(soln.x, np.array([1.0, 1.0]), thresh=1e-4),
"Wrong xmin")
self.assertTrue(
array_compare(soln.resid, rosenbrock(soln.x), thresh=1e-10),
"Wrong resid")
# print(soln.jacobian, rosenbrock_jacobian(soln.x))
# self.assertTrue(array_compare(soln.jacobian, rosenbrock_jacobian(soln.x), thresh=2.5e0), "Wrong Jacobian")
self.assertTrue(abs(soln.f) < 1e-10, "Wrong fmin")
def runTest(self):
n, m = 4, 6
np.random.seed(0) # (fixing random seed)
A = np.random.rand(m, n)
b = np.random.rand(m)
objfun = lambda x: np.dot(A, x) - b
xmin = np.linalg.lstsq(A, b)[0]
fmin = np.dot(objfun(xmin), objfun(xmin))
x0 = np.zeros((n, ))
soln = dfbgn.solve(objfun, x0) # reduced space
print(soln)
self.assertTrue(array_compare(soln.x, xmin, thresh=1e-2), "Wrong xmin")
self.assertTrue(
array_compare(soln.resid, objfun(soln.x), thresh=1e-10),
"Wrong resid")
# self.assertTrue(array_compare(soln.jacobian, A, thresh=1e-6), "Wrong Jacobian") # should get exact Jacobian for linear problems
self.assertTrue(abs(soln.f - fmin) < 1e-4, "Wrong fmin")
return rosenbrock(x) * (1.0 + 1e-2 * np.random.normal(size=(2, )))
# Define the starting point
x0 = np.array([-1.2, 1.0])
# Set random seed (for reproducibility)
np.random.seed(0)
print("Demonstrate noise in function evaluation:")
for i in range(5):
print("objfun(x0) = %s" % str(rosenbrock_noisy(x0)))
print("")
# Call DFBGN
soln = dfbgn.solve(rosenbrock_noisy, x0, fixed_block=2)
# Display output
print(soln)
# Compare with a derivative-based solver
import scipy.optimize as opt
soln = opt.least_squares(rosenbrock_noisy, x0)
print("")
print("** SciPy results **")
print("Solution xmin = %s" % str(soln.x))
print("Objective value f(xmin) = %.10g" % (2.0 * soln.cost))
print("Needed %g objective evaluations" % soln.nfev)
print("Exit flag = %g" % soln.status)
# DFBGN example: minimize the Rosenbrock function
from __future__ import print_function
import numpy as np
import dfbgn
# Define the objective function
def rosenbrock(x):
return np.array([10.0 * (x[1] - x[0] ** 2), 1.0 - x[0]])
# Define the starting point
x0 = np.array([-1.2, 1.0])
# For optional extra output details
# import logging
# logging.basicConfig(level=logging.INFO, format='%(message)s')
# DFBGN is a randomized algorithm - set random seed for reproducibility
np.random.seed(0)
# Call DFBGN
soln = dfbgn.solve(rosenbrock, x0, fixed_block=2)
# Display output
print(soln)
# DFBGN example: Solving a nonlinear system of equations
# Originally from:
# http://support.sas.com/documentation/cdl/en/imlug/66112/HTML/default/viewer.htm#imlug_genstatexpls_sect004.htm
from __future__ import print_function
from math import exp
import numpy as np
import dfbgn
# Want to solve:
# x1 + x2 - x1*x2 + 2 = 0
# x1 * exp(-x2) - 1 = 0
def nonlinear_system(x):
return np.array([x[0] + x[1] - x[0] * x[1] + 2, x[0] * exp(-x[1]) - 1.0])
# Warning: if there are multiple solutions, which one
# DFBGN returns will likely depend on x0!
x0 = np.array([0.1, -2.0])
# DFBGN is a randomized algorithm - set random seed for reproducibility
np.random.seed(0)
# Call DFBGN
soln = dfbgn.solve(nonlinear_system, x0, fixed_block=2)
# Display output
print(soln)