def test_moment_independant(self, ishigami_data, tmp):
ishigami_data_ = copy.deepcopy(ishigami_data)
ishigami_data_.space.max_points_nb = 5000
X = ishigami_data_.space.sampling(5000, 'olhs')
Y = ishigami_data_.func(X).flatten()
momi = moment_independent(X,
Y,
plabels=['x1', 'x2', 'x3'],
fname=os.path.join(tmp,
'moment_independent.pdf'))
npt.assert_almost_equal(momi[2]['Kolmogorov'], [0.236, 0.377, 0.107],
decimal=2)
npt.assert_almost_equal(momi[2]['Kuiper'], [0.257, 0.407, 0.199],
decimal=2)
npt.assert_almost_equal(momi[2]['Delta'], [0.211, 0.347, 0.162],
decimal=2)
npt.assert_almost_equal(momi[2]['Sobol'], [0.31, 0.421, 0.002],
decimal=2)
# Cramer
space = Space(corners=[[-5, -5], [5, 5]], sample=5000)
space.sampling(dists=['Normal(0, 1)', 'Normal(0, 1)'])
Y = [np.exp(x_i[0] + 2 * x_i[1]) for x_i in space]
X = np.array(space)
momi = moment_independent(X,
Y,
fname=os.path.join(tmp,
'moment_independent.pdf'))
npt.assert_almost_equal(momi[2]['Cramer'], [0.113, 0.572], decimal=2)
def test_space_evaluation(settings_ishigami):
f_3d = Ishigami()
space = Space(settings_ishigami['space']['corners'])
space.sampling(2, 'halton')
targets_space = f_3d(space)
f_data_base = np.array([5.25, 4.2344145]).reshape(2, 1)
npt.assert_almost_equal(targets_space, f_data_base)
def test_discrepancy():
corners = [[0.5, 0.5], [6.5, 6.5]]
space_1 = Space(corners)
space_2 = Space(corners)
space_1 += [[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]]
space_2 += [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]]
assert Space.discrepancy(space_1, space_1.corners) == pytest.approx(0.0081, abs=1e-4)
assert Space.discrepancy(space_2, space_2.corners) == pytest.approx(0.0105, abs=1e-4)
space_1 = (2.0 * space_1.values - 1.0) / (2.0 * 6.0)
assert Space.discrepancy(space_1) == pytest.approx(0.0081, abs=1e-4)
space = np.array([[2, 1, 1, 2, 2, 2],
[1, 2, 2, 2, 2, 2],
[2, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 2, 2],
[1, 2, 2, 2, 1, 1],
[2, 2, 2, 2, 1, 1],
[2, 2, 2, 1, 2, 2]])
space = (2.0 * space - 1.0) / (2.0 * 2.0)
assert Space.discrepancy(space, method='MD') == pytest.approx(2.5000, abs=1e-4)
assert Space.discrepancy(space, method='WD') == pytest.approx(1.3680, abs=1e-4)
assert Space.discrepancy(space, method='CD') == pytest.approx(0.3172, abs=1e-4)
def test_mst(tmp):
sample = np.array([[0.25, 0.5], [0.6, 0.4], [0.7, 0.2]])
mean, std, edges = Space.mst(sample, fname=os.path.join(tmp, 'mst.pdf'))
assert mean == pytest.approx(0.2938, abs=1e-4)
assert std == pytest.approx(0.0702, abs=1e-4)
npt.assert_equal(edges, [[0, 1], [1, 2]])
def branin_data(settings_ishigami):
data = {}
data['func'] = Branin()
data['dists'] = [ot.Uniform(-5, 10), ot.Uniform(0, 15)]
data['point'] = [2., 2.]
data['target_point'] = data['func'](data['point'])
data['space'] = Space(
[[-7, 0], [10, 15]],
settings_ishigami['space']['sampling']['init_size'],
settings_ishigami['space']['resampling']['resamp_size'], ['x1', 'x2'])
data['space'].sampling(10, kind='halton', discrete=0)
data['target_space'] = data['func'](data['space'])
return Datatest(data)
def g_function_data(settings_ishigami):
data = {}
data['func'] = G_Function()
data['dists'] = [ot.Uniform(0, 1)] * 4
data['point'] = [0.5, 0.2, 0.7, 0.1]
data['target_point'] = data['func'](data['point'])
data['space'] = Space(
[[0, 0, 0, 0], [1, 1, 1, 1]],
settings_ishigami['space']['sampling']['init_size'],
settings_ishigami['space']['resampling']['resamp_size'],
['x1', 'x2', 'x3', 'x4'])
data['space'].sampling(10, kind='halton', discrete=2)
data['target_space'] = data['func'](data['space'])
return Datatest(data)
def ishigami_data(settings_ishigami):
data = {}
data['func'] = Ishigami()
x1 = ot.Uniform(-3.1415, 3.1415)
data['dists'] = [x1] * 3
data['point'] = [2.20, 1.57, 3]
data['target_point'] = data['func'](data['point'])
data['space'] = Space(
settings_ishigami['space']['corners'],
settings_ishigami['space']['sampling']['init_size'],
settings_ishigami['space']['resampling']['resamp_size'],
settings_ishigami['snapshot']['plabels'])
data['space'].sampling(150,
settings_ishigami['space']['sampling']['method'])
data['target_space'] = data['func'](data['space'])
return Datatest(data)
def mascaret_data(settings_ishigami):
data = {}
fun = db_Mascaret()
data['func'] = lambda x: fun(x).reshape(-1, 14)[:, 0:3]
data['func'].x = fun.x[0:3]
x1 = ot.Uniform(15., 60.)
x2 = ot.Normal(4035., 400.)
data['dists'] = [x1, x2]
data['point'] = [31.54, 4237.025]
data['target_point'] = data['func'](data['point'])[0]
data['space'] = Space(
[[15.0, 2500.0], [60, 6000.0]],
settings_ishigami['space']['sampling']['init_size'],
settings_ishigami['space']['resampling']['resamp_size'], ['Ks', 'Q'])
data['space'].sampling(50,
settings_ishigami['space']['sampling']['method'])
data['target_space'] = data['func'](data['space'])
return Datatest(data)
def mufi_data(settings_ishigami):
data = {}
f_e = Forrester('e')
f_c = Forrester('c')
data['dists'] = [ot.Uniform(0.0, 1.0)]
data['point'] = [0.65]
data['target_point'] = f_e(data['point'])
data['space'] = Space(
[[0.0], [1.0]],
10,
settings_ishigami['space']['resampling']['resamp_size'],
['fidelity', 'x'],
multifidelity=[5.1, 13.0])
data['space'].sampling(10, 'halton')
working_space = np.array(data['space'])
data['target_space'] = np.vstack([
f_e(working_space[working_space[:, 0] == 0][:, 1:]),
f_c(working_space[working_space[:, 0] == 1][:, 1:])
])
data['func'] = [f_e, f_c]
return Datatest(data)
#samples sizes for samling error init_size5 = 200 init_size4 = 150 init_size3 = 100 init_size2 = 80 init_size1 = 60 #sample size used for trunctation error init_size = 1000 indim = 2 # inputs dim plabels = ['Ks', 'Q'] space = Space(corners) # Build the learning samples #training sample for truncation error (1 sample) x_train = np.array(space.sampling(init_size, 'halton')) #training samples for sampling error (init_size varies) x_train5 = np.array(space.sampling(init_size5, 'halton')) x_train4 = np.array(space.sampling(init_size4, 'halton')) x_train3 = np.array(space.sampling(init_size3, 'halton')) x_train2 = np.array(space.sampling(init_size2, 'halton')) x_train1 = np.array(space.sampling(init_size1, 'halton')) #training sample for estimation of LC metrics (large init_size)
np.array(sample_kde)[-1, 1],
c='b',
marker='D',
s=60)
ticks = np.linspace(0, 1, num=5)
plt.colorbar(contour, ticks=ticks)
plt.show()
# WD plot
fig = plt.figure()
ax = fig.gca()
ax.set_xlim(mini, maxi)
ax.set_ylim(mini, maxi)
f_ = np.array([
Space.discrepancy(np.vstack([np.array(sample_kde)[:-1], s]), method='WD')
for s in positions.T
])[:, None]
f_ = np.reshape(f_, xx.shape)
contour = ax.contourf(xx, yy, f_)
ax.scatter(np.array(sample_kde)[:-1, 0],
np.array(sample_kde)[:-1, 1],
c='k',
marker='o')
plt.colorbar(contour)
plt.show()
# 1D line at y=0.5
# fig = plt.figure()
# x = np.linspace(0, 1, 100)[:, None]
# x = np.concatenate([x, np.ones((100, 1)) * 0.5], axis=1)
60122.3076923077, 60229.23076923078, 60336.15384615386, 60443.07692307694,
60550.0, 60654.545454545456, 60759.09090909091, 60863.63636363637,
60968.18181818182, 61072.72727272728, 61177.272727272735,
61281.81818181819, 61386.36363636365, 61490.9090909091, 61595.45454545456,
61700.0, 61818.75, 61937.5, 62056.25, 62175.0
]
in_dim = len(corners) # input dim
Nl = 1000 # learning sample size
Nt = 1000 # test sample size
plabels = ['Ks_{min1}', 'Ks_{min2}', 'Ks_{min3}', 'Q']
dists = [
'BetaMuSigma(4031, 400, 1000, 6000).getDistribution()',
'Uniform(15., 60.)', 'Uniform(15., 60.)', 'Uniform(15., 60.)'
]
distsOT = dists_to_ot(dists)
space = Space(corners)
#Get the Data Base for UQ
Case = Mascaret_new()
X = Case.data_input
x_l = X[0:799, :]
x_t = X[800:999, :]
# Build the learning sample
#x_l = ot.LHSExperiment(ot.ComposedDistribution(distsOT), Nl, True, True).generate() #LHS distribution
#x_l = [list(x_l[i]) for i in range(Nl)]
#x_l = np.array(x_l)
doe_l = doe(x_l)
doe_t = doe(x_t)
# Build the training sample
def test_space(settings_ishigami, seed):
corners = settings_ishigami['space']['corners']
space = Space(corners)
assert space.max_points_nb == np.inf
space = Space(corners, sample=10)
assert space.max_points_nb == 10
space = Space(corners, sample=10, nrefine=6,
plabels=['x', 'y', 'z'])
assert space.max_points_nb == 16
space += (1, 2, 3)
npt.assert_array_equal(space.values, [(1, 2, 3)])
space.empty()
npt.assert_array_equal(space.values, np.empty((0, 3)))
space += [(1, 2, 3), (1, 1, 3)]
npt.assert_array_equal(space.values, [(1, 2, 3), (1, 1, 3)])
space2 = Space(corners, space.values)
npt.assert_array_equal(space2.values, [(1, 2, 3), (1, 1, 3)])
s1 = space.sampling()
assert len(s1) == 10
space2 = Space(corners,
sample=settings_ishigami['space']['sampling']['init_size'],
nrefine=settings_ishigami['space']['resampling']['resamp_size'])
s2 = space2.sampling(10, kind='lhsc')
assert len(s2) == 10
assert np.any(s1 != s2)
space.empty()
space += (1, 2, 3)
space += (1, 2, 3)
assert len(space) == 1
space = Space(corners, sample=16, duplicate=True)
space += (1, 2, 3)
space += (1, 2, 3)
assert len(space) == 2
with pytest.raises(ValueError):
space += (1, 2)
assert len(space) == 2
space += (1, 7, 3)
assert len(space) == 2
space.sampling(17)
assert len(space) == 16
space.empty()
dists = ['Uniform(0., 1.)', 'Uniform(-1., 2.)', 'Uniform(-2., 3.)']
space.sampling(5, kind='halton', dists=dists)
out = [(0.5, 0.0, -1.0), (0.25, 1.0, 0.0), (0.75, -0.67, 1.0),
(0.125, 0.33, 2.0), (0.625, 1.33, -1.8)]
npt.assert_almost_equal(space, out, decimal=1)
space = Space(corners, sample=np.array([(1, 2, 3), (1, 1, 3)]))
assert space.doe_init == 2
assert space.max_points_nb == 2
test_settings = copy.deepcopy(settings_ishigami)
test_settings['space']['corners'][1] = [np.pi, -np.pi, np.pi]
with pytest.raises(ValueError):
Space(test_settings['space']['corners'])
import numpy as np
from scipy.spatial import distance
from sklearn import preprocessing
from sklearn.neighbors import NearestNeighbors
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
from batman.space import Space
from batman.visualization import doe, response_surface, reshow
from batman.functions import Branin
import openturns as ot
# Problem definition: f(sample) -> data
corners = np.array([[-5, 0], [10, 14]])
sample = Space(corners)
sample.sampling(20)
doe(sample, fname='init_doe.pdf')
fun_branin = Branin()
def fun(x):
return -fun_branin(x)
data = fun(sample)
# Algo
def random_uniform_ring(
#samples sizes for samling error
init_size5 = 200
init_size4 = 150
init_size3 = 100
init_size2 = 50
init_size1 = 40
#sample size used for trunctation error
init_size = 1000
indim = 2 # inputs dim
plabels = ['Ks', 'Q']
space = Space(corners)
# Build the learning samples
x_train = np.array(space.sampling(
init_size, 'halton')) #training sample for truncation error (1 sample)
x_train5 = np.array(space.sampling(
init_size5,
'halton')) #training samples for sampling error (init_size varies)
x_train4 = np.array(space.sampling(init_size4, 'halton'))
x_train3 = np.array(space.sampling(init_size3, 'halton'))
x_train2 = np.array(space.sampling(init_size2, 'halton'))
x_train1 = np.array(space.sampling(init_size1, 'halton'))
x_trainr = np.array(space.sampling(