def test__balance_basis_base_case(self):
tree = u"(a,b);"
t = TreeNode.read([tree])
exp_basis = np.array([[-np.sqrt(1. / 2), np.sqrt(1. / 2)]])
exp_keys = [t.name]
res_basis, res_keys = _balance_basis(t)
npt.assert_allclose(exp_basis, res_basis)
self.assertListEqual(exp_keys, res_keys)
def test__balance_basis_base_case(self):
tree = u"(a,b);"
t = TreeNode.read([tree])
exp_basis = np.array([[-np.sqrt(1. / 2), np.sqrt(1. / 2)]])
exp_keys = [t.name]
res_basis, res_keys = _balance_basis(t)
npt.assert_allclose(exp_basis, res_basis)
self.assertListEqual(exp_keys, res_keys)
def test__balance_basis_unbalanced(self):
tree = u"((a,b)c, d);"
t = TreeNode.read([tree])
exp_basis = np.array(
[[-np.sqrt(1. / 6), -np.sqrt(1. / 6),
np.sqrt(2. / 3)], [-np.sqrt(1. / 2),
np.sqrt(1. / 2), 0]])
exp_keys = [t.name, t[0].name]
res_basis, res_keys = _balance_basis(t)
npt.assert_allclose(exp_basis, res_basis)
self.assertListEqual(exp_keys, res_keys)
def test__balance_basis_unbalanced(self):
tree = u"((a,b)c, d);"
t = TreeNode.read([tree])
exp_basis = np.array(
[[-np.sqrt(1. / 6), -np.sqrt(1. / 6), np.sqrt(2. / 3)],
[-np.sqrt(1. / 2), np.sqrt(1. / 2), 0]]
)
exp_keys = [t.name, t[0].name]
res_basis, res_keys = _balance_basis(t)
npt.assert_allclose(exp_basis, res_basis)
self.assertListEqual(exp_keys, res_keys)
def ilr_phylogenetic_differential(
differential: pd.DataFrame,
tree: skbio.TreeNode) -> (pd.DataFrame, skbio.TreeNode):
t = tree.copy()
t.bifurcate()
diff, _tree = match_tips(differential.T, t)
_tree = rename_internal_nodes(_tree)
in_nodes = [n.name for n in _tree.levelorder() if not n.is_tip()]
basis = _balance_basis(_tree)[0]
basis = pd.DataFrame(basis.T, index=diff.columns, columns=in_nodes)
diff_balances = (diff @ basis).T
diff_balances.index.name = 'featureid'
return diff_balances, t
def multinomial_bioms(k, D, N, M, min_sv=0.11, max_sv=5.0, sigma_sq=0.1):
""" Simulates biom tables from multinomial.
Parameters
----------
k : int
Number of latent dimensions.
D : int
Number of microbes.
N : int
Number of samples.
M : int
Average sequencing depth.
Returns
-------
dict of np.array
Ground truth parameters.
"""
dims, hdims, total = D, k, N
eigs = min_sv + (max_sv - min_sv) * np.linspace(0, 1, hdims)
eigvectors = ortho_group.rvs(dims - 1)[:, :hdims]
W = np.matmul(eigvectors, np.diag(np.sqrt(eigs - sigma_sq)))
sigma_sq = sigma_sq
sigma = np.sqrt(sigma_sq)
z = np.random.normal(size=(total, hdims))
eta = np.random.normal(np.matmul(z, W.T), sigma).astype(np.float32)
tree = random_linkage(D)
Psi = _balance_basis(tree)[0]
prob = closure(np.exp(eta @ Psi))
depths = np.random.poisson(M, size=N)
Y = np.vstack([np.random.multinomial(depths[i], prob[i])
for i in range(N)])
return dict(
sigma=sigma,
W=W,
Psi=Psi,
tree=tree,
eta=eta,
z=z,
Y=Y,
depths=depths,
eigs=eigs,
eigvectors=eigvectors
)
def ilr_phylogenetic_ordination(
table: pd.DataFrame,
tree: skbio.TreeNode,
pseudocount: float = 0.5,
top_k_var: int = 10,
clades: list = None
) -> (OrdinationResults, skbio.TreeNode, pd.DataFrame):
t = tree.copy()
t.bifurcate()
_table, _tree = match_tips(table, t)
_tree = rename_internal_nodes(_tree)
if not clades:
in_nodes = [n.name for n in _tree.levelorder() if not n.is_tip()]
basis = _balance_basis(_tree)[0]
_table = add_pseudocount(_table, pseudocount)
basis = pd.DataFrame(basis.T, index=_table.columns, columns=in_nodes)
balances = np.log(_table) @ basis
var = balances.var(axis=0).sort_values(ascending=False)
clades = var.index[:top_k_var]
balances = balances[clades]
basis = basis[clades]
else:
clades = clades[0].split(',')
balances, basis = _fast_ilr(_tree, _table, clades, pseudocount=0.5)
var = balances.var(axis=0).sort_values(ascending=False)
balances.index.name = 'sampleid'
# feature metadata
eigvals = var
prop = var[clades] / var.sum()
balances = OrdinationResults(
short_method_name='ILR',
long_method_name='Phylogenetic Isometric Log Ratio Transform',
samples=balances,
features=pd.DataFrame(np.eye(len(clades)), index=clades),
eigvals=eigvals,
proportion_explained=prop)
basis.index.name = 'featureid'
return balances, _tree, basis
def multinomial_batch_bioms(k, D, N, M, C=2,
min_sv=0.11, max_sv=5.0, sigma_sq=0.1):
""" Simulates biom tables from multinomial with batch effects
Parameters
----------
k : int
Number of latent dimensions.
D : int
Number of microbes.
N : int
Number of samples.
M : int
Average sequencing depth.
C : int
Number of batches.
Returns
-------
dict of np.array
Ground truth parameters.
"""
dims, hdims, total = D, k, N
eigs = min_sv + (max_sv - min_sv) * np.linspace(0, 1, hdims)
eigvectors = ortho_group.rvs(dims - 1)[:, :hdims]
W = np.matmul(eigvectors, np.diag(np.sqrt(eigs - sigma_sq)))
sigma_sq = sigma_sq
sigma = np.sqrt(sigma_sq)
z = np.random.normal(size=(total, hdims))
eta = np.random.normal(np.matmul(z, W.T), sigma).astype(np.float32)
# Create ILR basis
tree = random_linkage(D)
Psi = _balance_basis(tree)[0]
# add batch effects
alpha = np.abs(np.random.normal(0, 0.5, size=(D)))
alphaILR = np.abs(Psi) @ alpha # variances must always be positive
m = np.zeros(D - 1)
B = np.random.multivariate_normal(m, np.diag(alphaILR), size=C)
batch_idx = np.random.randint(C, size=N)
eta = np.vstack([eta[i] + B[batch_idx[i]] for i in range(N)])
# Convert latent variables to observed counts
prob = closure(np.exp(eta @ Psi))
depths = np.random.poisson(M, size=N)
Y = np.vstack([np.random.multinomial(depths[i], prob[i])
for i in range(N)])
return dict(
sigma=sigma,
W=W,
Psi=Psi,
tree=tree,
eta=eta,
z=z,
Y=Y,
alpha=alpha,
alphaILR=alphaILR,
B=B,
batch_idx=batch_idx,
depths=depths,
eigs=eigs,
eigvectors=eigvectors
)