def _binom_logpmf(X, N, P):
val = binom.logpmf(
np.array([X], dtype=np.int64),
np.array([N], dtype=np.int64),
np.array([P], dtype=np.float64),
)
return val[0]
def _calc_llh(var_reads, ref_reads, omega, A, Z, psi):
K = len(psi)
assert Z.shape == (K, K)
assert var_reads.shape == ref_reads.shape == omega.shape
eta = util.softmax(psi)
phi = np.dot(Z, eta) # Kx1
var_phis = np.dot(A, phi)
logp = binom.logpmf(var_reads, ref_reads + var_reads, var_phis * omega)
return np.sum(logp)
def _integral_same_cluster(args):
phi1, V1_var_reads, V1_ref_reads, V1_omega, V2_var_reads, V2_ref_reads, V2_omega, logsub = args
V1_total_reads = V1_var_reads + V1_ref_reads
V2_total_reads = V2_var_reads + V2_ref_reads
X = np.array([V1_var_reads, V2_var_reads])
N = np.array([V1_total_reads, V2_total_reads])
P = np.array([V1_omega * phi1, V2_omega * phi1])
B = binom.logpmf(X, N, P)
logP = B[0] + B[1] - logsub
return np.exp(logP)
def integral_same_cluster(phi1, V1, V2, sidx, logsub):
binom_params = [(
V.var_reads[sidx],
V.total_reads[sidx],
V.omega_v[sidx] * phi1,
) for V in (V1, V2)]
X, N, P = [np.array(A) for A in zip(*binom_params)]
B = binom.logpmf(X, N, P)
# The `log(sqrt(2))` comes from computing the line integral. See theorem 6.3
# ("Evaluating a Scalar Line Integral") at
# https://openstax.org/books/calculus-volume-3/pages/6-2-line-integrals.
logP = np.log(np.sqrt(2)) + B[0] + B[1] - logsub
return np.exp(logP)
def calc_llh(var_reads, ref_reads, A, Z, psi):
total_reads = var_reads + ref_reads
mut_p = calc_mut_p(A, Z, psi)
mut_probs = binom.logpmf(var_reads, total_reads, mut_p)
return np.sum(mut_probs)
def binom_logpmf_scalar(X, N, P):
return binom.logpmf(
np.array([X]),
np.array([N]),
np.array([P]),
)[0]