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import time
from collections import defaultdict
import numpy as np
from numpy.testing import Tester, TestCase
import scipy.optimize
from scipy.optimize.optimize import rosen, rosen_der, rosen_hess
import test_functions as funcs
class _BenchOptimizers(object):
"""a framework for benchmarking the optimizer
Parameters
----------
function_name : string
fun : callable
der : callable
function that returns the derivative (jacobian, gradient) of fun
hess : callable
function that returns the hessian of fun
minimizer_kwargs : kwargs
additional keywords passed to the minimizer. e.g. tol, maxiter
"""
def __init__(self, function_name, fun, der=None, hess=None,
**minimizer_kwargs):
self.function_name = function_name
self.fun = fun
self.der = der
self.hess = hess
self.minimizer_kwargs = minimizer_kwargs
if "tol" not in minimizer_kwargs:
minimizer_kwargs["tol"] = 1e-4
self.results = []
def reset(self):
self.results = []
def add_result(self, result, t, name):
"""add a result to the list"""
result.time = t
result.name = name
if not hasattr(result, "njev"):
result.njev = 0
if not hasattr(result, "nhev"):
result.nhev = 0
self.results.append(result)
def print_results(self):
"""print the current list of results"""
results = self.average_results()
results = sorted(results, key=lambda x: (x.nfail, x.mean_time))
print("")
print("=========================================================")
print("Optimizer benchmark: %s" % (self.function_name))
print("dimensions: %d, extra kwargs: %s" % (results[0].ndim, str(self.minimizer_kwargs)))
print("averaged over %d starting configurations" % (results[0].ntrials))
print(" Optimizer nfail nfev njev nhev time")
print("---------------------------------------------------------")
for res in results:
print("%11s | %4d | %4d | %4d | %4d | %.6g" %
(res.name, res.nfail, res.mean_nfev, res.mean_njev, res.mean_nhev, res.mean_time))
def average_results(self):
"""group the results by minimizer and average over the runs"""
grouped_results = defaultdict(list)
for res in self.results:
grouped_results[res.name].append(res)
averaged_results = dict()
for name, result_list in grouped_results.items():
newres = scipy.optimize.OptimizeResult()
newres.name = name
newres.mean_nfev = np.mean([r.nfev for r in result_list])
newres.mean_njev = np.mean([r.njev for r in result_list])
newres.mean_nhev = np.mean([r.nhev for r in result_list])
newres.mean_time = np.mean([r.time for r in result_list])
newres.ntrials = len(result_list)
newres.nfail = len([r for r in result_list if not r.success])
try:
newres.ndim = len(result_list[0].x)
except TypeError:
newres.ndim = 1
averaged_results[name] = newres
return averaged_results.values()
def bench_run(self, x0, **minimizer_kwargs):
"""do an optimization test starting at x0 for all the optimizers"""
kwargs = self.minimizer_kwargs
fonly_methods = ["COBYLA", 'Powell']
for method in fonly_methods:
t0 = time.time()
res = scipy.optimize.minimize(self.fun, x0, method=method,
**kwargs)
t1 = time.time()
self.add_result(res, t1-t0, method)
gradient_methods = ['L-BFGS-B', 'BFGS', 'CG', 'TNC', 'SLSQP']
if self.der is not None:
for method in gradient_methods:
t0 = time.time()
res = scipy.optimize.minimize(self.fun, x0, method=method,
jac=self.der, **kwargs)
t1 = time.time()
self.add_result(res, t1-t0, method)
hessian_methods = ["Newton-CG", 'dogleg', 'trust-ncg']
if self.hess is not None:
for method in hessian_methods:
t0 = time.time()
res = scipy.optimize.minimize(self.fun, x0, method=method,
jac=self.der, hess=self.hess,
**kwargs)
t1 = time.time()
self.add_result(res, t1-t0, method)
class BenchSmoothUnbounded(TestCase):
"""Benchmark the optimizers with smooth, unbounded, functions"""
def bench_rosenbrock(self):
b = _BenchOptimizers("Rosenbrock function",
fun=rosen, der=rosen_der, hess=rosen_hess)
for i in range(10):
b.bench_run(np.random.uniform(-3,3,3))
b.print_results()
def bench_rosenbrock_tight(self):
b = _BenchOptimizers("Rosenbrock function",
fun=rosen, der=rosen_der, hess=rosen_hess,
tol=1e-8)
for i in range(10):
b.bench_run(np.random.uniform(-3,3,3))
b.print_results()
def bench_simple_quadratic(self):
s = funcs.SimpleQuadratic()
# print "checking gradient", scipy.optimize.check_grad(s.fun, s.der, np.array([1.1, -2.3]))
b = _BenchOptimizers("simple quadratic function",
fun=s.fun, der=s.der, hess=s.hess)
for i in range(10):
b.bench_run(np.random.uniform(-2,2,3))
b.print_results()
def bench_asymetric_quadratic(self):
s = funcs.AsymmetricQuadratic()
# print "checking gradient", scipy.optimize.check_grad(s.fun, s.der, np.array([1.1, -2.3]))
b = _BenchOptimizers("function sum(x**2) + x[0]",
fun=s.fun, der=s.der, hess=s.hess)
for i in range(10):
b.bench_run(np.random.uniform(-2,2,3))
b.print_results()
def bench_sin_1d(self):
fun = lambda x: np.sin(x[0])
der = lambda x: np.array([np.cos(x[0])])
b = _BenchOptimizers("1d sin function",
fun=fun, der=der, hess=None)
for i in range(10):
b.bench_run(np.random.uniform(-2,2,1))
b.print_results()
def bench_booth(self):
s = funcs.Booth()
# print "checking gradient", scipy.optimize.check_grad(s.fun, s.der, np.array([1.1, -2.3]))
b = _BenchOptimizers("Booth's function",
fun=s.fun, der=s.der, hess=None)
for i in range(10):
b.bench_run(np.random.uniform(0,10,2))
b.print_results()
def bench_beale(self):
s = funcs.Beale()
# print "checking gradient", scipy.optimize.check_grad(s.fun, s.der, np.array([1.1, -2.3]))
b = _BenchOptimizers("Beale's function",
fun=s.fun, der=s.der, hess=None)
for i in range(10):
b.bench_run(np.random.uniform(0,10,2))
b.print_results()
def bench_LJ(self):
s = funcs.LJ()
# print "checking gradient", scipy.optimize.check_grad(s.get_energy, s.get_gradient, np.random.uniform(-2,2,3*4))
natoms = 4
b = _BenchOptimizers("%d atom Lennard Jones potential" % (natoms),
fun=s.get_energy, der=s.get_gradient, hess=None)
for i in range(10):
b.bench_run(np.random.uniform(-2,2,natoms*3))
b.print_results()
#def main():
# bench_rosenbrock()
# bench_simple_quadratic()
# bench_asymetric_quadratic()
# bench_sin_1d()
# bench_booth()
# bench_beale()
# bench_LJ()
if __name__ == "__main__":
Tester().bench(extra_argv=dict())
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