def test_dataset_bootstrap_iter(self):
""" bootstrap_iter(data_dict) """
# make data
N = 100
a0 = dict(n=gvar(1,1),a=[gvar(2,2),gvar(100,100)])
dset = Dataset()
for ai in raniter(a0,30):
dset.append(ai)
a = avg_data(dset)
# do bootstrap -- calculate means
bs_mean = Dataset()
for ai in bootstrap_iter(dset,N):
for k in ai:
bs_mean.append(k,np.average(ai[k],axis=0))
for x in ai[k]:
self.assertTrue( #
x in numpy.asarray(dset[k]),
"Bootstrap element not in original dataset.")
a_bs = avg_data(bs_mean,bstrap=True)
# 6 sigma tests
an_mean = a['n'].mean
an_sdev = a['n'].sdev
self.assertGreater(6*an_sdev/N**0.5,abs(an_mean-a_bs['n'].mean))
self.assertGreater(6*an_sdev/N**0.5,abs(an_sdev-a_bs['n'].sdev))
def test_dataset_bootstrap_iter(self):
""" bootstrap_iter(data_dict) """
# make data
N = 100
a0 = dict(n=gvar(1, 1), a=[gvar(2, 2), gvar(100, 100)])
dset = Dataset()
for ai in raniter(a0, 30):
dset.append(ai)
a = avg_data(dset)
# do bootstrap -- calculate means
bs_mean = Dataset()
for ai in bootstrap_iter(dset, N):
for k in ai:
bs_mean.append(k, np.average(ai[k], axis=0))
for x in ai[k]:
self.assertTrue( #
x in numpy.asarray(dset[k]),
"Bootstrap element not in original dataset.")
a_bs = avg_data(bs_mean, bstrap=True)
# 6 sigma tests
an_mean = a['n'].mean
an_sdev = a['n'].sdev
self.assertGreater(6 * an_sdev / N**0.5, abs(an_mean - a_bs['n'].mean))
self.assertGreater(6 * an_sdev / N**0.5, abs(an_sdev - a_bs['n'].sdev))
def test_pade_gvar(self):
" pade_gvar(tayl, m, n) and Pade(tayl, order=(m,n))"
optprint('\n=========== Test pade_gvar')
e_exp = [
1.0, 1.0, 1.0 / 2.0, 1.0 / 6.0, 1.0 / 24.0, 1.0 / 120.0, 1.0 / 720.
]
def _scipy_pade(m, n):
return Pade._scipy_pade(e_exp[:m + n + 1], n)
def print_result(p, q):
optprint('num =', p)
optprint('den =', q)
def test_result(p, q, e_exp):
m = len(p) - 1
n = len(q) - 1
# test against scipy
p0, q0 = _scipy_pade(m, n)
try:
assert numpy.allclose(mean(p), p0)
except:
print(m, n, p0, p, q0, q)
assert numpy.allclose(mean(q), q0)
# test that errors correlate with input coefficients
num = powerseries.PowerSeries(p, order=m + n)
den = powerseries.PowerSeries(q, order=m + n)
ratio = (num / den).c / e_exp[:m + n + 1]
assert numpy.allclose(mean(ratio), 1.)
assert numpy.allclose(sdev(ratio), 0.0)
# print('scipy', _scipy_pade(1,1), pade_svd(e_exp, 3,2, rtol=0.01))
# 1% noise --- automatically reduces to (2,1)
e_exp_noise = [x * gvar('1.0(1)') for x in e_exp]
p, q = pade_gvar(e_exp_noise, 3, 2)
print_result(p, q)
self.assertEqual(len(p), 3)
self.assertEqual(len(q), 2)
test_result(p, q, e_exp_noise)
# 30% noise --- automatically reduces to (1,1)
e_exp_noise = [x * gvar('1.0(3)') for x in e_exp]
p, q = pade_gvar(e_exp_noise, 3, 2)
self.assertEqual(len(p), 2)
self.assertEqual(len(q), 2)
test_result(p, q, e_exp_noise)
# 30% noise, rtol=None --- no reduction
e_exp_noise = [x * gvar('1.0(3)') for x in e_exp]
p, q = pade_gvar(e_exp_noise, 3, 2, rtol=None)
self.assertEqual(len(p), 4)
self.assertEqual(len(q), 3)
test_result(p, q, e_exp_noise)
def test_integral_gvar(self):
def f(x, a=gvar(1, 1)):
return a * 3 * x**2
ans = ode.integral(f, (1, 2), tol=1e-10)
self.assertAlmostEqual(ans.mean, 7)
self.assertAlmostEqual(ans.sdev, 7)
a = gvar(1, 1)
def f(x, a=a):
return a * numpy.array([[1.], [2 * x], [3 * x**2]])
ans = ode.integral(f, (1, 2))
self.assert_arraysclose(mean(ans), [[1], [3], [7]])
self.assert_arraysclose(sdev(ans), [[1], [3], [7]])
def f(x, a=a):
return dict(a=a, b=[2 * a * x, 3 * a * x**2])
ans = ode.integral(f, (1, 2))
self.assertAlmostEqual(ans['a'].mean, 1.)
self.assert_arraysclose(mean(ans['b']), [3, 7])
self.assertAlmostEqual(ans['a'].sdev, 1.)
self.assert_arraysclose(sdev(ans['b']), [3, 7])
self.assertTrue(
gv.equivalent(ans,
dict(a=a, b=[3 * a, 7 * a]),
rtol=1e-6,
atol=1e-6))
def test_autocorr(self):
""" dataset.autocorr """
N = 10000
eps = 10. / float(N)**0.5
x = gvar(2, 0.1)
a = np.array([x() for i in range(N)])
a = (a[:-2] + a[1:-1] + a[2:]) / 3.
ac_ex = np.zeros(a.shape, float)
ac_ex[:3] = np.array([1., 0.66667, 0.33333])
ac_a = autocorr(a)
self.assertLess(numpy.std(ac_a - ac_ex) * 2, eps)
b = np.array([[x(), x()] for i in range(N)])
b = (b[:-2] + b[1:-1] + b[2:]) / 3.
ac_ex = np.array(list(zip(ac_ex, ac_ex)))
ac_b = autocorr(b)
self.assertLess(numpy.std(ac_b - ac_ex), eps)
c = dict(a=a, b=b)
ac_c = autocorr(c)
self.assert_arraysequal(ac_c['a'], ac_a)
self.assert_arraysequal(ac_c['b'], ac_b)
def test_gvar(self):
x = gvar(['0(1)', '1(1)', '3(1)'])
x0 = x[0]
y = self.f(x)
yp= self.Df(x)
s = cspline.CSpline(x, y, deriv=[yp[0], yp[-1]], warn=False)
for xi in x:
self.assert_gvclose(self.f(xi), s(xi))
self.assert_gvclose(self.Df(xi), s.D(xi))
self.assert_gvclose(self.integf(xi, x0), s.integ(xi))
x = np.arange(0.4, 3., 0.4)
for xi in x:
self.assertAlmostEqual(self.f(xi), mean(s(xi)))
self.assertGreater(1e-9, sdev(s(xi)))
self.assertAlmostEqual(self.Df(xi), mean(s.D(xi)))
self.assertGreater(1e-9, sdev(s.D(xi)))
self.assertAlmostEqual(self.D2f(xi), mean(s.D2(xi)))
self.assertGreater(1e-9, sdev(s.D2(xi)))
self.assertAlmostEqual(mean(self.integf(xi, x0.mean)), mean(s.integ(xi)))
self.assert_gvclose(s.integ(xi), self.integf(xi, x0))
def test_autocorr(self):
""" dataset.autocorr """
N = 10000
eps = 10./float(N)**0.5
x = gvar(2,0.1)
a = np.array([x() for i in range(N)])
a = (a[:-2]+a[1:-1]+a[2:])/3.
ac_ex = np.zeros(a.shape,float)
ac_ex[:3] = np.array([1.,0.66667,0.33333])
ac_a = autocorr(a)
self.assertLess(numpy.std(ac_a-ac_ex)*2,eps)
b = np.array([[x(),x()] for i in range(N)])
b = (b[:-2]+b[1:-1]+b[2:])/3.
ac_ex = np.array(list(zip(ac_ex,ac_ex)))
ac_b = autocorr(b)
self.assertLess(numpy.std(ac_b-ac_ex),eps)
c = dict(a=a,b=b)
ac_c = autocorr(c)
self.assert_arraysequal(ac_c['a'],ac_a)
self.assert_arraysequal(ac_c['b'],ac_b)
def test_integral_gvar(self):
def f(x, a=gvar(1,1)):
return a * 3 * x**2
ans = ode.integral(f, (1,2), tol=1e-10)
self.assertAlmostEqual(ans.mean, 7)
self.assertAlmostEqual(ans.sdev, 7)
a = gvar(1, 1)
def f(x, a=a):
return a * numpy.array([[1.], [2 * x], [3 * x**2]])
ans = ode.integral(f, (1, 2))
self.assert_arraysclose(mean(ans), [[1], [3], [7]])
self.assert_arraysclose(sdev(ans), [[1], [3], [7]])
def f(x, a=a):
return dict(a=a, b=[2 * a * x, 3 * a * x**2])
ans = ode.integral(f, (1, 2))
self.assertAlmostEqual(ans['a'].mean, 1.)
self.assert_arraysclose(mean(ans['b']), [3, 7])
self.assertAlmostEqual(ans['a'].sdev, 1.)
self.assert_arraysclose(sdev(ans['b']), [3, 7])
self.assertTrue(gv.equivalent(
ans,
dict(a=a, b=[3 * a, 7 * a]),
rtol=1e-6, atol=1e-6)
)
def test_avg_data(self):
""" avg_data """
self.assertTrue(avg_data([]) is None)
self.assertEqual(avg_data(dict()), BufferDict())
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
avg_data(dict(s=[1.], v=[1., 2.]))
self.assertEqual(len(w), 1)
with self.assertRaises(ValueError):
avg_data(dict(s=[], v=[1., 2.]), warn=False)
with self.assertRaises(ValueError):
avg_data(dict(s=[], v=[]))
with self.assertRaises(ValueError):
avg_data([1, 2, "s"])
mean = avg_data([1])
self.assertEqual(mean.mean, 1.)
self.assertEqual(mean.sdev, 0.)
#
mean = avg_data([1, 2])
self.assertAlmostEqual(mean.mean, 1.5)
self.assertAlmostEqual(mean.var,
sum((vi - 1.5)**2 for vi in [1, 2]) / 4.)
mean2 = avg_data(np.array([1., 2.]))
self.assertEqual(mean.mean, mean2.mean)
self.assertEqual(mean.sdev, mean2.sdev)
#
mean = avg_data([1, 2], spread=True)
self.assertAlmostEqual(mean.mean, 1.5)
self.assertAlmostEqual(mean.var,
sum((vi - 1.5)**2 for vi in [1, 2]) / 2.)
#
mean = avg_data([1, 2], median=True)
self.assertAlmostEqual(mean.mean, 1.5)
self.assertAlmostEqual(mean.var, 0.5**2 / 2.)
#
mean = avg_data([1, 2], median=True, spread=True)
self.assertAlmostEqual(mean.mean, 1.5)
self.assertAlmostEqual(mean.var, 0.5**2)
#
mean = avg_data([1, 2, 3])
self.assertAlmostEqual(mean.mean, 2.0)
self.assertAlmostEqual(mean.var,
sum((vi - 2.)**2 for vi in [1, 2, 3]) / 9.)
#
mean = avg_data([1, 2, 3], noerror=True)
self.assertAlmostEqual(mean, 2.0)
#
mean = avg_data([[1], [2], [3]])
self.assertAlmostEqual(mean[0].mean, 2.0)
self.assertAlmostEqual(mean[0].var,
sum((vi - 2.)**2 for vi in [1, 2, 3]) / 9.)
mean = avg_data([[1], [2], [3]], noerror=True)
self.assertAlmostEqual(mean[0], 2.0)
mean = avg_data([1, 2, 3], spread=True)
self.assertAlmostEqual(mean.mean, 2.0)
self.assertAlmostEqual(mean.var,
sum((vi - 2.)**2 for vi in [1, 2, 3]) / 3.)
#
mean = avg_data([1, 2, 3], median=True)
self.assertAlmostEqual(mean.mean, 2.0)
self.assertAlmostEqual(mean.var, 1. / 3.)
#
mean = avg_data([[1], [2], [3]], median=True)
self.assertAlmostEqual(mean[0].mean, 2.0)
self.assertAlmostEqual(mean[0].var, 1. / 3.)
#
mean = avg_data([1, 2, 3], median=True, spread=True)
self.assertAlmostEqual(mean.mean, 2.0)
self.assertAlmostEqual(mean.var, 1.)
#
mean = avg_data([1, 2, 3, 4, 5, 6, 7, 8, 9], median=True)
self.assertAlmostEqual(mean.mean, 5)
self.assertAlmostEqual(mean.var, 3.**2 / 9.)
#
mean = avg_data([1, 2, 3, 4, 5, 6, 7, 8, 9], median=True, spread=True)
self.assertAlmostEqual(mean.mean, 5.)
self.assertAlmostEqual(mean.var, 3.**2)
#
mean = avg_data([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], median=True)
self.assertAlmostEqual(mean.mean, 5.5)
self.assertAlmostEqual(mean.var, 3.5**2 / 10.)
#
mean = avg_data([1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
median=True,
spread=True)
self.assertAlmostEqual(mean.mean, 5.5)
self.assertAlmostEqual(mean.var, 3.5**2)
#
data = dict(s=[1, 2, 3], v=[[1, 1], [2, 2], [3, 3]])
mean = avg_data(data, median=True, spread=True)
self.assertAlmostEqual(mean['s'].mean, 2.0)
self.assertAlmostEqual(mean['s'].var, 1.0)
self.assertEqual(mean['v'].shape, (2, ))
self.assert_gvclose(mean['v'], [gvar(2, 1), gvar(2, 1)])
mean = avg_data(data, median=True, noerror=True)
self.assertAlmostEqual(mean['s'], 2.0)
self.assertEqual(mean['v'].shape, (2, ))
self.assert_arraysclose(mean['v'], [2, 2])
mean = avg_data(data, noerror=True)
self.assertAlmostEqual(mean['s'], 2.0)
self.assertEqual(mean['v'].shape, (2, ))
self.assert_arraysclose(mean['v'], [2, 2])
""" eg5.py - Code for "y has No Error Bars" and "SVD Cuts and Roundoff Error" Created by Peter Lepage on 2013-02-12. Copyright (c) 2013 G. Peter Lepage. All rights reserved. """ from __future__ import print_function # makes this work for python2 and 3 from gvar import * from lsqfit import nonlinear_fit import functools import inspect import sys ranseed([123]) ygen = gvar(0.02, 0.2) - 0.005 print (ygen) y = [gvar(ygen(), ygen.sdev) for i in range(20)] ystr = [yi.fmt(2) for yi in y] y = gvar(ystr) print (ystr[:]) print log_prior = BufferDict(loga = log(gvar(0.02, 0.02))) sqrt_prior = BufferDict(sqrta = sqrt(gvar(0.02, 0.02))) prior = BufferDict(a = gvar(0.02, 0.02)) stdout = sys.stdout for p in [prior, log_prior, sqrt_prior]: key = list(p.keys())[0]
from __future__ import print_function # makes this work for python2 and 3 from gvar import * from lsqfit import nonlinear_fit import lsqfit import functools import inspect import sys import vegas from outputsplitter import log_stdout DO_PLOT = True if False: ranseed(12345) ygen = gvar(0.015, 0.2) print(ygen) # y = [gi for gi in bootstrap_iter(ygen, 20)] y = [gvar(ygen(), ygen.sdev) for i in range(16000)] ystr = [yi.fmt(2) for yi in y] y = gvar(fmt(y, 2)) else: y = gvar([ '-0.17(20)', '-0.03(20)', '-0.39(20)', '0.10(20)', '-0.03(20)', '0.06(20)', '-0.23(20)', '-0.23(20)', '-0.15(20)', '-0.01(20)', '-0.12(20)', '0.05(20)', '-0.09(20)', '-0.36(20)', '0.09(20)', '-0.07(20)', '-0.31(20)', '0.12(20)', '0.11(20)', '0.13(20)' ]) # print (y)
def make_random(self, a, g='1.0(1)'):
a = numpy.asarray(a)
ans = numpy.empty(a.shape, object)
for i in numpy.ndindex(a.shape):
ans[i] = a[i] * gvar(g)
return ans
def f(x, a=gvar(1, 1)):
return a * 3 * x**2
def f(x, a=gvar(1,1)):
return a * 3 * x**2
""" eg5.py - Code for "y has No Error Bars" and "SVD Cuts and Roundoff Error" Created by Peter Lepage on 2013-02-12. Copyright (c) 2013 G. Peter Lepage. All rights reserved. """ from __future__ import print_function # makes this work for python2 and 3 from gvar import * from lsqfit import nonlinear_fit import functools import inspect import sys ranseed([123]) ygen = gvar(0.02, 0.2) - 0.005 print (ygen) y = [gvar(ygen(), ygen.sdev) for i in range(20)] ystr = [yi.fmt(2) for yi in y] y = gvar(ystr) print (ystr[:]) print log_prior = BufferDict() log_prior['log(a)'] = log(gvar(0.02, 0.02)) sqrt_prior = BufferDict() sqrt_prior['sqrt(a)'] = sqrt(gvar(0.02, 0.02)) prior = BufferDict(a = gvar(0.02, 0.02)) stdout = sys.stdout
def test_avg_data(self):
""" avg_data """
self.assertTrue(avg_data([]) is None)
self.assertEqual(avg_data(dict()),BufferDict())
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
avg_data(dict(s=[1.],v=[1.,2.]))
self.assertEqual(len(w), 1)
with self.assertRaises(ValueError):
avg_data(dict(s=[],v=[1.,2.]), warn=False)
with self.assertRaises(ValueError):
avg_data(dict(s=[], v=[]))
with self.assertRaises(ValueError):
avg_data([1,2,"s"])
mean = avg_data([1])
self.assertEqual(mean.mean,1.)
self.assertEqual(mean.sdev,0.)
#
mean = avg_data([1,2])
self.assertAlmostEqual(mean.mean,1.5)
self.assertAlmostEqual(mean.var,sum((vi-1.5)**2
for vi in [1,2])/4.)
mean2 = avg_data(np.array([1.,2.]))
self.assertEqual(mean.mean,mean2.mean)
self.assertEqual(mean.sdev,mean2.sdev)
#
mean = avg_data([1,2],spread=True)
self.assertAlmostEqual(mean.mean,1.5)
self.assertAlmostEqual(mean.var,sum((vi-1.5)**2
for vi in [1,2])/2.)
#
mean = avg_data([1,2],median=True)
self.assertAlmostEqual(mean.mean,1.5)
self.assertAlmostEqual(mean.var,0.5**2/2.)
#
mean = avg_data([1,2],median=True,spread=True)
self.assertAlmostEqual(mean.mean,1.5)
self.assertAlmostEqual(mean.var,0.5**2)
#
mean = avg_data([1,2,3])
self.assertAlmostEqual(mean.mean,2.0)
self.assertAlmostEqual(mean.var,sum((vi-2.)**2
for vi in [1,2,3])/9.)
#
mean = avg_data([1,2,3], noerror=True)
self.assertAlmostEqual(mean, 2.0)
#
mean = avg_data([[1],[2],[3]])
self.assertAlmostEqual(mean[0].mean,2.0)
self.assertAlmostEqual(mean[0].var,sum((vi-2.)**2
for vi in [1,2,3])/9.)
mean = avg_data([[1],[2],[3]], noerror=True)
self.assertAlmostEqual(mean[0], 2.0)
mean = avg_data([1,2,3],spread=True)
self.assertAlmostEqual(mean.mean,2.0)
self.assertAlmostEqual(mean.var,sum((vi-2.)**2
for vi in [1,2,3])/3.)
#
mean = avg_data([1,2,3],median=True)
self.assertAlmostEqual(mean.mean,2.0)
self.assertAlmostEqual(mean.var,1./3.)
#
mean = avg_data([[1],[2],[3]],median=True)
self.assertAlmostEqual(mean[0].mean,2.0)
self.assertAlmostEqual(mean[0].var,1./3.)
#
mean = avg_data([1,2,3],median=True,spread=True)
self.assertAlmostEqual(mean.mean,2.0)
self.assertAlmostEqual(mean.var,1.)
#
mean = avg_data([1,2,3,4,5,6,7,8,9],median=True)
self.assertAlmostEqual(mean.mean,5)
self.assertAlmostEqual(mean.var,3.**2/9.)
#
mean = avg_data([1,2,3,4,5,6,7,8,9],median=True,spread=True)
self.assertAlmostEqual(mean.mean,5.)
self.assertAlmostEqual(mean.var,3.**2)
#
mean = avg_data([1,2,3,4,5,6,7,8,9,10],median=True)
self.assertAlmostEqual(mean.mean,5.5)
self.assertAlmostEqual(mean.var,3.5**2/10.)
#
mean = avg_data([1,2,3,4,5,6,7,8,9,10],median=True,spread=True)
self.assertAlmostEqual(mean.mean,5.5)
self.assertAlmostEqual(mean.var,3.5**2)
#
data = dict(s=[1,2,3],v=[[1,1],[2,2],[3,3]])
mean = avg_data(data,median=True,spread=True)
self.assertAlmostEqual(mean['s'].mean,2.0)
self.assertAlmostEqual(mean['s'].var,1.0)
self.assertEqual(mean['v'].shape,(2,))
self.assert_gvclose(mean['v'],[gvar(2,1),gvar(2,1)])
mean = avg_data(data, median=True, noerror=True)
self.assertAlmostEqual(mean['s'],2.0)
self.assertEqual(mean['v'].shape,(2,))
self.assert_arraysclose(mean['v'], [2,2])
mean = avg_data(data, noerror=True)
self.assertAlmostEqual(mean['s'],2.0)
self.assertEqual(mean['v'].shape,(2,))
self.assert_arraysclose(mean['v'], [2,2])
import tee
DO_PLOT = True
sys_stdout = sys.stdout
# ranseed(12345)
# ygen = gvar(0.015, 0.2)
# print(ygen)
# y = [gi for gi in bootstrap_iter(ygen, 20)]
# y = [gvar(ygen(), ygen.sdev) for i in range(20)]
# ystr = [yi.fmt(2) for yi in y]
# y = gvar(fmt(y, 2))
y = gvar([
'-0.17(20)', '-0.03(20)', '-0.39(20)', '0.10(20)', '-0.03(20)', '0.06(20)',
'-0.23(20)', '-0.23(20)', '-0.15(20)', '-0.01(20)', '-0.12(20)',
'0.05(20)', '-0.09(20)', '-0.36(20)', '0.09(20)', '-0.07(20)', '-0.31(20)',
'0.12(20)', '0.11(20)', '0.13(20)'
])
# print (y)
print
log_prior = BufferDict()
log_prior['log(a)'] = log(gvar(0.02, 0.02))
sqrt_prior = BufferDict()
sqrt_prior['sqrt(a)'] = sqrt(gvar(0.02, 0.02))
prior = BufferDict(a=gvar(0.02, 0.02))
stdout = sys.stdout
for p in [prior, log_prior, sqrt_prior]:
key = list(p.keys())[0]
def make_random(self, a, g='1.0(1)'):
a = numpy.asarray(a)
ans = numpy.empty(a.shape, object)
for i in numpy.ndindex(a.shape):
ans[i] = a[i] * gvar(g)
return ans