def _svd(self, left, right):
"""
Singular Value Decomposition of left and right field.
**Arguments:**
*array*
left field `xarray.DataArray`;
right field `xarray.DataArray`;
**Return:**
*array*
U: collumns are sigular vectors of the left field;
V: collumns are sigular vectors of the right field;
s: sigular values of covariance matirx of left and right field.
"""
Cxy = xr.cov(left, right, dim='time')
U, s, V = np.linalg.svd(Cxy, full_matrices=False)
# U column is eigenvectors for left, V column is for right
V = V.T
self._U = U
self._V = V
self._s = s
def test_autocov(da_a, dim):
# Testing that the autocovariance*(N-1) is ~=~ to the variance matrix
# 1. Ignore the nans
valid_values = da_a.notnull()
da_a = da_a.where(valid_values)
expected = ((da_a - da_a.mean(dim=dim))**2).sum(dim=dim, skipna=False)
actual = xr.cov(da_a, da_a, dim=dim) * (valid_values.sum(dim) - 1)
assert_allclose(actual, expected)
def test_cov(da_a, da_b, dim, ddof):
if dim is not None:
def np_cov_ind(ts1, ts2, a, x):
# Ensure the ts are aligned and missing values ignored
ts1, ts2 = broadcast(ts1, ts2)
valid_values = ts1.notnull() & ts2.notnull()
# While dropping isn't ideal here, numpy will return nan
# if any segment contains a NaN.
ts1 = ts1.where(valid_values)
ts2 = ts2.where(valid_values)
return np.ma.cov(
np.ma.masked_invalid(ts1.sel(a=a, x=x).data.flatten()),
np.ma.masked_invalid(ts2.sel(a=a, x=x).data.flatten()),
ddof=ddof,
)[0, 1]
expected = np.zeros((3, 4))
for a in [0, 1, 2]:
for x in [0, 1, 2, 3]:
expected[a, x] = np_cov_ind(da_a, da_b, a=a, x=x)
actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof)
assert_allclose(actual, expected)
else:
def np_cov(ts1, ts2):
# Ensure the ts are aligned and missing values ignored
ts1, ts2 = broadcast(ts1, ts2)
valid_values = ts1.notnull() & ts2.notnull()
ts1 = ts1.where(valid_values)
ts2 = ts2.where(valid_values)
return np.ma.cov(
np.ma.masked_invalid(ts1.data.flatten()),
np.ma.masked_invalid(ts2.data.flatten()),
ddof=ddof,
)[0, 1]
expected = np_cov(da_a, da_b)
actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof)
assert_allclose(actual, expected)
def test_autocov(da_a, dim):
# Testing that the autocovariance*(N-1) is ~=~ to the variance matrix
# 1. Ignore the nans
valid_values = da_a.notnull()
# Because we're using ddof=1, this requires > 1 value in each sample
da_a = da_a.where(valid_values.sum(dim=dim) > 1)
expected = ((da_a - da_a.mean(dim=dim)) ** 2).sum(dim=dim, skipna=True, min_count=1)
actual = xr.cov(da_a, da_a, dim=dim) * (valid_values.sum(dim) - 1)
assert_allclose(actual, expected)
def test_cov(da_a, da_b, dim, ddof):
if dim is not None:
def np_cov_ind(ts1, ts2, a, x):
# Ensure the ts are aligned and missing values ignored
ts1, ts2 = broadcast(ts1, ts2)
valid_values = ts1.notnull() & ts2.notnull()
ts1 = ts1.where(valid_values)
ts2 = ts2.where(valid_values)
return np.cov(
ts1.sel(a=a, x=x).data.flatten(),
ts2.sel(a=a, x=x).data.flatten(),
ddof=ddof,
)[0, 1]
expected = np.zeros((3, 4))
for a in [0, 1, 2]:
for x in [0, 1, 2, 3]:
expected[a, x] = np_cov_ind(da_a, da_b, a=a, x=x)
actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof)
assert_allclose(actual, expected)
else:
def np_cov(ts1, ts2):
# Ensure the ts are aligned and missing values ignored
ts1, ts2 = broadcast(ts1, ts2)
valid_values = ts1.notnull() & ts2.notnull()
ts1 = ts1.where(valid_values)
ts2 = ts2.where(valid_values)
return np.cov(ts1.data.flatten(), ts2.data.flatten(), ddof=ddof)[0,
1]
expected = np_cov(da_a, da_b)
actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof)
assert_allclose(actual, expected)
def test_covcorr_consistency(da_a, da_b, dim):
# Testing that xr.corr and xr.cov are consistent with each other
# 1. Broadcast the two arrays
da_a, da_b = broadcast(da_a, da_b)
# 2. Ignore the nans
valid_values = da_a.notnull() & da_b.notnull()
da_a = da_a.where(valid_values)
da_b = da_b.where(valid_values)
expected = xr.cov(da_a, da_b, dim=dim,
ddof=0) / (da_a.std(dim=dim) * da_b.std(dim=dim))
actual = xr.corr(da_a, da_b, dim=dim)
assert_allclose(actual, expected)
plt.title('Correlation between dCO2 and windspeed',fontsize=16)
plt.tight_layout()
plt.show()
import sys
sys.exit()
# %%
#pCO22
covariance=xr.cov(co2,pco2_intrp,dim='time')
corr=xr.corr(co2,pco2_intrp,dim='time')
#corr=xr.corr(co2,newprod,dim='time')
fig=plt.figure(figsize=(20,12))
ax1=fig.add_subplot(3,2,1)
m=plot_basemap()
lo,la=np.meshgrid(newprod.lon.values,newprod.lat.values)
lo1,la1=m(lo,la)
span=max(abs(covariance.min()),covariance.max()).round(3)
m.contourf(lo1,la1,covariance,cmap='bwr',levels=np.arange(-span,span+(span/20),span/20))#,levels=np.arange(-0.001,0.0012,0.0002))
#m.contourf(lo1,la1,covariance,cmap='bwr',levels=np.arange(-0.0015,0.0016,0.0001),extend='max')#span+(span/20),span/20))#,levels=np.arange(-0.001,0.0012,0.0002))
plt.colorbar()
plt.title('Covariance between pCO2 and new production',fontsize=16)