def solve_nonlinear(self, params, unknowns, resids):
power = params['power']
method_dict = params['method_dict']
dist = method_dict['distribution']
rule = method_dict['rule']
n = len(power)
if rule != 'rectangle':
points, weights = cp.generate_quadrature(order=n - 1,
domain=dist,
rule=rule)
# else:
# points, weights = quadrature_rules.rectangle(n, method_dict['distribution'])
poly = cp.orth_chol(n - 1, dist)
# poly = cp.orth_bert(n-1, dist)
# double check this is giving me good orthogonal polynomials.
# print poly, '\n'
p2 = cp.outer(poly, poly)
# print 'chol', cp.E(p2, dist)
norms = np.diagonal(cp.E(p2, dist))
print 'diag', norms
expansion, coeff = cp.fit_quadrature(poly,
points,
weights,
power,
retall=True,
norms=norms)
# expansion, coeff = cp.fit_quadrature(poly, points, weights, power, retall=True)
mean = cp.E(expansion, dist)
print 'mean cp.E =', mean
# mean = sum(power*weights)
print 'mean sum =', sum(power * weights)
print 'mean coeff =', coeff[0]
std = cp.Std(expansion, dist)
print mean
print std
print np.sqrt(np.sum(coeff[1:]**2 * cp.E(poly**2, dist)[1:]))
# std = np.sqrt(np.sum(coeff[1:]**2 * cp.E(poly**2, dist)[1:]))
# number of hours in a year
hours = 8760.0
# promote statistics to class attribute
unknowns['mean'] = mean * hours
unknowns['std'] = std * hours
print 'In ChaospyStatistics'
def test_orthogonals():
dist = cp.Iid(cp.Normal(), dim)
cp.orth_gs(order, dist)
cp.orth_ttr(order, dist)
cp.orth_chol(order, dist)
print("\nFirst Order Indices")
print(pd.DataFrame(Sensitivities,columns=['Smc','Spc','Sa'],index=row_labels).round(3))
# print("\nRelative errors")
# rel_errors=np.column_stack(((S_mc - s**2)/s**2,(S_pc - s**2)/s**2))
# print(pd.DataFrame(rel_errors,columns=['Error Smc','Error Spc'],index=row_labels).round(3))
# Polychaos convergence
Npc_list = np.logspace(1, 3, 10).astype(int)
error = []
for i, Npc in enumerate(Npc_list):
Zpc = jpdf.sample(Npc)
Ypc = linear_model(w, Zpc.T)
Npol = 4
poly = cp.orth_chol(Npol, jpdf)
approx = cp.fit_regression(poly, Zpc, Ypc, rule="T")
s_pc = cp.Sens_m(approx, jpdf)
error.append(LA.norm((s_pc - s**2)/s**2))
plt.figure()
plt.semilogy(Npc_list, error)
_=plt.xlabel('Nr Z')
_=plt.ylabel('L2-norm of error in Sobol indices')
# # Scatter plots of data, z-slices, and linear model
fig=plt.figure()
Ndz = 10 # Number of slices of the Z-axes
Zslice = np.zeros((Nrv, Ndz)) # array for mean-values in the slices
# example orthogonalization schemes
# a normal random variable
n = cp.Normal(0, 1)
x = np.linspace(0,1, 50)
# the polynomial order of the orthogonal polynomials
polynomial_order = 3
poly = cp.orth_bert(polynomial_order, n, normed=True)
print('Bertran recursion {}'.format(poly))
ax = plt.subplot(221)
ax.set_title('Bertran recursion')
_=plt.plot(x, poly(x).T)
_=plt.xticks([])
poly = cp.orth_chol(polynomial_order, n, normed=True)
print('Cholesky decomposition {}'.format(poly))
ax = plt.subplot(222)
ax.set_title('Cholesky decomposition')
_=plt.plot(x, poly(x).T)
_=plt.xticks([])
poly = cp.orth_ttr(polynomial_order, n, normed=True)
print('Discretized Stieltjes / Thre terms reccursion {}'.format(poly))
ax = plt.subplot(223)
ax.set_title('Discretized Stieltjes ')
_=plt.plot(x, poly(x).T)
poly = cp.orth_gs(polynomial_order, n, normed=True)
print('Modified Gram-Schmidt {}'.format(poly))
ax = plt.subplot(224)
def test_orth_chol():
dist = cp.Normal(0, 1)
orth1 = cp.orth_ttr(5, dist, normed=True)
orth2 = cp.orth_chol(5, dist, normed=True)
eps = cp.sum((orth1-orth2)**2)
assert np.allclose(eps(np.linspace(-100, 100, 5)), 0)
def test_orth_chol():
dist = cp.Normal(0, 1)
orth1 = cp.orth_ttr(5, dist, normed=True)
orth2 = cp.orth_chol(5, dist, normed=True)
eps = cp.sum((orth1-orth2)**2)
assert np.allclose(eps(np.linspace(-100, 100, 5)), 0)
