def test_pcs(self):
"""PCs match the reference solution?"""
pcs = self.eofobj.pcs(npcs=self.neofs)
pcs *= sign_adjustments(pcs.T, self.pcs.T).T
err = error(pcs, self.pcs)
assert_almost_equal(err, 0., places=2)
# Check that cross correlations are zero.
cpcs = np.corrcoef(pcs[:, 0], pcs[:, 1])[0, 1]
assert_almost_equal(cpcs, 0.)
def test_eofs(self):
"""EOFs match the reference solution?"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofs(neofs=self.neofs)
# Coerce the sign of the EOFs so that they match the sign of the
# reference solution.
eofs *= sign_adjustments(eofs, self.eofs)
err = error(eofs, self.eofs)
assert_almost_equal(err, 0.)
def test_pcs(self):
"""PCs match the reference solution?"""
pcs = self.eofobj.pcs(npcs=self.neofs)
pcs *= sign_adjustments(pcs.T, self.pcs.T).T
err = error(pcs, self.pcs)
assert_almost_equal(err, 0., places=2)
# Check that cross correlations are zero.
cpcs = np.corrcoef(pcs[:, 0], pcs[:, 1])[0,1]
assert_almost_equal(cpcs, 0.)
def test_eofs(self):
"""EOFs match the reference solution?"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofs(neofs=self.neofs)
# Coerce the sign of the EOFs so that they match the sign of the
# reference solution.
eofs *= sign_adjustments(eofs, self.eofs)
err = error(eofs, self.eofs)
assert_almost_equal(err, 0.)
def test_eofsascovariance(self):
"""
EOFs as covariance between PCs and input field match the
reference solution?
"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofsAsCovariance(neofs=self.neofs)
# Adjust the EOFs so they are scaled as normal EOFs:
# c_m = e_m l_m^(0.5) / s
# where c_m is the correlation between the m'th PC and the input
# fields, e_m is the m'th EOF, l_m is the m'th eigenvalue and s is the
# vector of standard deviations of the input fields (see Wilks, 2006,
# Statistical Methods in the Atmospheric Sciences). Since these are
# covariance fields there is no need to multiply by the standard
# deviation.
l = np.var(self.pcs, axis=0, ddof=1)
e = eofs / np.sqrt(l[:, np.newaxis])
e *= sign_adjustments(e, self.eofs)
err = error(e, self.eofs)
assert_almost_equal(err, 0.)
def test_eofsascovariance(self):
"""
EOFs as covariance between PCs and input field match the
reference solution?
"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofsAsCovariance(neofs=self.neofs)
# Adjust the EOFs so they are scaled as normal EOFs:
# c_m = e_m l_m^(0.5) / s
# where c_m is the correlation between the m'th PC and the input
# fields, e_m is the m'th EOF, l_m is the m'th eigenvalue and s is the
# vector of standard deviations of the input fields (see Wilks, 2006,
# Statistical Methods in the Atmospheric Sciences). Since these are
# covariance fields there is no need to multiply by the standard
# deviation.
l = np.var(self.pcs, axis=0, ddof=1)
e = eofs / np.sqrt(l[:, np.newaxis])
e *= sign_adjustments(e, self.eofs)
err = error(e, self.eofs)
assert_almost_equal(err, 0.)
def test_eofsascorrelation(self):
"""
EOFs as correlation between PCs and input field match the
reference solution?
"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofsAsCorrelation(neofs=self.neofs)
# Adjust the EOFs so they are scaled as normal EOFs:
# c_m = e_m l_m^(0.5) / s
# where c_m is the correlation between the m'th PC and the input
# fields, e_m is the m'th EOF, l_m is the m'th eigenvalue and s is the
# vector of standard deviations of the input fields (see Wilks, 2006,
# Statistical Methods in the Atmospheric Sciences).
l = np.var(self.pcs, axis=0, ddof=1)
s = np.std(self.sf, axis=0, ddof=1)
e = s[np.newaxis] * eofs / np.sqrt(l[:, np.newaxis])
e *= sign_adjustments(e, self.eofs)
err = error(e, self.eofs)
assert_almost_equal(err, 0.)
maxval = np.abs(eofs).max()
assert_true(maxval <= 1.000000001)
def test_eofsascorrelation(self):
"""
EOFs as correlation between PCs and input field match the
reference solution?
"""
# Compute the EOFs using the solver.
eofs = self.eofobj.eofsAsCorrelation(neofs=self.neofs)
# Adjust the EOFs so they are scaled as normal EOFs:
# c_m = e_m l_m^(0.5) / s
# where c_m is the correlation between the m'th PC and the input
# fields, e_m is the m'th EOF, l_m is the m'th eigenvalue and s is the
# vector of standard deviations of the input fields (see Wilks, 2006,
# Statistical Methods in the Atmospheric Sciences).
l = np.var(self.pcs, axis=0, ddof=1)
s = np.std(self.sf, axis=0, ddof=1)
e = s[np.newaxis] * eofs / np.sqrt(l[:, np.newaxis])
e *= sign_adjustments(e, self.eofs)
err = error(e, self.eofs)
assert_almost_equal(err, 0.)
maxval = np.abs(eofs).max()
assert_true(maxval <= 1.000000001)
