class CheckLib(unittest.TestCase):
def setUp(self):
# load c++ library
self.lib = IntegralLibrary('../difference/difference_pylink.so')
self.target_result = {
0: 1.64493406684822643647241516664602518923 + 3.1415926535897932384626433832795028842j,
1: 2.08781123053685858754509217178101012328 - 6.2831853071795864769252867665590057684j,
2: -5.94029019737039970544633397517750766917 + 4.2570651807194096861418776386549427857j
}
self.epsrel = 1e-2
def check_result(self, computed_series, epsrel):
# convert result to sympy expressions
integral_with_prefactor = sp.sympify( computed_series.replace(',','+I*').replace('+/-','*value+error*') )
for order in range(3):
value = complex( integral_with_prefactor.coeff('eps',order).coeff('value') )
error = complex( integral_with_prefactor.coeff('eps',order).coeff('error') )
# check that the uncertainties are reasonable
self.assertLessEqual(error.real, abs(2*epsrel * self.target_result[order].real))
self.assertLessEqual(error.imag, abs(2*epsrel * self.target_result[order].imag))
# check that the desired uncertainties are reached
self.assertLessEqual(error.real, abs(epsrel * value.real) )
self.assertLessEqual(error.imag, abs(epsrel * value.imag) )
# check integral value
self.assertAlmostEqual( value.real, self.target_result[order].real, delta=3.*epsrel*abs(self.target_result[order].real) )
self.assertAlmostEqual( value.imag, self.target_result[order].imag, delta=3.*epsrel*abs(self.target_result[order].imag) )
def test_Vegas(self):
# choose integrator
self.lib.use_Vegas(flags=2, epsrel=self.epsrel) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib()
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Suave(self):
# choose integrator
self.lib.use_Suave(flags=2, epsrel=self.epsrel) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib()
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Divonne(self):
# choose integrator
self.lib.use_Divonne(flags=2, epsrel=self.epsrel, border=1e-8) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib()
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Cuhre(self):
# choose integrator
self.lib.use_Cuhre(flags=2, epsrel=self.epsrel) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib()
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
class CheckLib(unittest.TestCase):
def setUp(self):
# load c++ library
self.lib = IntegralLibrary(
'../userdefined_cpp/userdefined_cpp_pylink.so')
# full analytic result for func(y)=1:
# (4^-eps (-2 + 2^eps))/((-1 + eps) eps^2)
# = 1/eps^2 + (1 - Log[2] - Log[4])/eps + 1/2 (2 - 2 Log[2] - Log[2]^2 - 2 Log[4] + 2 Log[2] Log[4] + Log[4]^2) + O[eps]
# = 1.0000000000000000000/eps^2 - 1.0794415416798359283/eps + 0.60214400703386905808 + O[eps]
self.target_result = {
-2: 1.0,
-1: -1.0794415416798359283,
0: 0.60214400703386905808
}
self.epsrel = 1e-4
self.maxeval = 10**8
self.epsabs_tol = 1e-15
def check_result(self, computed_series, epsrel):
# convert result to sympy expressions
integral_with_prefactor = sp.sympify(
computed_series.replace(',',
'+I*').replace('+/-', '*value+error*'))
for order in range(-2, 0):
value = complex(
integral_with_prefactor.coeff('eps', order).coeff('value'))
error = complex(
integral_with_prefactor.coeff('eps', order).coeff('error'))
# check that the uncertainties are reasonable
self.assertLessEqual(
error.real,
abs(2 * epsrel * self.target_result[order].real) +
self.epsabs_tol)
self.assertLessEqual(
error.imag,
abs(2 * epsrel * self.target_result[order].imag) +
self.epsabs_tol)
# check that the desired uncertainties are reached
self.assertLessEqual(error.real,
abs(epsrel * value.real) + self.epsabs_tol)
self.assertLessEqual(error.imag,
abs(epsrel * value.imag) + self.epsabs_tol)
# check integral value
self.assertAlmostEqual(
value.real,
self.target_result[order].real,
delta=3. * epsrel * abs(self.target_result[order].real) +
self.epsabs_tol)
self.assertAlmostEqual(
value.imag,
self.target_result[order].imag,
delta=3. * epsrel * abs(self.target_result[order].imag) +
self.epsabs_tol)
def test_Vegas(self):
# choose integrator
self.lib.use_Vegas(
flags=2, epsrel=self.epsrel,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Suave(self):
# choose integrator
self.lib.use_Suave(
flags=2, epsrel=self.epsrel, maxeval=self.maxeval,
nnew=10**5) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Divonne(self):
# choose integrator
self.lib.use_Divonne(
flags=2, epsrel=self.epsrel, border=1e-12,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Cuhre(self):
# choose integrator
self.lib.use_Cuhre(
flags=2, epsrel=self.epsrel,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
class CheckLib(unittest.TestCase):
def setUp(self):
# load c++ library
self.lib = IntegralLibrary(
'../one_integration_variable/one_integration_variable_pylink.so')
self.target_result = {-1: 0.0, 0: -0.5, 1: -0.25}
self.epsrel = 1e-11
self.epsabs = 1e-10
self.maxeval = 10**5
def check_result(self, computed_series, epsrel, epsabs):
# convert result to sympy expressions
integral_with_prefactor = sp.sympify(
computed_series.replace(',',
'+I*').replace('+/-', '*value+error*'))
for order in range(-1, 2):
value = complex(
integral_with_prefactor.coeff('eps', order).coeff('value'))
error = complex(
integral_with_prefactor.coeff('eps', order).coeff('error'))
# check that the desired uncertainties are reached
self.assertLessEqual(error.real, epsabs)
self.assertLessEqual(error.imag, epsabs)
# check integral value
self.assertAlmostEqual(value.real,
self.target_result[order].real,
delta=3. * epsabs)
self.assertAlmostEqual(value.imag,
self.target_result[order].imag,
delta=3. * epsabs)
def test_Vegas(self):
# choose integrator
# can only reach ~2e-9 accuracy with Vegas
self.lib.use_Vegas(
flags=0, epsrel=self.epsrel, epsabs=2e-9,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel, 2e-9)
def test_Suave(self):
# choose integrator
self.lib.use_Suave(
flags=0, epsrel=self.epsrel, epsabs=self.epsabs,
maxeval=5000) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_Divonne(self):
# choose integrator
self.lib.use_Divonne(
flags=0,
epsrel=self.epsrel,
epsabs=self.epsabs,
border=1e-8,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_Cuhre(self):
# choose integrator
self.lib.use_Cuhre(
flags=0,
epsrel=self.epsrel,
epsabs=self.epsabs,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_CQuad(self):
# choose integrator
self.lib.use_CQuad(verbose=False,
epsrel=self.epsrel,
epsabs=self.epsabs)
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_Qmc_default_transform(self):
# choose integrator
self.lib.use_Qmc(verbosity=0,
epsrel=self.epsrel,
epsabs=self.epsabs,
seed=3212,
transform='korobov3',
fitfunction='polysingular')
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_Qmc_no_transform(self):
# choose integrator
self.lib.use_Qmc(verbosity=0,
epsrel=self.epsrel,
epsabs=self.epsabs,
seed=3212,
transform='none',
fitfunction='none')
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
def test_Qmc_Korobov2x1_transform(self):
# choose integrator
self.lib.use_Qmc(verbosity=0,
epsrel=self.epsrel,
epsabs=self.epsabs,
seed=3212,
transform='Korobov2x1')
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
)
# check
self.check_result(str_integral_with_prefactor, self.epsrel,
self.epsabs)
class CheckLib(unittest.TestCase):
def setUp(self):
# load c++ library
self.lib = IntegralLibrary(
'../userdefined_cpp/userdefined_cpp_pylink.so')
self.target_result = {-2: 0.095206, -1: -2.561, 0: 21.120, 1: -78.7}
self.real_parameters = [0.77]
self.epsrel = 1e-3
self.maxeval = 10**8
self.epsabs_tol = 1e-15
def check_result(self, computed_series, epsrel):
# convert result to sympy expressions
integral_with_prefactor = sp.sympify(
computed_series.replace(',',
'+I*').replace('+/-', '*value+error*'))
for order in range(-2, 2):
value = complex(
integral_with_prefactor.coeff('eps', order).coeff('value'))
error = complex(
integral_with_prefactor.coeff('eps', order).coeff('error'))
# check that the uncertainties are reasonable
self.assertLessEqual(
error.real,
abs(2 * epsrel * self.target_result[order].real) +
self.epsabs_tol)
self.assertLessEqual(
error.imag,
abs(2 * epsrel * self.target_result[order].imag) +
self.epsabs_tol)
# check that the desired uncertainties are reached
self.assertLessEqual(error.real,
abs(epsrel * value.real) + self.epsabs_tol)
self.assertLessEqual(error.imag,
abs(epsrel * value.imag) + self.epsabs_tol)
# check integral value
self.assertAlmostEqual(
value.real,
self.target_result[order].real,
delta=3. * epsrel * abs(self.target_result[order].real) +
self.epsabs_tol)
self.assertAlmostEqual(
value.imag,
self.target_result[order].imag,
delta=3. * epsrel * abs(self.target_result[order].imag) +
self.epsabs_tol)
def test_Vegas(self):
# choose integrator
self.lib.use_Vegas(
flags=2, epsrel=self.epsrel,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
self.real_parameters)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Suave(self):
# choose integrator
self.lib.use_Suave(
flags=2, epsrel=self.epsrel,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
self.real_parameters)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Divonne(self):
# choose integrator
self.lib.use_Divonne(
flags=2, epsrel=self.epsrel, border=1e-8,
maxeval=self.maxeval) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
self.real_parameters)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
def test_Cuhre(self):
# choose integrator
# Note: Need `mineval` because Cuhre underestimates the error
self.lib.use_Cuhre(flags=2,
epsrel=self.epsrel,
maxeval=self.maxeval,
mineval=6 *
10**4) # ``flags=2``: verbose --> see Cuba manual
# integrate
str_integral_without_prefactor, str_prefactor, str_integral_with_prefactor = self.lib(
self.real_parameters)
# check
self.check_result(str_integral_with_prefactor, self.epsrel)
