def test_variogram_cloud_3():
n = 100
x = np.zeros(n)
y = np.zeros(n)
v = np.zeros(n)
(hc, gc) = variogram.cloud(x, y, v)
assert (hc.shape[0] == n * (n - 1) / 2 and gc.shape[0] == n * (n - 1) / 2)
def main():
"""
Plots variogram cloud of cobalt concentration measurments.
"""
jura_data = np.genfromtxt('data.txt', names=True)
hc, gc = variogram.cloud(jura_data['X'], jura_data['Y'], jura_data['Co'])
plt.scatter(hc, gc, s=10)
plt.xlabel('distance')
plt.ylabel('Squared differences of concentrations')
plt.xlim(xmin=0)
plt.ylim(ymin=0)
plt.title('Variogram cloud of measured cobalt concentrations (mg/kg)')
plt.show()
def main():
"""
Plots experimental variogram of cobalt concentration data.
"""
lag = 0.1 # width of bin
nlag = 40 # number of bins
jura_data = np.genfromtxt('data.txt', names=True)
hc, gc = variogram.cloud(jura_data['X'], jura_data['Y'], jura_data['Co'])
he, ge = variogram.experimental(hc, gc, lag, nlag)
plt.scatter(he, ge, s=30) # marker size 's' set to 30
variance = np.var(jura_data['Co'])
# variance presented as dashed line
plt.axhline(variance, linestyle='--')
plt.scatter(he, ge)
# axes labels
plt.xlabel('distance')
plt.ylabel('gamma')
# axes limits
plt.xlim(xmin=0, xmax=lag * nlag)
plt.ylim(ymin=0)
plt.title('Experimental variogram of cobalt concentration (mg/kg)')
plt.show()
def main():
"""
Plots different variogram models and compares them to experimental data.
"""
lag = 0.1
nlag = 40
jura_data = np.genfromtxt('data.txt', names=True)
hc, gc = variogram.cloud(jura_data['X'], jura_data['Y'], jura_data['Co'])
he, ge = variogram.experimental(hc, gc, lag, nlag)
# Print one figure with 4 subplots, subplot syntax: (rows, columns, number)
# Each figure represents a different variogram model for the same data
plt.figure(1)
# Gaussian
plt.subplot(221)
x = np.linspace(0, nlag * lag, 1000)
y = model.gaussian(x, 10, 0.9) + 3.0
plt.scatter(he, ge, s=30)
variance = np.var(jura_data['Co'])
plt.axhline(variance, linestyle='--')
plt.xlim(xmin=0, xmax=lag * nlag)
plt.ylim(ymin=0)
plt.title('Gaussian')
plt.plot(x, y)
# Exponential
plt.subplot(222)
x = np.linspace(0, nlag * lag, 1000)
y = model.exponential(x, 12.5, 1.5)
plt.scatter(he, ge, s=30)
variance = np.var(jura_data['Co'])
plt.axhline(variance, linestyle='--')
plt.xlim(xmin=0, xmax=lag * nlag)
plt.ylim(ymin=0)
plt.title('Exponential')
plt.plot(x, y)
# Spherical
plt.subplot(223)
x = np.linspace(0, nlag * lag, 1000)
y = model.spherical(x, 13, 1.5)
plt.scatter(he, ge, s=30)
variance = np.var(jura_data['Co'])
plt.axhline(variance, linestyle='--')
plt.xlim(xmin=0, xmax=lag * nlag)
plt.ylim(ymin=0)
plt.xlabel('distance')
plt.ylabel('gamma')
plt.title('Spherical')
plt.plot(x, y)
# Pure nugget
plt.subplot(224)
x = np.linspace(0, nlag * lag, 1000)
y = model.nugget(x, 13)
plt.scatter(he, ge, s=30) # marker size 's' set to 30
variance = np.var(jura_data['Co'])
plt.axhline(variance, linestyle='--')
plt.xlim(xmin=0, xmax=lag * nlag)
plt.ylim(ymin=0)
plt.title('Nugget')
plt.plot(x, y)
plt.show()
def main():
"""
Performs cross validation for different model variograms.
"""
jura_data = np.genfromtxt('data.txt', names=True)
x, y, v = jura_data['X'], jura_data['Y'], jura_data['Co']
success, Q1, Q2, MSE, cR = cross_validation.orthonormal_residuals(
x, y, v, model_function1)
print('function type, success, Q1, Q2, MSE, cR')
print('1', success, Q1, Q2, MSE, cR)
success, Q1, Q2, MSE, cR = cross_validation.orthonormal_residuals(
x, y, v, model_function2)
print('2', success, Q1, Q2, MSE, cR)
success, Q1, Q2, MSE, cR = cross_validation.orthonormal_residuals(
x, y, v, model_function3)
print('3', success, Q1, Q2, MSE, cR)
success, Q1, Q2, MSE, cR = cross_validation.orthonormal_residuals(
x, y, v, model_function4)
print('4', success, Q1, Q2, MSE, cR)
success, Q1, Q2, MSE, cR, v_est, v_var, v, normalized_error = cross_validation.orthonormal_residuals(
x, y, v, model_function5, return_values=True)
print('5', success, Q1, Q2, MSE, cR)
plt.figure(1)
plt.subplot(221)
plt.scatter(v_est, v[1:], marker='o')
plt.plot(v_est, v_est)
plt.xlabel('Estimation')
plt.ylabel('True value')
plt.axis('scaled')
plt.xlim(xmin=0)
plt.ylim(ymin=0)
plt.subplot(222)
plt.hist(normalized_error, normed=1)
x_draw = np.linspace(-5, 5, 100)
plt.plot(x_draw, norm.pdf(x_draw, 0, 1))
plt.xlabel('Normalised error')
plt.ylabel('pdf')
plt.title('Histogram of normalised error')
plt.subplot(223)
plt.scatter(x[1:],
y[1:],
s=10 * np.abs(normalized_error),
c=np.abs(normalized_error))
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Normalised error')
hc, gc = variogram.cloud(x[1:], y[1:, ], normalized_error)
nlag = 8
lag = (np.max((np.max(x), np.max(y))) - np.min(
(np.min(x), np.min(y)))) * 2 / 3 / nlag
he, ge = variogram.experimental(hc, gc, lag, nlag)
plt.subplot(224)
plt.scatter(he, ge)
plt.axhline(1, linestyle='--')
plt.ylim([0.0, 1.1 * np.max(ge)])
plt.xlabel('Estimation')
plt.ylabel('True value')
plt.title('Variogram of normalised error')
plt.show()
def main():
"""
Application of conditional simulations to Pb data
"""
jura_data = np.genfromtxt('data.txt', names=True)
ns = nscore.transform(jura_data['Pb'])
y = ns.direct(jura_data['Pb'])
hc, gc = variogram.cloud(jura_data['X'], jura_data['Y'], y)
nlag = 50
hmax = 2 * np.max(hc) / 3
lag = hmax / nlag
he, ge = variogram.experimental(hc, gc, lag, nlag)
hm = np.linspace(0, hmax, 300)
vm = model_function(hm)
cm = covmodel(hm)
plt.figure(1)
plt.scatter(he, ge)
plt.plot(hm, vm)
plt.plot(hm, cm)
plt.xlabel('h')
plt.ylabel('gamma(h)')
nx = 60
ny = 60
xmin = 1.6
xmax = 4.2
ymin = 0.8
ymax = 3.4
xi, yi = np.meshgrid(np.linspace(xmin, xmax, nx),
np.linspace(ymin, ymax, ny))
v_est, v_var = kriging.ordinary_mesh(jura_data['X'], jura_data['Y'], y,
xi.flatten(), yi.flatten(),
model_function)
v_sim1 = sgs.conditional(jura_data['X'], jura_data['Y'], y, xi.flatten(),
yi.flatten(), covmodel, 15)
v_sim2 = sgs.conditional(jura_data['X'], jura_data['Y'], y, xi.flatten(),
yi.flatten(), covmodel, 15)
v_sim3 = sgs.conditional(jura_data['X'], jura_data['Y'], y, xi.flatten(),
yi.flatten(), covmodel, 15)
plt.figure(2)
plt.subplot(221)
grid = v_est.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Kriging')
plt.colorbar()
plt.subplot(222)
grid = v_sim1.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 1')
plt.colorbar()
plt.subplot(223)
grid = v_sim2.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 2')
plt.colorbar()
plt.subplot(224)
grid = v_sim3.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 3')
plt.colorbar()
real_est = ns.back(v_est)
real_sim1 = ns.back(v_sim1)
real_sim2 = ns.back(v_sim2)
real_sim3 = ns.back(v_sim3)
plt.figure(3)
plt.subplot(221)
grid = real_est.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Kriging')
plt.colorbar()
plt.subplot(222)
grid = real_sim1.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 1')
plt.colorbar()
plt.subplot(223)
grid = real_sim2.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 2')
plt.colorbar()
plt.subplot(224)
grid = real_sim3.reshape((nx, ny))
plt.imshow(grid,
extent=(xi.min(), xi.max(), yi.min(), yi.max()),
interpolation='nearest')
plt.title('Simulation 3')
plt.colorbar()
# histograms
plt.figure(4)
plt.subplot(221)
plt.hist(jura_data['Pb'])
plt.title('Pb measurements')
plt.subplot(222)
plt.hist(real_est)
plt.title('Kriged values')
plt.subplot(223)
plt.hist(real_sim1)
plt.title('Simulated 1 values')
plt.subplot(224)
plt.hist(real_sim2)
plt.title('Simulated 2 values')
plt.show()
def test_variogram_cloud():
x = np.array([3.0])
y = np.array([2.0])
v = np.array([1.0])
(hc, gc) = variogram.cloud(x, y, v)
assert (hc.size == 0 and gc.size == 0)
def test_variogram_cloud_2():
x = np.array([2.0, 3.0])
y = np.array([2.0, 3.0])
v = np.array([1.0, 2.0])
(hc, gc) = variogram.cloud(x, y, v)
assert (hc[0] == np.sqrt(2.0) and gc[0] == 0.5)