def test_sampling_3d(self):
x_c = np.linspace(0.0, 100.0, 100)
y_c = np.linspace(0.0, 100.0, 100)
z_c = np.linspace(0.0, 100.0, 100)
x, y, z = np.meshgrid(x_c, y_c, z_c)
x = np.reshape(x, len(x_c) * len(y_c) * len(z_c))
y = np.reshape(y, len(x_c) * len(y_c) * len(z_c))
z = np.reshape(z, len(x_c) * len(y_c) * len(z_c))
rng = np.random.RandomState(1479373475)
field = rng.rand(len(x))
bins = np.arange(0, 100, 10)
bin_centres, gamma = vario_estimate_unstructured(
(x, y, z),
field,
bins,
sampling_size=2000,
sampling_seed=1479373475,
)
var = 1.0 / 12.0
self.assertAlmostEqual(gamma[0], var, places=2)
self.assertAlmostEqual(gamma[len(gamma) // 2], var, places=2)
self.assertAlmostEqual(gamma[-1], var, places=2)
def test_doubles(self):
x = np.arange(1, 11, 1, dtype=np.double)
z = np.array(
(41.2, 40.2, 39.7, 39.2, 40.1, 38.3, 39.1, 40.0, 41.1, 40.3),
dtype=np.double,
)
bins = np.arange(1, 11, 1, dtype=np.double)
bin_centres, gamma = vario_estimate_unstructured([x], z, bins)
self.assertAlmostEqual(gamma[0], 0.4917, places=4)
def fit_model_var(coords_df, x_c, y_c, values):
# fit the model varigrom to the experimental variogram
bin_num = 40 # number of bins in the experimental variogram
# first get the coords and determine distances
x_delta = max(x_c) - min(x_c) # distance across x coords
y_delta = max(y_c) - min(y_c) # distance across y coords
max_dist = np.sqrt(
np.square(x_delta +
y_delta)) / 4 # assume correlated over 1/4 of distance
# setup bins for the variogram
bins_c = np.linspace(0, max_dist,
bin_num) # bin edges in variogram, bin_num of bins
# compute the experimental variogram
bin_cent_c, gamma_c = gs.vario_estimate_unstructured((x_c, y_c), values,
bins_c)
# bin_center_c is the "lag" of the bin, gamma_c is the value
gamma_c = smooth(
gamma_c, 5
) # smooth the experimental variogram to help fitting - moving window with 5 samples
# fit the model variogram
# potential models are: Gaussian, Exponential, Matern, Rational, Stable, Linear,
# Circular, Spherical, and Intersection
fit_var = gs.Stable(dim=2)
fit_var.fit_variogram(bin_cent_c,
gamma_c,
nugget=False,
estimator='cressie') # fit the model variogram
# print('max distance', max_dist,'var len scale', fit_var.len_scale)
# check to see of range of varigram is very small (problem with fit), it so, set it to a value
# also check to see if it is too long and set it to a value
if fit_var.len_scale < max_dist / 3: # check if too short
fit_var.len_scale = max_dist / 3 # set to value
# print('too short, set len_scale to: ', max_dist/3)
elif fit_var.len_scale > max_dist * 1.5: # check if too long
fit_var.len_scale = max_dist # set to value
# print('too long, set len_scale to: ', max_dist)
plt_var = False
if plt_var:
# plot the variogram to show fit and print out variogram paramters
# should make it save to pdf file
ax1 = fit_var.plot(x_max=max_dist) # plot model variogram
ax1.plot(bin_cent_c, gamma_c) # plot experimental variogram
# krig_plots.savefig()
plt.close('all')
return fit_var
def test_sampling_1d(self):
x = np.linspace(0.0, 100.0, 21000)
rng = np.random.RandomState(1479373475)
field = rng.rand(len(x))
bins = np.arange(0, 100, 10)
bin_centres, gamma = vario_estimate_unstructured(
[x], field, bins, sampling_size=5000, sampling_seed=1479373475)
var = 1.0 / 12.0
self.assertAlmostEqual(gamma[0], var, places=2)
self.assertAlmostEqual(gamma[len(gamma) // 2], var, places=2)
self.assertAlmostEqual(gamma[-1], var, places=2)
def test_uncorrelated_2d(self):
x_c = np.linspace(0.0, 100.0, 60)
y_c = np.linspace(0.0, 100.0, 60)
x, y = np.meshgrid(x_c, y_c)
x = np.reshape(x, len(x_c) * len(y_c))
y = np.reshape(y, len(x_c) * len(y_c))
rng = np.random.RandomState(1479373475)
field = rng.rand(len(x))
bins = np.arange(0, 100, 10)
bin_centres, gamma = vario_estimate_unstructured((x, y), field, bins)
var = 1.0 / 12.0
self.assertAlmostEqual(gamma[0], var, places=2)
self.assertAlmostEqual(gamma[len(gamma) // 2], var, places=2)
self.assertAlmostEqual(gamma[-1], var, places=2)
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)
pt.imshow(herten_log_trans.T, origin='lower', aspect='equal')
pt.show()
# create an unstructured grid for the variogram estimation
x_u, y_u = create_unstructured_grid(x_s, y_s)
###############################################################################
# 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 #################################
###############################################################################
def test_list(self):
x = np.arange(1, 11, 1, dtype=np.double)
z = [41.2, 40.2, 39.7, 39.2, 40.1, 38.3, 39.1, 40.0, 41.1, 40.3]
bins = np.arange(1, 11, 1, dtype=np.double)
bin_centres, gamma = vario_estimate_unstructured([x], z, bins)
self.assertAlmostEqual(gamma[1], 0.7625, places=4)
def test_np_int(self):
x = np.arange(1, 5, 1, dtype=np.int)
z = np.array((10, 20, 30, 40), dtype=np.int)
bins = np.arange(1, 11, 1, dtype=np.int)
bin_centres, gamma = vario_estimate_unstructured([x], z, bins)
self.assertAlmostEqual(gamma[0], 50.0, places=4)
(303509.4197523619, 4279629.689766085, 8053.049483835099),
(336316.405356571, 4261479.748583805, -1756.358124546427),
(0.22299463811939535, -0.11978828465250713, 0.9674317331109259),
]
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
