def test_rescale(self):
model1 = Exponential()
model2 = Exponential(rescale=2.1)
model3 = Exponential(rescale=2.1, len_scale=2.1)
self.assertAlmostEqual(model1.integral_scale,
2.1 * model2.integral_scale)
self.assertAlmostEqual(model1.integral_scale, model3.integral_scale)
def test_extdrift(self):
ext_drift = []
cond_drift = []
for i, grid in enumerate(self.grids):
dim = i + 1
model = Exponential(
dim=dim,
var=2,
len_scale=10,
anis=[0.9, 0.8],
angles=[2, 1, 0.5],
)
srf = SRF(model)
field = srf(grid)
ext_drift.append(field)
field = field.reshape(self.grid_shape[:dim])
cond_drift.append(field[self.data_idx[:dim]])
for Model in self.cov_models:
for dim in self.dims:
model = Model(
dim=dim,
var=2,
len_scale=10,
anis=[0.5, 0.2],
angles=[0.4, 0.2, 0.1],
)
extdrift = krige.ExtDrift(
model,
self.cond_pos[:dim],
self.cond_val,
cond_drift[dim - 1],
)
field_1, __ = extdrift.unstructured(
self.grids[dim - 1], ext_drift=ext_drift[dim - 1]
)
field_1 = field_1.reshape(self.grid_shape[:dim])
field_2, __ = extdrift.structured(
self.pos[:dim], ext_drift=ext_drift[dim - 1]
)
# extdrift.plot()
self.assertAlmostEqual(
np.max(np.abs(field_1 - field_2)), 0.0, places=2
)
for i, val in enumerate(self.cond_val):
self.assertAlmostEqual(
field_2[self.data_idx[:dim]][i], val, places=2
)
def setUp(self):
self.test_dir = tempfile.mkdtemp()
# structured field with a size 100x100x100 and a grid-size of 1x1x1
x = y = z = range(100)
model = Gaussian(dim=3, var=0.6, len_scale=20)
self.srf_structured = SRF(model)
self.srf_structured((x, y, z), mesh_type="structured")
# unstrucutred field
seed = MasterRNG(19970221)
rng = np.random.RandomState(seed())
x = rng.randint(0, 100, size=10000)
y = rng.randint(0, 100, size=10000)
model = Exponential(
dim=2, var=1, len_scale=[12.0, 3.0], angles=np.pi / 8.0
)
self.srf_unstructured = SRF(model, seed=20170519)
self.srf_unstructured([x, y])
import numpy as np from gstools import SRF, Exponential, Stable, vario_estimate_unstructured # generate a synthetic field with an exponential model x = np.random.RandomState(19970221).rand(1000) * 100.0 y = np.random.RandomState(20011012).rand(1000) * 100.0 model = Exponential(dim=2, var=2, len_scale=8) srf = SRF(model, mean=0, seed=19970221) field = srf((x, y)) # estimate the variogram of the field with 40 bins bins = np.arange(40) bin_center, gamma = vario_estimate_unstructured((x, y), field, bins) # fit the variogram with a stable model. (no nugget fitted) fit_model = Stable(dim=2) fit_model.fit_variogram(bin_center, gamma, nugget=False) # output ax = fit_model.plot(x_max=40) ax.plot(bin_center, gamma) print(fit_model)
###############################################################################
# estimate the variogram on an unstructured grid ##############################
###############################################################################
bins = np.linspace(0, 10, 50)
print('Estimating unstructured variogram')
bin_center, gamma = vario_estimate_unstructured(
(x_u, y_u),
herten_log_trans.reshape(-1),
bins,
sampling_size=2000,
sampling_seed=19920516,
)
# fit an exponential model
fit_model = Exponential(dim=2)
fit_model.fit_variogram(bin_center, gamma, nugget=False)
pt.plot(bin_center, gamma)
plot_variogram(fit_model, x_max=bins[-1])
###############################################################################
# estimate the variogram on a structured grid #################################
###############################################################################
# estimate the variogram on a structured grid
# use only every 10th value, otherwise calculations would take very long
x_s_skip = x_s[::10]
y_s_skip = y_s[::10]
herten_trans_skip = herten_log_trans[::10, ::10]
p.show()
###############################################################################
# Variogram Analysis
# ^^^^^^^^^^^^^^^^^^
#
# Next, we need to compute a variogram for the temperature probe data and fit that variogram to an exponential model
bins = np.linspace(0, 12300, 1000)
bin_center, gamma = vario_estimate_unstructured(
project["Observed Temperature"].points.T,
project["Observed Temperature"]["temperature (C)"],
bins,
)
fit_model = Exponential(dim=3)
fit_model.fit_variogram(bin_center, gamma, nugget=False)
plt.figure(figsize=(10, 5))
plt.plot(bin_center, gamma)
plot_variogram(fit_model, x_max=bins[-1], ax=plt.gca())
plt.xlabel("Lag Distance")
plt.ylabel("Variogram")
plt.show()
###############################################################################
# Performing the Kriging
# ^^^^^^^^^^^^^^^^^^^^^^
# Then we pass the fitted exponential model when instantiating the kriging operator from GSTools.
# Create the kriging model
import numpy as np
import matplotlib.pyplot as pt
from gstools import SRF, Exponential
from gstools.random import MasterRNG
# creating our own unstructured grid
seed = MasterRNG(19970221)
rng = np.random.RandomState(seed())
x = rng.randint(0, 100, size=10000)
y = rng.randint(0, 100, size=10000)
model = Exponential(dim=2, var=1, len_scale=[12.0, 3.0], angles=np.pi / 8.0)
srf = SRF(model, seed=20170519)
field = srf((x, y))
srf.vtk_export("field")
pt.tricontourf(x, y, field.T)
pt.axes().set_aspect("equal")
pt.show()
import numpy as np import matplotlib.pyplot as plt from gstools import SRF, Gaussian, Exponential # the grid x = np.arange(100) y = np.arange(100) # a smooth Gaussian covariance model model = Gaussian(dim=2, var=1, len_scale=10) srf = SRF(model, generator='VectorField') srf((x, y), mesh_type='structured', seed=19841203) srf.plot() # a rougher exponential covariance model model2 = Exponential(dim=2, var=1, len_scale=10) srf.model = model2 srf((x, y), mesh_type='structured', seed=19841203) srf.plot()
