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#!/usr/bin/env python
# run tests with: python -m unittest discover
import os
import sys
import re
import urllib2
import unittest
import fityk
DATA_URL_BASE = "http://www.itl.nist.gov/div898/strd/nls/data/LINKS/DATA/"
CACHE_DIR = os.path.join(os.path.dirname(__file__), "strd_data")
VERBOSE = 1 # 0, 1, 2 or 3
class NistParameter:
def __init__(self, name, start1, start2, param_str, stddev_str):
self.name = name
self.start1 = float(start1)
self.start2 = float(start2)
self.value_str = param_str
self.value = float(param_str)
self.stddev_str = stddev_str
self.stddev = float(stddev_str)
class NistReferenceData:
def __init__(self, name):
self.name = name
self.data = []
self.model = None
self.parameters = []
self.dof = None
self.ssr = None
def __str__(self):
return "<NistReferenceData: %d points, %d param.>" % (
len(self.data), len(self.parameters))
def open_nist_data(name):
name_ext = name + ".dat"
local_file = os.path.join(CACHE_DIR, name_ext)
if os.path.exists(local_file):
text = open(local_file).read()
else:
sys.stderr.write("Local data copy not found. Trying itl.nist.gov...\n")
text = urllib2.urlopen(DATA_URL_BASE + name_ext).read()
if not os.path.isdir(CACHE_DIR):
os.mkdir(CACHE_DIR)
open(local_file, "wb").write(text)
return text
def read_reference_data(name):
refdat = NistReferenceData(name)
text = open_nist_data(name)
n_data = int(re.search("\nNumber of Observations: +(\d+)", text).group(1))
refdat.dof = int(re.search("\nDegrees of Freedom: +(\d+)", text).group(1))
# correct wrong number in one of the files:
if name == "Rat43":
refdat.dof = 11
refdat.ssr = float(re.search("\nResidual Sum of Squares:(.+)\n", text)
.group(1))
data_start = re.search("Data: +y +x\s+", text).end()
for line in text[data_start:].splitlines():
x, y = line.split()
refdat.data.append((float(x), float(y)))
param_block = re.search(
#"Start 1 +Start 2 +Parameter +Standard Deviation\s+(.+?\n)\r?\n",
"Start 1 +Start 2 +Parameter +Standard Deviation\s+((.+?=.+\n)+)",
text).group(1)
for line in param_block.splitlines():
tokens = line.split()
tokens.remove('=')
refdat.parameters.append(NistParameter(*tokens))
assert len(refdat.data) == n_data
assert n_data - len(refdat.parameters) == refdat.dof, \
"%d - %d != %d" % (n_data, len(refdat.parameters), refdat.dof)
model = re.search("\n *y += *(.*?) +\+ +e", text, flags=re.DOTALL).group(1)
repl = { "[": "(", "]": ")", "**": "^", "arctan": "atan" }
for key in repl:
model = model.replace(key, repl[key])
refdat.model = re.sub("\s{2,}", " ", model)
return refdat
def has_nlopt():
ftk = fityk.Fityk()
return "NLopt" in ftk.get_info("compiler")
def run(data_name, fit_method, easy=True):
uses_gradient = (fit_method in ("mpfit", "levenberg_marquardt"))
if uses_gradient:
tolerance = { "wssr": 1e-10, "param": 4e-7, "err": 5e-3 }
else:
tolerance = { "wssr": 1e-7, "param": 1e-4 }
if fit_method == "nelder_mead_simplex":
tolerance["err"] = 5e-5
#if fit_method in ("mpfit", "levenberg_marquardt"):
if VERBOSE > 0:
print "Testing %s (start%s) on %-10s" % (fit_method, easy+1, data_name),
if VERBOSE > 1:
print
ref = read_reference_data(data_name)
if VERBOSE > 2:
print ref.model
ftk = fityk.Fityk()
if VERBOSE < 3:
ftk.execute("set verbosity=-1")
y, x = zip(*ref.data)
ftk.load_data(0, x, y, [1]*len(x), data_name)
par_names = [p.name for p in ref.parameters]
par_inits = ["~%g" % (p.start2 if easy else p.start1)
for p in ref.parameters]
ftk.execute("define OurFunc(%s) = %s" % (", ".join(par_names), ref.model))
ftk.execute("F = OurFunc(%s)" % ", ".join(par_inits))
ftk.execute("set fitting_method=" + fit_method)
ftk.execute("set pseudo_random_seed=1234567")
#ftk.execute("set numeric_format='%.10E'")
ftk.execute("set lm_stop_rel_change=1e-16")
#ftk.execute("set lm_max_lambda=1e+50")
ftk.execute("set nm_convergence=1e-10")
if fit_method == "mpfit":
ftk.execute("set ftol_rel=1e-18")
ftk.execute("set xtol_rel=1e-18")
if fit_method == "genetic_algorithms":
ftk.execute("set max_wssr_evaluations=5e5")
elif not uses_gradient:
ftk.execute("set max_wssr_evaluations=2e4")
try:
ftk.execute("fit")
#ftk.execute("set fitting_method=levenberg_marquardt")
#ftk.execute("fit")
except fityk.ExecuteError as e:
print "fityk.ExecuteError: %s" % e
return False
ssr = ftk.get_ssr()
ssr_diff = (ssr - ref.ssr) / ref.ssr
# Lanczos1 and Lanczos2 have near-zero SSR, we need to be more tolerant
if ssr < 1e-20:
tolerance["wssr"] *= 1e8
elif ssr < 1e-10:
tolerance["wssr"] *= 1e2
ok = (abs(ssr_diff) < tolerance["wssr"])
if ref.ssr > 1e-10 and ssr_diff < -1e-10:
print "Eureka! %.10E < %.10E" % (ssr, ref.ssr)
fmt = " %8s %13E %13E %+.1E"
if VERBOSE > 2 or (VERBOSE == 2 and not ok):
print fmt % ("SSR", ssr, ref.ssr, ssr_diff)
our_func = ftk.all_functions()[0]
for par in ref.parameters:
calc_value = our_func.get_param_value(par.name)
val_diff = (calc_value - par.value) / par.value
param_ok = (abs(val_diff) < tolerance["param"])
err_ok = True
if "err" in tolerance:
vname = our_func.var_name(par.name)
calc_err = ftk.calculate_expr("$%s.error" % vname)
err_diff = (calc_err - par.stddev) / par.stddev
err_ok = (abs(err_diff) < tolerance["err"])
if VERBOSE > 2 or (VERBOSE == 2 and (not param_ok or not err_ok)):
print fmt % (par.name, calc_value, par.value, val_diff)
if "err" in tolerance:
print fmt % ("+/-", calc_err, par.stddev, err_diff)
ok = (ok and param_ok and err_ok)
if VERBOSE == 1:
print("OK" if ok else "FAILED")
return ok
datasets = [
# lower difficulty
"Misra1a", "Chwirut2", "Chwirut1", "Lanczos3",
"Gauss1", "Gauss2", "DanWood", "Misra1b",
# average difficulty (skipping Nelson which is y(x1,x2))
"Kirby2", "Hahn1", "MGH17",
"Lanczos1", "Lanczos2", "Gauss3",
"Misra1c", "Misra1d", "Roszman1", "ENSO",
# higher difficulty
"MGH09", "Thurber", "BoxBOD",
"Rat42", "MGH10", "Eckerle4",
"Rat43", "Bennett5"
]
# L-M finds local minimum when starting from start1 for:
lm_fails = ["MGH17", "BoxBOD", "MGH10", "Eckerle4"]
mpfit_fails = ["MGH17", "BoxBOD", "MGH10", "MGH09", "Bennett5"] #, "ENSO"
nm_fails = ["MGH17", "BoxBOD", "ENSO", "Eckerle4", "MGH09", "Bennett5"]
nl_nm_fails = ["MGH17", "BoxBOD", "MGH10", "ENSO"]
class TestSequenceFunctions(unittest.TestCase):
def setUp(self):
global VERBOSE
VERBOSE = 0
def test_levmar(self):
for data_name in datasets:
self.assertTrue(run(data_name, "mpfit", easy=True))
self.assertTrue(run(data_name, "levenberg_marquardt", True))
self.assertIs(run(data_name, "mpfit", easy=False),
data_name not in mpfit_fails)
self.assertIs(run(data_name, "levenberg_marquardt", False),
data_name not in lm_fails)
def test_nelder_mead(self):
for data_name in datasets:
## Lanczos* converge slowly with gradient-less methods, avoid
if "Lanczos" in data_name:
continue
self.assertTrue(run(data_name, "nelder_mead_simplex", easy=True))
self.assertTrue(run(data_name, "nlopt_nm", easy=True))
self.assertIs(run(data_name, "nelder_mead_simplex", easy=False),
data_name not in nm_fails)
self.assertIs(run(data_name, "nlopt_nm", easy=False),
data_name not in nl_nm_fails)
def test_ga(self):
# Since in these problems parameter domains are not defined,
# we only have starting point, methods that have random-search element
# don't work well.
# Like Genetic Algorithms. Additionally, GA are not very practical for
# most of tasks -- slow and require adjusting plenty of parameters.
# But still it may solve some cases where other methods fail:
self.assertTrue(run("BoxBOD", "genetic_algorithms", easy=False))
@unittest.skipIf(not has_nlopt(), "Fityk compiled w/o NLopt support.")
def test_nlopt(self):
# Selected methods from NLopt library.
# For this test suite (which may not be representative for real
# problems) the best NLopt method is Nelder-Mead (tested above).
# The methods below can be useful as well.
# (I haven't tried all algorithms, but almost all).
self.assertTrue(run("MGH17", "nlopt_lbfgs", easy=False))
for data_name in ["BoxBOD", "Eckerle4", "ENSO"]:
self.assertTrue(run(data_name, "nlopt_var2", easy=False))
for data_name in ["BoxBOD", "Eckerle4", "ENSO"]:
self.assertTrue(run(data_name, "nlopt_praxis", easy=False))
for data_name in ["Thurber", "BoxBOD", "Rat43"]:
self.assertTrue(run(data_name, "nlopt_bobyqa", easy=False))
for data_name in ["Rat42", "Eckerle4"]:
self.assertTrue(run(data_name, "nlopt_sbplx", easy=False))
def try_method(method):
all_count = 0
ok_count = 0
for data_name in datasets:
for is_easy in (True, False):
ok = run(data_name, method, is_easy)
all_count += 1
if ok:
ok_count += 1
sys.stdout.flush()
print "OK: %2d / %2d" % (ok_count, all_count)
if __name__ == '__main__':
if len(sys.argv) > 2 and sys.argv[1] == 'method':
# syntax: ./test_nist.py method nlopt_bobyqa
try_method(sys.argv[2])
else:
unittest.main()
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