def hscattergram(data, pwdist, lag, tol):
'''
Input: (data) NumPy array with three columns, the first two
columns should be the x and y coordinates, and
third should be the measurements of the variable
of interest
(lag) the lagged distance of interest
(tol) the allowable tolerance about (lag)
(pwdist) a square pairwise distance matrix
Output: h-scattergram figure showing the distribution of
measurements taken at a certain lag and tolerance
'''
# calculate the pairwise distances
indices = variograms.lagindices(pwdist, lag, tol)
# collect the head and tail measurements
head = data[indices[:, 0], 2]
tail = data[indices[:, 1], 2]
# create a scatterplot with equal axes
fig, ax = subplots()
ax.scatter(head, tail, marker="o", facecolor="none", edgecolor="k", alpha=0.5)
ax.set_aspect("equal")
# set the labels and the title
ax.set_ylabel("$z(u+h)$")
ax.set_xlabel("$z(u)$")
ax.set_title("Lags Between " + str(lag - tol) + " and " + str(lag + tol))
# grab the limits of the axes
xmin, xmax = ax.get_xlim()
ymin, ymax = ax.get_ylim()
# calculate the covariance and annotate
cv = variograms.covariance(data, indices)
ax.text(xmin * 1.25, ymin * 1.050, 'Covariance = {:3.2f}'.format(cv))
# calculate the semivariance and annotate
sv = variograms.semivariance(data, indices)
ax.text(xmin * 1.25, ymin * 1.025, 'Semivariance = {:3.2f}'.format(sv))
show()
def anisotropiclags(data, pwdist, lag, tol, angle, atol):
'''
SPatial ANIsotropy PLOT
'''
index = variograms.lagindices(pwdist, lag, tol)
anindex = variograms.anilagindices(data, pwdist, lag, tol, angle, atol)
fig, ax = subplots()
# plot the lagged distances
for pair in index:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'k-', lw=2, alpha=0.25)
# plot the lagged distances within
# the anisotropy angle and tolerance
for pair in anindex:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'r-', lw=1)
ax.set_xlabel('X')
ax.set_ylabel('Y')
def anisotropiclags(data, pwdist, lag, tol, angle, atol):
'''
SPatial ANIsotropy PLOT
'''
index = variograms.lagindices(pwdist, lag, tol)
anindex = variograms.anilagindices(data, pwdist, lag, tol, angle, atol)
fig, ax = subplots()
# plot the lagged distances
for pair in index:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'k-', lw=2, alpha=0.25)
# a sanity check
# mx, my = np.mean( x ), np.mean( y )
# br = utilities.bearing( ( hx, hy ), ( tx, ty ) )
# ax.text( mx, my, '{0:3.2f}'.format( br ) )
# plot the lagged distances within
# the anisotropy angle and tolerance
for pair in anindex:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'r-', lw=1)
ax.set_xlabel('X')
ax.set_ylabel('Y')
def anisotropiclags(data, pwdist, lag, tol, angle, atol):
'''
SPatial ANIsotropy PLOT
'''
index = variograms.lagindices(pwdist, lag, tol)
anindex = variograms.anilagindices(data, pwdist, lag, tol, angle, atol)
fig, ax = subplots()
# plot the lagged distances
for pair in index:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'k-', lw=2, alpha=0.25)
# plot the lagged distances within
# the anisotropy angle and tolerance
for pair in anindex:
head, tail = data[pair]
hx, hy, hz = head
tx, ty, tz = tail
x = [hx, tx]
y = [hy, ty]
ax.plot(x, y, 'r-', lw=1)
ax.set_xlabel('X')
ax.set_ylabel('Y')
def hscattergram(data, pwdist, lag, tol):
'''
Input: (data) NumPy array with three columns, the first two
columns should be the x and y coordinates, and
third should be the measurements of the variable
of interest
(lag) the lagged distance of interest
(tol) the allowable tolerance about (lag)
(pwdist) a square pairwise distance matrix
Output: h-scattergram figure showing the distribution of
measurements taken at a certain lag and tolerance
'''
# calculate the pairwise distances
indices = variograms.lagindices(pwdist, lag, tol)
# collect the head and tail measurements
head = data[indices[:, 0], 2]
tail = data[indices[:, 1], 2]
# create a scatterplot with equal axes
fig, ax = subplots()
ax.scatter(head,
tail,
marker="o",
facecolor="none",
edgecolor="k",
alpha=0.5)
ax.set_aspect("equal")
# set the labels and the title
ax.set_ylabel("$z(u+h)$")
ax.set_xlabel("$z(u)$")
ax.set_title("Lags Between " + str(lag - tol) + " and " + str(lag + tol))
# grab the limits of the axes
xmin, xmax = ax.get_xlim()
ymin, ymax = ax.get_ylim()
# calculate the covariance and annotate
cv = variograms.covariance(data, indices)
ax.text(xmin * 1.25, ymin * 1.050, 'Covariance = {:3.2f}'.format(cv))
# calculate the semivariance and annotate
sv = variograms.semivariance(data, indices)
ax.text(xmin * 1.25, ymin * 1.025, 'Semivariance = {:3.2f}'.format(sv))
show()
def laghistogram(data, pwdist, lags, tol):
'''
Input: (data) NumPy array with three columns, the first two
columns should be the x and y coordinates, and
third should be the measurements of the variable
of interest
(pwdist) the pairwise distances
(lags) the lagged distance of interest
(tol) the allowable tolerance about (lag)
Output: lag histogram figure showing the number of
distances at each lag
'''
# collect the distances at each lag
indices = [variograms.lagindices(pwdist, lag, tol) for lag in lags]
# record the number of indices at each lag
indices = [len(i) for i in indices]
# create a bar plot
fig, ax = subplots()
ax.bar(lags + tol, indices)
ax.set_ylabel('Number of Lags')
ax.set_xlabel('Lag Distance')
ax.set_title('Lag Histogram')
show()
def laghistogram(data, pwdist, lags, tol):
'''
Input: (data) NumPy array with three columns, the first two
columns should be the x and y coordinates, and
third should be the measurements of the variable
of interest
(pwdist) the pairwise distances
(lags) the lagged distance of interest
(tol) the allowable tolerance about (lag)
Output: lag histogram figure showing the number of
distances at each lag
'''
# collect the distances at each lag
indices = [variograms.lagindices(pwdist, lag, tol) for lag in lags]
# record the number of indices at each lag
indices = [len(i) for i in indices]
# create a bar plot
fig, ax = subplots()
ax.bar(lags + tol, indices)
ax.set_ylabel('Number of Lags')
ax.set_xlabel('Lag Distance')
ax.set_title('Lag Histogram')
show()
