def cov(self, relative=False) -> np.ndarray:
""" Return covariance matrix :math:`\\mathrm{Cov}(d^{(n)}_i, d^{(n)}_j)`
If no errors have been added, a zero matrix is returned.
Args:
relative: "Relative to data", i.e.
:math:`\\mathrm{Cov}(d^{(n)}_i, d^{(n)}_j) /
(d^{(n)}_i \\cdot d^{(n)}_j)`
Returns:
``self.n x self.nbins x self.nbins`` array
"""
data = self.data()
cov = np.tile(self.abs_cov, (self.n, 1, 1))
cov += np.einsum("ij,ki,kj->kij", self.rel_cov, data, data)
if self.poisson_errors:
cov += corr2cov(
np.tile(np.eye(self.nbins), (self.n, 1, 1)),
# Normal poisson errors are sqrt(data_i). What happens if
# data is normalized from N to N', i.e.
# Sum(data_normalized) = N'?
# Let N/N' = scale
# Then the errors should be
# sqrt(data) / scale = sqrt(data/scale) / sqrt(scale) =
# = sqrt(data_normalized) / sqrt(scale)
# Hence:
np.sqrt(data) / np.sqrt(self.poisson_errors_scale),
)
if not relative:
return cov
else:
return abs2rel_cov(cov, data)
def add_rel_err_corr(self, err, corr) -> None:
"""
Add error from relative errors and correlation matrix.
Args:
err: see argument of :py:meth:`.add_err_corr`
corr: see argument of :py:meth:`.add_err_corr`
"""
err = self._interpret_input(err, "err")
corr = self._interpret_input(corr, "corr")
self.add_rel_err_cov(corr2cov(corr, err))
def add_err_corr(self, err, corr) -> None:
""" Add error from errors vector and correlation matrix.
Args:
err: ``self.n x self.nbins`` vector of errors for each data point
and bin or self.nbins vector of uniform errors per data point or
float (uniform error per bin and datapoint)
corr: ``self.n x self.nbins x self.nbins`` correlation matrices
or ``self.nbins x self.nbins`` correlation matrix
"""
err = self._interpret_input(err, "err")
corr = self._interpret_input(corr, "corr")
self.add_err_cov(corr2cov(corr, err))
def test_corr2cov(self):
for dataset, data in self.data.items():
with self.subTest(dataset=dataset):
self.assertAllClose(
corr2cov(data["corr"], data["err"]), data["cov"]
)