def association(gene, context, return_snps=False):
#capture context
n_snps_in_model, i, cov, snps = context.provide_calculation(gene)
#some stats
snps_used = i[Constants.SNP]
n_snps_used = len(snps_used)
n_snps_in_cov = context.get_n_in_covariance(gene)
zscore, effect_size, sigma_g_2 = numpy.nan, numpy.nan, numpy.nan
if n_snps_used > 0:
i_weight = i[WDBQF.K_WEIGHT]
i_zscore = i[Constants.ZSCORE]
i_beta = i[Constants.BETA]
# sigma from reference
variances = numpy.diag(cov)
i_sigma_l = numpy.sqrt(variances)
#da calculeishon
sigma_g_2 = float(d(d(i_weight,cov),i_weight))
if sigma_g_2 >0:
try:
zscore = numpy.sum(i_weight * i_zscore * i_sigma_l) / numpy.sqrt(sigma_g_2)
effect_size = numpy.sum(i_weight * i_beta * (i_sigma_l**2))/ sigma_g_2
except Exception as e:
logging.log(9, "Unexpected exception when calculating zscore: %s, %s", gene, str(e))
r = (gene, zscore, effect_size, sigma_g_2, n_snps_in_model, n_snps_in_cov, n_snps_used)
if return_snps:
return r, set(snps_used)
else:
return r
def _get(variants, ids, cutoff, regularization, f=True):
geno = [variants[x] for x in ids]
cov = numpy.cov(geno)
sigma = cov[:len(ids) - 1, :len(ids) - 1]
rho = cov[-1:, :-1][0]
sigma_inv, n_indep, eigen = Math.crpinv(sigma, cutoff, regularization)
w = d(rho, sigma_inv)
s = math.sqrt(d(rho, w)) if f else math.sqrt(d(w, d(sigma, w)))
return w, s, n_indep, eigen
def _get_multi(geno, typed, cutoff, regularization):
cov = numpy.cov(geno)
sigma_tt = cov[:typed.shape[0], :typed.shape[0]]
sigma_it = cov[typed.shape[0]:, :typed.shape[0]]
sigma_inv, n_indep, eigen = Math.crpinv(sigma_tt, cutoff, regularization)
w = d(sigma_it, sigma_inv)
zscore = d(w, typed.zscore)
_w = d(sigma_it, sigma_inv)
variance = numpy.sum(numpy.multiply(sigma_it, _w), axis=1)
return zscore, variance, sigma_tt.shape[0], n_indep
def get_Boley_undirected(tp):
"""Boley et al define an undirected graph which "corresponds to" a
directed graph. Its adjacency matrix is G**s = (Pi * P + P' *
Pi)/2, where Pi is the steady-state set out along a diagonal and P
is the transition probability matrix. But we will get the
transition probability matrix:
P**s = (P + inv(Pi) * P.T * Pi) / 2
Note that this matrix is not necessarily symmetric.
"""
from numpy import dot as d
P = tp
Pi = np.diag(get_steady_state(tp))
return (P + d(d(np.linalg.inv(Pi), P.T), Pi)) / 2.0
def association(gene, context, return_snps=False):
#capture context
n_snps_in_model, i, cov, snps = context.provide_calculation(gene)
if logging.getLogger().getEffectiveLevel() < 10:
d_ = numpy.linalg.eig(cov)[0]
if numpy.sum(numpy.less(d_, 1e-6)):
logging.info("Gene %s has covariance close to singular", gene)
#some stats
snps_used = i[Constants.SNP]
n_snps_used = len(snps_used)
n_snps_in_cov = context.get_n_in_covariance(gene)
zscore, effect_size, sigma_g_2 = numpy.nan, numpy.nan, numpy.nan
if n_snps_used > 0:
i_weight = i[WDBQF.K_WEIGHT]
i_zscore = i[Constants.ZSCORE]
i_beta = i[Constants.BETA]
# sigma from reference
variances = numpy.diag(cov)
i_sigma_l = numpy.sqrt(variances)
#da calcooleishon
sigma_g_2 = float(d(d(i_weight, cov), i_weight))
if sigma_g_2 > 0:
try:
zscore = numpy.sum(
i_weight * i_zscore * i_sigma_l) / numpy.sqrt(sigma_g_2)
effect_size = numpy.sum(i_weight * i_beta *
(i_sigma_l**2)) / sigma_g_2
except Exception as e:
logging.log(
9, "Unexpected exception when calculating zscore: %s, %s",
gene, str(e))
r = (gene, zscore, effect_size, sigma_g_2, n_snps_in_model, n_snps_in_cov,
n_snps_used)
if return_snps:
return r, set(snps_used)
else:
return r
def _get_z(variants, ids, gwas_slice, cutoff, regularization, f=True):
w, s, n_indep, eigen = _get(variants, ids, cutoff, regularization, f=f)
z = d(w, gwas_slice.zscore) / s if s > 0 else None
return z, s, n_indep, eigen
def RSP_and_FE_distances(A, beta, C=None):
"""Calculate the randomised shortest path distance and free-energy
distance, as defined in "Developments in the theory of randomized
shortest paths with a comparison of graph node distances",
Kivim\"{a}ki, Shimbo, and Saerens, Physica A, 2013.
Arguments
- A: Adjacency matrix, whose elements represent affinities between
nodes, which define the reference transition
probabilities. A can be asymmetric (for directed graphs).
Distances between nodes that are not strongly connected
are Inf.
- beta beta should lie more or less between 10^-8 and 20, but this
depends on the size of the graph and the magnitude of the
costs. When beta --> 0, we obtain the commute cost distances.
When beta --> \infty, we obtain the shortest path (lowest
cost) distances.
- C Cost matrix, whose elements represent the cost of traversing
an edge of the graph. Infinite costs can be marked as zeros
(zero costs are anyway not allowed). If C is not provided,
then the costs will be set by default as c_ij = 1/a_ij.
Returns D_RSP: the RSP dissimilarity matrix
D_FE: the free energy distance matrix
Original Matlab code and comments (c) Ilkka Kivim\"{a}ki 2013
Transliterated to Python/Numpy by James McDermott
<*****@*****.**>. Helpful guides to this type of
transliteration:
http://mathesaurus.sourceforge.net/matlab-numpy.html,
http://wiki.scipy.org/NumPy_for_Matlab_Users,
http://wiki.scipy.org/Tentative_NumPy_Tutorial
"""
max = np.finfo('d').max
eps = 0.00000001
# If A is integer-valued, and beta is floating-point, can get an
# error in the matrix inversion, so convert A to float here. I
# can't explain why beta being floating-point is related to the
# problem. Anyway, this also converts in case it was a matrix, or
# was sparse.
A = np.array(A, dtype=np.float)
A[A < eps] = 0.0
n, m = A.shape
if n != m:
raise ValueError("The input matrix A must be square")
if C is None:
C = A.copy()
C[A >= eps] = 1.0/A[A >= eps]
C[A < eps] = max
# check beta value?
if beta < eps or beta > 20.0:
raise ValueError("The value for beta is outside the expected range, 0 to 20.0")
ones = np.ones(n)
onesT = np.ones((n, 1))
I = np.eye(n)
# Computation of Pref, the reference transition probability matrix
tmp = A.copy()
s = np.sum(tmp, 1)
s[s == 0] = 1 # avoid zero-division
Pref = tmp / (s * onesT).T
# Computation of the W and Z matrices
W = np.exp(-beta * C) * Pref
# compute Z
Z = linalg.inv(I - W)
# Computation of Z*(C.*W)*Z avoiding zero-division errors:
numerator = d(d(Z, (C * W)), Z)
D_nonabs = np.zeros((n, n))
indx = (numerator > 0) & (Z > 0)
D_nonabs[indx] = numerator[indx] / Z[indx]
D_nonabs[~indx] = np.infty
# D_nonabs above actually gives the expected costs of non-hitting paths
# from i to j.
# Expected costs of hitting paths -- avoid a possible inf-inf
# which can arise with isolated nodes and would give a NaN -- we
# prefer to have inf in that case.
C_RSP = np.zeros((n, n))
diag_D = d(onesT, np.diag(D_nonabs).reshape((1, n)))
indx = ~np.isinf(diag_D)
C_RSP[indx] = D_nonabs[indx] - diag_D[indx]
C_RSP[~indx] = np.infty
# symmetrization
D_RSP = 0.5 * (C_RSP + C_RSP.T)
# Free energies and symmetrization:
Dh_1 = np.diag(1.0/np.diag(Z))
Zh = d(Z, Dh_1)
# If there any 0 values in Zh (because of isolated nodes), taking
# log will raise a divide-by-zero error -- ignore it
np.seterr(divide='ignore')
FE = -np.log(Zh)/beta
np.seterr(divide='raise')
D_FE = 0.5 * (FE + FE.T)
# Just in case, set diagonals to zero:
np.fill_diagonal(D_RSP, 0.0)
np.fill_diagonal(D_FE, 0.0)
return D_RSP, D_FE
