def _inverse_cdf(self):
""" This module will calculate the inverse of CDF which wil be used to getting the ensembla
of X and Y from the ensemble of U and V
The statistics module is used to estimate teh CDF, which uses the kernel method of cdf estimation.
To estimate the inverse of the CDF, interpolation method is used, first cdf is estiamted at 100 points,
now interpolation function is generated to relate cdf at 100 points to the data.
"""
# if U and V are nore already generated
if self.U is None:
self.generate_uv(n)
#estimate teh inverse cdf of x and y
x2, x1 = st.cpdf(self.X, kernal="Epanechnikov", n=100)
self._inverse_cdf_x = interp1d(x2,x1)
y2, y1 = st.cpdf(self.Y, kernal="Epanechnikov", n=100)
self._inverse_cdf_y = interp1d(y2,y1)
X1 = self._inverse_cdf_x(self.U)
Y1 = self._inverse_cdf_y(self.V)
return X1, Y1
def _inverse_cdf(self):
"""
This module will calculate the inverse of CDF
which will be used in getting the ensemble of X and Y from
the ensemble of U and V
The statistics module is used to estimate the CDF, which uses
kernel methold of cdf estimation
To estimate the inverse of CDF, interpolation method is used, first cdf
is estimated at 100 points, now interpolation function is generated
to relate cdf at 100 points to data
"""
x2, x1 = st.cpdf(self.X, kernel='Epanechnikov', n=100)
self._inv_cdf_x = interp1d(x2, x1)
y2, y1 = st.cpdf(self.Y, kernel='Epanechnikov', n=100)
self._inv_cdf_y = interp1d(y2, y1)
def restrict(self,x,grid,domain):
edges = scipy.r_[domain[0],(grid[1:]+grid[:-1])/2.,domain[-1]] #concatenate
# estimating the cumulative density to make the estimation conservative
cum = statistics.cpdf(x,edges[1:-1],h=self.h)
rho = scipy.zeros_like(grid)
rho[0]=cum[0]/(edges[1]-edges[0])
rho[1:-1]=(cum[1:]-cum[:-1])/(edges[2:-1]-edges[1:-2])
rho[-1]=(1.-cum[-1])/(edges[-1]-edges[-2])
return rho
def _inverse_cdf(self):
"""
This module will calculate the inverse of CDF
which will be used in getting the ensemble of X and Y from
the ensemble of U and V
The statistics module is used to estimate the CDF, which uses
kernel methold of cdf estimation
To estimate the inverse of CDF, interpolation method is used, first cdf
is estimated at 100 points, now interpolation function is generated
to relate cdf at 100 points to data
"""
x2, x1 = st.cpdf(self.X, kernel = 'Epanechnikov', n = 100)
self._inv_cdf_x = interp1d(x2, x1)
y2, y1 = st.cpdf(self.Y, kernel = 'Epanechnikov', n = 100)
self._inv_cdf_y = interp1d(y2, y1)
def restrict(self, x, grid, domain):
edges = scipy.r_[domain[0], (grid[1:] + grid[:-1]) / 2.,
domain[-1]] #concatenate
# estimating the cumulative density to make the estimation conservative
cum = statistics.cpdf(x, edges[1:-1], h=self.h)
rho = scipy.zeros_like(grid)
rho[0] = cum[0] / (edges[1] - edges[0])
rho[1:-1] = (cum[1:] - cum[:-1]) / (edges[2:-1] - edges[1:-2])
rho[-1] = (1. - cum[-1]) / (edges[-1] - edges[-2])
return rho
def bias_correction(oc, mc, mp, nonzero = True):
"""
Input:
oc: observed current
mc: modeled current
mp: modeled prediction
Output:
mp_adjusted: adjusted modeled prediction
"""
# convert the input arrays into one dimension
oc = oc.flatten()
mc = mc.flatten()
mp = mp.flatten()
# Instead of directly inverting the CDF, linear interpolation using
# interp1d is used to invert the CDF.
F_oc, OC = st.cpdf(oc, n=1000)
if nonzero:
OC[OC<0] = 0
f = interp1d(F_oc, OC, bounds_error=False)
F1 = st.cpdf(mc, mp)
mp_adjusted = f(F1)
if nonzero:
mp_adjusted[mp_adjusted>0] = mp_adjusted[mp_adjusted>0] + np.sum(
mp_adjusted[mp_adjusted<0])/(np.sum(mp_adjusted>0))
mp_adjusted[mp_adjusted<0] = 0
return mp_adjusted
def th_dry_wet(rsm, fwet):
"""
Parameters:
rsm: 2d numpy array
relative soil moisture
fwet: float
fraction of the pixels undergoing wetting
Output:
th: float
threshold of the soil moisture for the pixels undergoing drying/wetting
"""
f_x, x = st.cpdf(rsm[~np.isnan(rsm)].flatten(), h=0.05)
foo = interp1d(f_x, x)
if fwet<min(f_x):
th = x.min()
elif fwet>max(f_x):
th = x.max()
else:
th = foo(fwet)
return th
def th_dry_wet(rsm, fwet):
"""
Parameters:
rsm: 2d numpy array
relative soil moisture
fwet: float
fraction of the pixels undergoing wetting
Output:
th: float
threshold of the soil moisture for the pixels undergoing drying/wetting
"""
f_x, x = st.cpdf(rsm[~np.isnan(rsm)].flatten(), h=0.05)
foo = interp1d(f_x, x)
if fwet < min(f_x):
th = x.min()
elif fwet > max(f_x):
th = x.max()
else:
th = foo(fwet)
return th
import scikits.statsmodels.api as sm
import matplotlib.pyplot as plt
import statistics
# generate some data
data = np.random.randn(100)
# estimate ecdf
ecdf = sm.tools.tools.ECDF(data)
# plot the ecdf using step function
plt.clf()
plt.step(ecdf.x, ecdf.y)
plt.xlabel('data', fontsize=20)
plt.ylabel('Empirical CDF', fontsize=15)
plt.savefig('/home/tomer/articles/python/tex/images/ecdf.png')
# evaluate value of ecdf at some data poing (say at 0)
print(ecdf(0))
# using kernels to estimate the pdf and cdf
y, x = statistics.cpdf(data, kernel='Epanechnikov')
# plot the ecdf using step function
plt.clf()
plt.plot(ecdf.x, ecdf.y, label='Ordinary')
plt.plot(x, y, label='Kernel')
plt.xlabel('data', fontsize=20)
plt.ylabel('Empirical CDF', fontsize=15)
plt.legend(loc='best')
plt.savefig('/home/tomer/articles/python/tex/images/kernel.png')
import scikits.statsmodels.api as sm
import matplotlib.pyplot as plt
import statistics
# generate some data
data = np.random.randn(100)
# estimate ecdf
ecdf = sm.tools.tools.ECDF(data)
# plot the ecdf using step function
plt.clf()
plt.step(ecdf.x, ecdf.y)
plt.xlabel('data', fontsize=20)
plt.ylabel('Empirical CDF', fontsize=15)
plt.savefig('/home/tomer/articles/python/tex/images/ecdf.png')
# evaluate value of ecdf at some data poing (say at 0)
print(ecdf(0))
# using kernels to estimate the pdf and cdf
y,x = statistics.cpdf(data, kernel = 'Epanechnikov')
# plot the ecdf using step function
plt.clf()
plt.plot(ecdf.x, ecdf.y, label='Ordinary')
plt.plot(x, y, label='Kernel')
plt.xlabel('data', fontsize=20)
plt.ylabel('Empirical CDF', fontsize=15)
plt.legend(loc='best')
plt.savefig('/home/tomer/articles/python/tex/images/kernel.png')
