def test_1d_gauss_hermite_quadrature(recurrence_algorithm):
distribution = Normal(2, 2)
abscissas, weights = quad_gaussian(
10, distribution, recurrence_algorithm=recurrence_algorithm)
assert abscissas.shape == (1, 11)
assert weights.shape == (11, )
assert numpy.allclose(numpy.sum(abscissas * weights, -1),
distribution.mom(1))
assert numpy.allclose(numpy.sum(abscissas**2 * weights, -1),
distribution.mom(2))
def test_3d_gauss_hermite_quadrature(recurrence_algorithm):
distribution = Iid(Normal(0, 1), 3)
abscissas, weights = quad_gaussian(
3, distribution, recurrence_algorithm=recurrence_algorithm)
assert abscissas.shape == (3, 4**3)
assert weights.shape == (4**3, )
kloc = numpy.eye(3, dtype=int)
assert numpy.allclose(numpy.sum(abscissas * weights, -1),
distribution.mom(kloc))
assert numpy.allclose(numpy.sum(abscissas**2 * weights, -1),
distribution.mom(2 * kloc))
"""
Created: Fri Jul 26 09:57:16 2019
@author: Christopher Albert <*****@*****.**>
"""
import time
from chaospy import Normal, J, generate_quadrature
params = [Normal(mu=0.999, sigma=0.0052),
Normal(mu=27.1, sigma=17.0),
Normal(mu=0.318, sigma=0.1),
Normal(mu=0.015, sigma=0.0087),
Normal(mu=0.0817, sigma=0.0077),
Normal(mu=1.309, sigma=0.086),
Normal(mu=2.19, sigma=0.22)]
dist = J(*params)
#%%
t = time.time()
nodes, weights = generate_quadrature(4, dist, rule='G', sparse=True)
print('time elapsed: {} s'.format(time.time() - t))
#%% save to disk
def save(approx):
with open('pce.pickle', 'wb') as filehandler:
pickle.dump(approx, filehandler)
#%%
indata = np.load('indata.npy')
outdata = np.load('outdata.npy')
with open('pce.pickle', 'rb') as filehandler:
approx = pickle.load(filehandler)
params = OrderedDict()
data = np.genfromtxt('params_1998.txt', dtype=None, encoding=None)
for param in data:
if(param[1] == 'Normal'):
params[param[0]] = Normal(param[2], param[3])
#%%
distribution = J(*params.values())
#%%
F0 = E(approx, distribution)
dF = Std(approx, distribution)
#%%
F0[0] = F0[1]
dF[0] = dF[1]
plt.plot(np.arange(len(F0))-38, F0, 'k')
plt.fill_between(np.arange(len(F0))-38,F0-dF, F0+dF, color='k', alpha=0.3)
plt.ylim(-100,200)
plt.xlabel('t')
#%%
data = np.genfromtxt('2019-07_run_1998/params.txt',
skip_header=1,
dtype=('|U64', '|U64', float, float))
labels = data['f0'] # parameter labels
mean = data['f2'] # E0
std = data['f3'] # sqrt(Var0)
s = sqrt(log(std**2 / mean**2 + 1))
mu = log(mean) - 0.5 * s**2
params = []
for k in range(len(mu)):
params.append(Normal(mu=mu[k], sigma=s[k]))
dist = J(*params)
#%%
nodes, weights = generate_quadrature(4, dist, rule='G', sparse=True)
expansion = orth_ttr(3, dist)
#%%
approx = fit_quadrature(expansion, nodes, weights, outdata)
#%%
F0 = E(approx, dist)
dF = Std(approx, dist)
import numpoly
import chaospy as cpy
import numpy as np
from time import time
from chaospy import Normal, generate_expansion
if __name__ == '__main__':
prior_mean = 0.
prior_sigma = 5.
dim = 2
prior = cpy.Iid(Normal(prior_mean, prior_sigma), dim)
poly_order = 2
abscissas, weights = cpy.generate_quadrature(poly_order,
prior,
rule='gaussian')
expansion = generate_expansion(poly_order, prior, retall=False)
def forward_model(params):
return np.prod(np.exp(-params**2))
evals = np.array([forward_model(sample) for sample in abscissas.T])
surrogate = cpy.fit_quadrature(expansion, abscissas, weights, evals)
coefficients = np.array(surrogate.coefficients)
indeterminants = surrogate.indeterminants
exponents = surrogate.exponents