def test_seed_different(self):
"""
Test different seed -> different result in MISER
"""
func = lambda x: x**2
npoints = 50000
res, error = mcmiser(func, npoints, [0.], [1.], seed=[1234,5678])
res2, error2 = mcmiser(func, npoints, [0.], [1.], seed=[1235,5678])
assert res != res2, "{0} == {1}".format(res, res2)
assert error != error2
def test_integer_seed(self):
"""
Check that MISER works with an integer seed.
"""
func = lambda x: x**2
npoints = 50000
res, error = mcmiser(func, npoints, [0.], [1.], seed=12345)
res2, error2 = mcmiser(func, npoints, [0.], [1.], seed=12345)
assert res == res2, "{0} != {1}".format(res, res2)
assert error == error2
def test_seed(self):
"""
Test same seed -> same result in MISER
"""
func = lambda x: x**2
npoints = 50000
res, error = mcmiser(func, npoints, [0.], [1.], seed=[1234,5678])
res2, error2 = mcmiser(func, npoints, [0.], [1.], seed=[1234,5678])
assert res == res2, "{0} != {1}".format(res, res2)
assert error == error2
def forward_model(self, src, dist, R, h, sigma, src_type):
"""FWD model functions
Evaluates potential at point (dist) by a basis source located at (src).
dist can be a 1D point on the morphology loop or a 3D point
in 3D space. src is a 1D point of the morphology loop.
Utlizies sk monaco monte carlo method if available, otherwise defaults
to scipy integrate
Parameters
----------
x : float
R : float
h : float
sigma : float
src_type : basis_3D.key
Returns
-------
pot : float
value of potential at specified distance from the source
"""
if isinstance(dist, float):
if self.skmonaco_available:
pot, err = mcmiser(self.int_pot_1D_mc,
npoints=1e5,
xl=[-2**1.5 * R],
xu=[2**1.5 * R + self.cell.max_dist],
seed=42,
nprocs=num_cores,
args=(src, dist, R, src_type))
else:
pot, err = integrate.quad(self.int_pot_1D,
-2**1.5 * R,
2**1.5 * R + self.cell.max_dist,
args=(src, dist, R, src_type))
return pot / (4.0 * np.pi * sigma)
elif len(dist) == 3:
if self.skmonaco_available:
pot, err = mcmiser(self.int_pot_3D_mc,
npoints=1e5,
xl=[-2**1.5 * R],
xu=[2**1.5 * R + self.cell.max_dist],
seed=42,
nprocs=num_cores,
args=(src, dist[0], dist[1], dist[2], R,
src_type))
else:
pot, err = integrate.quad(self.int_pot_3D,
-2**1.5 * R,
2**1.5 * R + self.cell.max_dist,
args=(src, dist[0], dist[1], dist[2],
R, src_type))
return pot / (4.0 * np.pi * sigma)
def test_args2(self):
"""
Check that MISER works with arguments (2)
"""
func_noargs = lambda x: x**2
func_args = lambda x, a: a*x**2
npoints = 50000
res_noargs, error_noargs = mcmiser(func_noargs, npoints, [0.],[1.], seed=12345)
res_args, error_args = mcmiser(func_args, npoints, [0.],[1.], seed=12345, args=(2,))
self.assertEqual(2*res_noargs, res_args)
self.assertEqual(2*error_noargs, error_args)
def b_pot_3d_mc(x, R, h, sigma, basis_func=bf.gauss_rescale_3D):
"""
Calculate potential in the 3D case using Monte Carlo integration.
It utilizes the MISER algorithm
"""
pot, err = mcmiser(int_pot_3D_mc, npoints=1e5,
xl=[-R, -R, -R], xu=[R, R, R],
nprocs=4, args=(x, R, h, basis_func))
pot *= 1./(4.0*pi*sigma)
return pot
def _get_results_errors(self):
results, errors = [], []
for itrial in range(self.ntrials):
res, err = mcmiser(self.f,self.npoints,self.lbound,self.ubound,
seed=itrial+self.seed)
results.append(res)
errors.append(err)
results = np.array(results)
errors = np.array(errors)
return results, errors
def b_pot_3d_mc(x, R, h, sigma, basis_func=bf.gauss_rescale_3D):
"""
Calculate potential in the 3D case using Monte Carlo integration.
It utilizes the MISER algorithm
"""
pot, err = mcmiser(int_pot_3D_mc,
npoints=1e5,
xl=[-R, -R, -R],
xu=[R, R, R],
nprocs=4,
args=(x, R, h, basis_func))
pot *= 1. / (4.0 * pi * sigma)
return pot
def forward_model(self, x, R, h, sigma, src_type):
"""FWD model functions
Evaluates potential at point (x,0) by a basis source located at (0,0)
Utlizies sk monaco monte carlo method if available, otherwise defaults
to scipy integrate
Parameters
----------
x : float
R : float
h : float
sigma : float
src_type : basis_3D.key
Returns
-------
pot : float
value of potential at specified distance from the source
"""
if src_type.__name__ == "gauss_3D":
if x == 0: x = 0.0001
pot = special.erf(x / (np.sqrt(2) * R / 3.0)) / x
elif src_type.__name__ == "gauss_lim_3D":
if x == 0: x = 0.0001
d = R / 3.
if x < R:
e = np.exp(-(x / (np.sqrt(2) * d))**2)
erf = special.erf(x / (np.sqrt(2) * d))
pot = 4 * np.pi * ((d**2) * (e - np.exp(-4.5)) + (1 / x) *
((np.sqrt(np.pi / 2) * (d**3) * erf) - x *
(d**2) * e))
else:
pot = 15.28828 * (d)**3 / x
pot /= (np.sqrt(2 * np.pi) * d)**3
elif src_type.__name__ == "step_3D":
Q = 4. * np.pi * (R**3) / 3.
if x < R:
pot = (Q * (3 - (x / R)**2)) / (2. * R)
else:
pot = Q / x
pot *= 3 / (4 * np.pi * R**3)
else:
if skmonaco_available:
pot, err = mcmiser(self.int_pot_3D_mc,
npoints=1e5,
xl=[-R, -R, -R],
xu=[R, R, R],
seed=42,
nprocs=num_cores,
args=(x, R, h, src_type))
else:
pot, err = integrate.tplquad(self.int_pot_3D,
-R,
R,
lambda x: -R,
lambda x: R,
lambda x, y: -R,
lambda x, y: R,
args=(x, R, h, src_type))
pot *= 1. / (4.0 * np.pi * sigma)
return pot
def check_trial_run(self,*args,**kwargs):
res, err = mcmiser(self.f, self.npoints, self.lbound, self.ubound, *args, **kwargs)
error_in_mean = abs(res-self.analytical_value)
assert error_in_mean < 3*self.mean_sigma,\
"Error in mean = {}\n\
Expected error = {}".format(error_in_mean,self.mean_sigma)
def test_wrong_nprocs(self):
"""
Raise a ValueError if nprocs < 1
"""
with self.assertRaises(ValueError):
mcmiser(lambda x: x**2,2000,xl=[0.],xu=[1.],nprocs=-1)
def test_wrong_npoints(self):
"""
Raise a ValueError if npoints < 2 in MISER.
"""
with self.assertRaises(ValueError):
mcmiser(lambda x: x**2,0,xl=[0.],xu=[1.])
def test_wrong_xl(self):
"""
Raise a ValueError if len(xl) != len(xu) in MISER.
"""
with self.assertRaises(ValueError):
mcmiser(lambda x: x**2,2000,xl=[0.,0.],xu=[1.])
def test_zero_volume(self):
"""
Passing empty integration volume to MISER raises ValueError.
"""
with self.assertRaises(ValueError):
mcmiser(lambda x:x**2, 20000, [0.],[0.])