def test_subspace(self):
for n in range(2, 7):
H_full = helmert(n, full=True)
H_partial = helmert(n)
for U in H_full[1:, :].T, H_partial.T:
C = np.eye(n) - np.ones((n, n)) / n
assert_allclose(U.dot(U.T), C)
assert_allclose(U.T.dot(U), np.eye(n-1), atol=1e-12)
def test_subspace(self):
for n in range(2, 7):
H_full = helmert(n, full=True)
H_partial = helmert(n)
for U in H_full[1:, :].T, H_partial.T:
C = np.eye(n) - np.full((n, n), 1 / n)
assert_allclose(U.dot(U.T), C)
assert_allclose(U.T.dot(U), np.eye(n - 1), atol=1e-12)
def inverse_ilr_transformation(data):
"""Inverse isometric logratio transformation (not vectorized).
Parameters
----------
data : 2d numpy array, shape [n_samples, n_coordinates]
Isometric log-ratio transformed coordinates in real space.
Returns
-------
out : 2d numpy array, shape [n_samples, n_coordinates+1]
Barycentric coordinates (closed) in simplex space.
Reference
---------
[1] Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R.
(2015). Modelling and Analysis of Compositional Data, pg. 37.
Chichester, UK: John Wiley & Sons, Ltd.
DOI: 10.1002/9781119003144
"""
dims = data.shape
out = np.zeros((dims[0], dims[1] + 1))
helmertian = helmert(dims[1] + 1)
for i in range(data.shape[0]):
out[i, :] = np.exp(np.dot(data[i, :], helmertian))
return closure(out)
def compositional_transform(self, add_pseudocount:bool=False):
"""calculated the three Aitchison geometry transforms for the Ab counts.
- alr uses the IgG1 counts as universal reference
- ilr contrasts are based on the SVD of clr
if add_pseudocount is set to true add 1 to prevent zero division, otherwise
cells with zero counts in the denominator create inf and have to be filtered
before downstream analysis, e.g.:
clr_filter = np.isfinite(clr).all(axis=1)
clr = clr[clr_filter,:]"""
if add_pseudocount:
self.clr_data = np.log((1+self.andat_raw.X)/gmean(self.andat_raw.X+1, axis=1).reshape(-1,1))
self.alr_data = np.log((1+self.andat_raw.X)/(self.andat_raw.X[:,-1]+1).reshape(-1,1))
U,s,Vt = np.linalg.svd(self.clr_data, full_matrices=False)
self.ilr_data = np.dot(U*s,helmert(len(s)).T)
else:
self.clr_data = np.log(self.andat_raw.X/gmean(self.andat_raw.X, axis=1).reshape(-1,1))
self.alr_data = np.log(self.andat_raw.X/(self.andat_raw.X[:,-1].reshape(-1,1)))
finite_clr = np.isfinite(self.clr_data).all(axis=1)
U,s,Vt = np.linalg.svd(self.clr_data[finite_clr,:], full_matrices=False)
self.ilr_data = np.dot(U*s,helmert(len(s)).T)
return
def inverse_ilr_transformation(data):
"""Inverse isometric logratio transformation (not vectorized).
Adapted from https://github.com/ofgulban/compoda.
Parameters
----------
data : 2d numpy array, shape [n_samples, n_coordinates]
Isometric log-ratio transformed coordinates in real space.
Returns
-------
out : 2d numpy array, shape [n_samples, n_coordinates+1]
Barycentric coordinates (closed) in simplex space.
Reference
---------
[1] Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R.
(2015). Modelling and Analysis of Compositional Data, pg. 37.
Chichester, UK: John Wiley & Sons, Ltd.
DOI: 10.1002/9781119003144
"""
return closure(
np.exp(np.einsum("ij,jk->ik", data, -helmert(data.shape[1] + 1))))
def time_helmert(self, size):
sl.helmert(size)
def test_orthogonality(self):
for n in range(1, 7):
H = helmert(n, full=True)
Id = np.eye(n)
assert_allclose(H.dot(H.T), Id, atol=1e-12)
assert_allclose(H.T.dot(H), Id, atol=1e-12)
def test_orthogonality(self):
for n in range(1, 7):
H = helmert(n, full=True)
Id = np.eye(n)
assert_allclose(H.dot(H.T), Id, atol=1e-12)
assert_allclose(H.T.dot(H), Id, atol=1e-12)
def time_helmert(self, size):
sl.helmert(size)
def __init__(self, n):
self.A = helmert(n, full=False)
self.tA = theano.shared(self.A)