def _reg_sweep(M: np.ndarray, C: np.ndarray, varobs: np.ndarray, error_threshold=None):
r"""
Performs multiple sweeps of the augmented covariance matrix and extracts the
regression coefficients :math:`\beta_{0} \cdots \beta_(d)` and residial covariance
for the regression of missing variables against observed variables for a given
missing data pattern. Translated from matlab to python from Palarea-Albaladejo
and Martín-Fernández (2008) [#ref_1]_. Note that this algorithm requires at least
two columns free of missing values.
Parameters
-----------
M : :class:`numpy.ndarray`
Array of means of shape :code:`(D, )`.
C : :class:`numpy.ndarray`
Covariance of shape :code:`(D, D)`.
varobs : :class:`numpy.ndarray`
Boolean array indicating which variables are included in the regression model,
of shape :code:`(D, )`
error_threshold : :class:`float`
Low-pass threshold at which an error will result, of shape :code:`(D, )`.
Effectively limiting mean values to :math:`e^{threshold}`.
Returns
--------
β : :class:`numpy.ndarray`
Array of estimated regression coefficients.
σ2_res : :class:`numpy.ndarray`
Residuals.
References
----------
.. [#ref_1] Palarea-Albaladejo J. and Martín-Fernández J. A. (2008)
A modified EM ALR-algorithm for replacing rounded zeros in compositional data sets.
Computers & Geosciences 34, 902–917.
doi: `10.1016/j.cageo.2007.09.015 <https://dx.doi.org/10.1016/j.cageo.2007.09.015>`__
"""
assert np.isfinite(M).all()
assert np.isfinite(C).all()
if error_threshold is not None:
assert (np.abs(M) < error_threshold).all() # avoid runaway expansion
dimension = M.size # p > 0
nvarobs = varobs.size # q > 0 # number of observed variables
dep = np.array([i for i in np.arange(dimension) if not i in varobs])
# Shift the non-zero element to the end for pivoting
reor = np.concatenate(([0], varobs + 1, dep + 1), axis=0) #
A = augmented_covariance_matrix(M, C)
A = A[reor, :][:, reor]
# Astart = A.copy(deep=True)
assert (np.diag(A) != 0).all() # Not introducing extra zeroes
A = _multisweep(A, range(nvarobs + 1))
"""
A is of form:
-D | E
E.T | F
"""
# if not np.isfinite(A).all(): # Typically caused by infs
# A[~np.isfinite(A)] = 0
assert np.isfinite(A).all()
β = A[0 : nvarobs + 1, nvarobs + 1 : dimension + 1]
σ2_res = A[nvarobs + 1 :, nvarobs + 1 :]
return β, σ2_res
def setUp(self):
self.G = augmented_covariance_matrix(np.array([1.1, 0.9]),
random_cov_matrix(2))
self.G3 = augmented_covariance_matrix(np.array([1.1, 0.9, 1.05]),
random_cov_matrix(3))