def p_y(n,y,M):
t_1 = m.exp(-0.5*n*y**2)
t_2 = m.erf((0.5*n)**(0.5)*(y-0.5*M))
t_3 = m.erf((0.5*n)**(0.5)*(y+0.5*M))
m_f1 = (n/(8*m.pi))**2
m_f2 = (n/(2*m.pi))**2/M
return m_f1*(t_1 - m_f2*(t_2 - t_3))
def output_branches(self):
outfile = open(self.fout + ".line.txt", "w")
for node in self.tree.traverse(strategy="postorder"):
if not node.is_leaf():
cn = self.name_coords[node.name]
childs = node.get_children()
cl = self.name_coords[childs[0].name]
cr = self.name_coords[childs[1].name]
l_mds_dis = self.innernode_dis_mds_matrix[node.name + ":" + childs[0].name]
l_tree_dis = self.innernode_dis_tree_matrix[node.name + ":" + childs[0].name]
r_mds_dis = self.innernode_dis_mds_matrix[node.name + ":" + childs[1].name]
r_tree_dis = self.innernode_dis_tree_matrix[node.name + ":" + childs[1].name]
l_ratio = (l_tree_dis - l_mds_dis)/l_mds_dis
r_ratio = (r_tree_dis - r_mds_dis)/r_mds_dis
lstroke = math.erf(l_ratio)
rstroke = math.erf(r_ratio)
if lstroke < 0:
lstroke = 2.0
else:
lstroke = 4.0*lstroke + 2.0
if rstroke < 0:
rstroke = 2.0
else:
rstroke = 4.0*rstroke + 2.0
outfile.write(repr(cn[0])+","+repr(cn[1])+","+repr(cl[0])+","+repr(cl[1])+","+repr(lstroke)+"\n")
outfile.write(repr(cn[0])+","+repr(cn[1])+","+repr(cr[0])+","+repr(cr[1])+","+repr(rstroke)+"\n")
outfile.close()
def dynamical_friction_sis(x, y, z, vx, vy, vz, M_sat):
x = x * units.kpc
y = y * units.kpc
z = z * units.kpc
r = np.sqrt(x**2 + y**2 + z**2)
vx = vx * units.km / units.s
vy = vy * units.km / units.s
vz = vz * units.km / units.s
v = np.sqrt(vx**2 + vy**2 + vz**2)
a = 10 # concentration parameter
# Density at distance r and a velocity v
rho = dens_sis(10, r.value, v.value) # a, r, v
v = v.to(units.kpc / units.s)
M_sat = M_sat * units.Msun
factor = - 4 * np.pi * G**2
Coulomb = coulomb_log(r)
sigma = v / np.sqrt(2)
X = v / ( np.sqrt(2) * sigma ) #Check this
F_dfx = factor * M_sat * rho * Coulomb / v**3 * ( erf(X) - 2*X/(np.sqrt(np.pi) * np.exp(-X**2)) ) * vx
F_dfy = factor * M_sat * rho * Coulomb / v**3 * ( erf(X) - 2*X/(np.sqrt(np.pi) * np.exp(-X**2)) ) * vy
F_dfz = factor * M_sat * rho * Coulomb / v**3 * ( erf(X) - 2*X/(np.sqrt(np.pi) * np.exp(-X**2)) ) * vz
F_dfx = F_dfx.to(units.kpc / units.Gyr**2)
F_dfy = F_dfy.to(units.kpc / units.Gyr**2)
F_dfz = F_dfz.to(units.kpc / units.Gyr**2)
return F_dfx.value, F_dfy.value, F_dfz.value
def response( t, sig, maxamp, maxt, fastconst, slowconst ):
"""
t=0 is assumed to be max of distribution
"""
# simplistic
#farg = t/sig
#f = 0.5*maxamp*np.exp( -0.5*farg*farg )#/sig/np.sqrt(2*3.14159)
#if t<0:
# s = 0.0
#else:
# s = 0.5*maxamp*np.exp( -t/config.slowconst )
# slow component shape: expo convolved with gaus
t_smax = 95.0 # peak of only slow component. numerically solved for det. smearing=3.5*15.625 ns, decay time const= 1500 ns
t_fmax = 105.0 # numerically solved for det. smearing=3.5*15.625 ns, decay time const= 6 ns
#dt_smax = -10.0 # expect slow comp peak to be 10 ns earlier than fast component peak
smax = np.exp( sig*sig/(2*slowconst*slowconst) - t_fmax/slowconst )*(1 - math.erf( (sig*sig - slowconst*t_fmax )/(np.sqrt(2)*sig*slowconst ) ) )
# normalize max at fast component peak
As = 0.3*maxamp/smax
s = As*np.exp( sig*sig/(2*slowconst*slowconst) - t/slowconst )*(1 - math.erf( (sig*sig - slowconst*t )/(np.sqrt(2)*sig*slowconst ) ) )
#s = np.exp( sig*sig/(2*slowconst*slowconst))*(1-math.erf( (sig*sig)/(np.sqrt(2)*sig*slowconst ) ) )
#s = maxamp*np.exp( sig*sig/(2*slowconst*slowconst) - t/slowconst )*(1 - math.erf( (sig*sig - slowconst*t )/(np.sqrt(2)*sig*slowconst ) ) )
# fast component: since time const is smaller than spe response, we model as simple gaussian
#
farg = t/sig
fmax = np.exp( -0.5*farg*farg )
Af = 0.8*maxamp
f = Af*np.exp( -0.5*farg*farg )
#return fastfraction*f + slowfraction*s
#print t, f, s
return f+s
def __call__(self, val):
import numpy
from math import sqrt, log, pi, erf
sigma_m = val
#sigma_m = abs(val[0])
dphi2 = self.dphi / 2
den = sqrt(2) * sigma_m / abs(self.zeta)# / 0.670
a = (self.tau + dphi2) / den
b = (self.tau - dphi2) / den
a = numpy.array([erf(a[i]) for i in range(len(a))])
b = numpy.array([erf(b[i]) for i in range(len(b))])
r = (a - b) / 2.0#(2 * self.dphi)
# ind = numpy.where(r > 0)[0]
# ret = r
# ret[ind] = numpy.log(r[ind])
ind = numpy.where(r <= 0)
if len(ind[0]) > 0:
r[ind] = 1e-7
#ret[ind] = 0
#print ind, r[ind], self.zeta[ind], self.tau[ind]
return numpy.log(r)
def black_calc():
stage4 = fmv * math.exp(-div * exp_term)
stage5 = (1.0 + math.erf(d1 / math.sqrt(2.0))) / 2.0
stage6 = exp_price * math.exp(-rate * exp_term)
stage7 = (1.0 + math.erf(d2 / math.sqrt(2.0))) / 2.0
c = (stage4*stage5)-(stage6*stage7)
return c
def calc_charge_loss_fraction_in_line(accelerator, **kwargs):
"""Calculate charge loss in a line
Keyword arguments:
twiss_at_entrance -- Twiss parameters at the start of first element
global_coupling -- Global coupling
energy_spread -- Relative energy spread
emittance -- [m·rad]
delta_rx -- [m]
delta_angle -- [rad]
hmax -- [m]
hmin -- [m]
vmax -- [m]
vmin -- [m]
"""
init_twiss, energy_spread, emittance, hmax, hmin, vmax, vmin = _process_loss_fraction_args(accelerator, **kwargs)
coupling = kwargs['global_coupling']
try:
twiss, m66 = pyaccel.optics.calc_twiss(accelerator, init_twiss = init_twiss, indices ='open')
betax, etax, betay, etay = twiss.betax, twiss.etax, twiss.betay, twiss.etay
if math.isnan(betax[-1]):
loss_fraction = 1.0
return (loss_fraction, None, None)
except (numpy.linalg.linalg.LinAlgError, pyaccel.optics.OpticsException, pyaccel.tracking.TrackingException):
loss_fraction = 1.0
return (loss_fraction, None, None)
emitx = emittance * 1 / (1 + coupling)
emity = emittance * coupling / (1 + coupling)
sigmax = numpy.sqrt(betax * emitx + (etax * energy_spread)**2)
sigmay = numpy.sqrt(betay * emity + (etax * energy_spread)**2)
h_vc = hmax - hmin
v_vc = vmax - vmin
co = twiss.co
rx, ry = co[0,:], co[2,:]
xlim_inf, xlim_sup = rx - hmin, hmax - rx
ylim_inf, ylim_sup = ry - vmin, vmax - ry
xlim_inf[xlim_inf < 0] = 0
xlim_sup[xlim_sup < 0] = 0
ylim_inf[ylim_inf < 0] = 0
ylim_sup[ylim_sup < 0] = 0
xlim_inf[xlim_inf > h_vc] = 0
xlim_sup[xlim_sup > h_vc] = 0
ylim_inf[ylim_inf > v_vc] = 0
ylim_sup[ylim_sup > v_vc] = 0
min_xfrac_inf = numpy.amin(xlim_inf/sigmax)
min_xfrac_sup = numpy.amin(xlim_sup/sigmax)
min_yfrac_inf = numpy.amin(ylim_inf/sigmay)
min_yfrac_sup = numpy.amin(ylim_sup/sigmay)
sqrt2 = math.sqrt(2)
x_surviving_fraction = 0.5*math.erf(min_xfrac_inf/sqrt2) + \
0.5*math.erf(min_xfrac_sup/sqrt2)
y_surviving_fraction = 0.5*math.erf(min_yfrac_inf/sqrt2) + \
0.5*math.erf(min_yfrac_sup/sqrt2)
surviving_fraction = x_surviving_fraction * y_surviving_fraction
loss_fraction = 1.0 - surviving_fraction
return loss_fraction, twiss, m66
def alpha2(a, N, Nmax, Nmin=1):
y = sqrt(pi*Nmin*Nmax)/(2.0*a) * exp((a * log2(sqrt(Nmax/Nmin)))**2.0)
y = y * exp((log(2.0)/(2.0*a))**2.0)
y = y * erf(a * log2(sqrt(Nmax/Nmin)) - log(2.0)/(2.0*a))
y += erf(a * log2(sqrt(Nmax/Nmin)) + log(2.0)/(2.0*a))
y -= N
return y # find alpha
def marg_rating(self):
if self._marg_rating is None:
s = self.sigmac2
sp4 = s+4
self._marg_rating = 0.5*log(2*pi*s/sp4)*exp(-9/(8*sp4))
self._marg_rating += log(erf(0.75*sqrt(0.5*s/sp4))
- erf(-0.25*(17*s+80)/sqrt(2*s*sp4)))
return self._marg_rating
def test_genz_gaussian_exact():
u = np.array([1, 21, 2], dtype=float)
a = np.array([1/10, 1/100, 1/500], dtype=float)
val = ti.genz_gaussian_exact(u, a)
exact = 62500*pow(np.pi, 3/2)*math.erf(1/10)*(math.erf(1/250) -
math.erf(1/500))*(math.erf(21/100) - math.erf(1/5))
assert np.allclose([val], [exact])
def transitionProbability(self, T_total, rho0, rhoBar,sigmaRhoSquared,tauEff):
# argument for the Error Function
x1 = -(self.rhoStar - rhoBar + (rhoBar - rho0)*np.exp(-T_total/tauEff))/(np.sqrt(sigmaRhoSquared*(1.-np.exp(-2.*T_total/tauEff))))
# transition probability
if rho0 == 0.:
return (1. + math.erf(x1))/2.
else:
return (1. - math.erf(x1))/2.
def alpha(self, a, Nmax, Nmin=1):
"""Numerically solve for Preston's a. Needed to estimate S using the lognormal"""
y = sqrt(pi*Nmin*Nmax)/(2.0*a) * exp((a * log2(sqrt(Nmax/Nmin)))**2.0)
y = y * exp((log(2.0)/(2.0*a))**2.0)
y = y * erf(a * log2(sqrt(Nmax/Nmin)) - log(2.0)/(2.0*a))
y += erf(a * log2(sqrt(Nmax/Nmin)) + log(2.0)/(2.0*a))
y -= self.N
return y # find alpha
def _cdf(self, x):
"""
Calculate cumulative distribution function in a certain point
"""
if isinstance(x, float):
return 1.0 / 2.0 * (1 + math.erf(x / np.sqrt(2)))
else:
return (
1.0 / 2.0 *
(1 + np.array([math.erf(n / np.sqrt(2)) for n in x]))
)
def test_erf():
table = [
(0.0, 0.0000000),
(0.05, 0.0563720),
(0.1, 0.1124629),
(0.15, 0.1679960),
(0.2, 0.2227026),
(0.25, 0.2763264),
(0.3, 0.3286268),
(0.35, 0.3793821),
(0.4, 0.4283924),
(0.45, 0.4754817),
(0.5, 0.5204999),
(0.55, 0.5633234),
(0.6, 0.6038561),
(0.65, 0.6420293),
(0.7, 0.6778012),
(0.75, 0.7111556),
(0.8, 0.7421010),
(0.85, 0.7706681),
(0.9, 0.7969082),
(0.95, 0.8208908),
(1.0, 0.8427008),
(1.1, 0.8802051),
(1.2, 0.9103140),
(1.3, 0.9340079),
(1.4, 0.9522851),
(1.5, 0.9661051),
(1.6, 0.9763484),
(1.7, 0.9837905),
(1.8, 0.9890905),
(1.9, 0.9927904),
(2.0, 0.9953223),
(2.1, 0.9970205),
(2.2, 0.9981372),
(2.3, 0.9988568),
(2.4, 0.9993115),
(2.5, 0.9995930),
(2.6, 0.9997640),
(2.7, 0.9998657),
(2.8, 0.9999250),
(2.9, 0.9999589),
(3.0, 0.9999779),
(3.1, 0.9999884),
(3.2, 0.9999940),
(3.3, 0.9999969),
(3.4, 0.9999985),
(3.5, 0.9999993),
(4.0, 1.0000000),
]
for x, y in table:
AlmostEqual(y, math.erf(x), tolerance=7)
AlmostEqual(-y, math.erf(-x), tolerance=7)
def erfContribution(dx, sigma, N):
"""
Solves for the distance to the closest periodic replica of x1 to x2. Integrates a gaussian of stdev sigma.
x1 and x2 are in reduced units, and N is the number of reduced units in the cubic system.
Quantities in dx must be in [-N, N].
Uses the same distance computation as GaussianContribution.
"""
half = float(N)/2.0
dist_vec = [ abs(abs(abs(x)-half)-half) for x in dx]
half_box = .5/sigma
my_erf = lambda x : - math.erf(-half_box - 2*half_box*x) + math.erf(half_box - 2*half_box*x)
contribution = reduce( mul, [ my_erf(x) for x in dist_vec] ) / 8
return contribution
def _phit(self, z, zstar):
"""
Model component of hitting target
:param z: Reading, in cm
:param zstar: Expected reading, from ray casting
:return p: Probability of 'hit'
"""
if z < self._max_z:
N = 1.0/math.sqrt(2*math.pi*self._sigmahit**2)*math.e**(-0.5*(z-zstar)**2/self._sigmahit**2)
eta = 0.5*(math.erf((self._max_z-zstar)/(self._sigmahit*math.sqrt(2))) + math.erf(zstar/(math.sqrt(2)*self._sigmahit)))
return N*eta
else:
return 0
def potentialNucEnergy(potential_onNuc_basis, basis_aParam2, intNucDist, nucCharge, swap): #Equation found for formula in Modern Quantum Chemistry by Szabo eqn A.33 pg 415 #Always assume potential_onNuc_basis is zeroed on the nucleus which charge is specified #TODO:Check answers with John a = potential_onNuc_basis b = a.T coeff = ((-2 * math.pi)/(a + b)) * nucCharge exponent = 0 f0_Function_input = 0 f0_Function = 1 potential_onNuc_basis_matrix = coeff a = basis_aParam2 b = a.T coeff = ((-2 * math.pi)/(a + b)) * nucCharge exponent = 0 f0_function_input = (a + b) * (intNucDist ** 2) f0_erf = np.power(f0_function_input, .5) for x in np.nditer(f0_erf, op_flags=['readwrite']): x[...] = math.erf(x) f0_Function = 0.5 * np.multiply(np.power((math.pi/f0_function_input), .5), f0_erf) basis_aParam2_matrix = np.multiply(coeff, f0_Function) a = potential_onNuc_basis b = basis_aParam2.T coeff = ((-2 * math.pi)/(a + b)) * nucCharge exponent = (-1 * (np.multiply(a,b)/(a + b)) * (intNucDist ** 2)) f0_function_input = ((a * 0) + np.power((b * intNucDist), 2.))/(a + b) f0_erf = np.power(f0_function_input, .5) for x in np.nditer(f0_erf, op_flags=['readwrite']): x[...] = math.erf(x) f0_Function = 0.5 * np.multiply(np.power((math.pi/f0_function_input), .5), f0_erf) basis_set1toset2_matrix = np.multiply(np.multiply(coeff, f0_Function), np.exp(exponent)) basis_set2toset1_matrix = basis_set1toset2_matrix.T if (swap): matrix1 = np.concatenate((basis_aParam2_matrix, basis_set1toset2_matrix)) matrix2 = np.concatenate((basis_set2toset1_matrix, potential_onNuc_basis_matrix)) matrix = np.concatenate((matrix1, matrix2), axis=1) else: matrix1 = np.concatenate((potential_onNuc_basis_matrix, basis_set2toset1_matrix)) matrix2 = np.concatenate((basis_set1toset2_matrix, basis_aParam2_matrix)) matrix = np.concatenate((matrix1, matrix2), axis=1) return matrix
def pvalue(x):
'''Cumulative distribution function for the standard normal distribution
python
import math
x=2.33
x=1.96
1-(1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
x=-2.33
(1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
'''
if x < 0:
return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
else:
return 1-(1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
def run(self):
from dials.algorithms.profile_model.gaussian_rs import \
PartialityCalculator3D
from dials.array_family import flex
calculator = PartialityCalculator3D(
self.experiment.beam,
self.experiment.goniometer,
self.experiment.scan,
self.sigma_m)
predicted = flex.reflection_table.from_predictions_multi(self.experiments)
predicted['bbox'] = predicted.compute_bbox(self.experiments)
# Remove any touching edges of scan to get only fully recorded
x0, x1, y0, y1, z0, z1 = predicted['bbox'].parts()
predicted = predicted.select((z0 > 0) & (z1 < 100))
assert(len(predicted) > 0)
# Compute partiality
partiality = calculator(
predicted['s1'],
predicted['xyzcal.px'].parts()[2],
predicted['bbox'])
# Should have all fully recorded
assert(len(partiality) == len(predicted))
from math import sqrt, erf
three_sigma = 0.5 * (erf(3.0 / sqrt(2.0)) - erf(-3.0 / sqrt(2.0)))
assert(partiality.all_gt(three_sigma))
# Trim bounding boxes
x0, x1, y0, y1, z0, z1 = predicted['bbox'].parts()
z0 = z0 + 1
z1 = z1 - 1
predicted['bbox'] = flex.int6(x0, x1, y0, y1, z0, z1)
predicted = predicted.select(z1 > z0)
assert(len(predicted) > 0)
# Compute partiality
partiality = calculator(
predicted['s1'],
predicted['xyzcal.px'].parts()[2],
predicted['bbox'])
# Should have all partials
assert(len(partiality) == len(predicted))
assert(partiality.all_le(1.0) and partiality.all_gt(0))
print 'OK'
def genDocument(cur):
mu = random.randrange(0, g_wordsNum)
sigma = random.randrange(1, 10*precision)/precision
docSize = random.randrange(10, 100)
cur.execute("INSERT INTO Documents (docName, docSize, mu, sigma)\
VALUES(\"\",\"" + str(docSize)+ "\",\"" + str(mu)+ "\", \"" + str(sigma) + "\" )")
docID = cur.lastrowid
yFrom = (1 + math.erf((0 - mu)/ (sigma * math.sqrt(2)))) / 2
yTo = (1 + math.erf((g_wordsNum - mu)/ (sigma * math.sqrt(2)))) / 2
for i in range(1, docSize):
addInvertedID(docID, randomWord(mu, sigma, yFrom, yTo), cur)
return docID
def prob_mean_larger(self, other):
"""
Probability that actual mean of this dist is larger than of another.
"""
if self.n == 0 or other.n == 0:
return 0.5
diff_mean = self.mean() - other.mean()
sigma1 = self.sigma()
sigma2 = other.sigma()
# If we have no data about variance of one of the distributions,
# we take it from another distribution.
if other.n == 1:
sigma2 = sigma1
if self.n == 1:
sigma1 = sigma2
diff_sigma = sqrt(sigma1**2 + sigma2**2)
if diff_sigma == 0:
if diff_mean > 0:
return 1
elif diff_mean < 0:
return 0
else:
return 0.5
p = 0.5 * (1 + erf(diff_mean / (sqrt(2) * diff_sigma)))
return p
def calc_stats(self, count, target, total):
num = max(len(target), 1)
r = {}
for t in ('pgs', 'objects', 'bytes'):
if total[t] == 0:
r[t] = {
'avg': 0,
'stddev': 0,
'sum_weight': 0,
'score': 0,
}
continue
avg = float(total[t]) / float(num)
dev = 0.0
# score is a measure of how uneven the data distribution is.
# score lies between [0, 1), 0 means perfect distribution.
score = 0.0
sum_weight = 0.0
for k, v in six.iteritems(count[t]):
# adjust/normalize by weight
if target[k]:
adjusted = float(v) / target[k] / float(num)
else:
adjusted = 0.0
# Overweighted devices and their weights are factors to calculate reweight_urgency.
# One 10% underfilled device with 5 2% overfilled devices, is arguably a better
# situation than one 10% overfilled with 5 2% underfilled devices
if adjusted > avg:
'''
F(x) = 2*phi(x) - 1, where phi(x) = cdf of standard normal distribution
x = (adjusted - avg)/avg.
Since, we're considering only over-weighted devices, x >= 0, and so phi(x) lies in [0.5, 1).
To bring range of F(x) in range [0, 1), we need to make the above modification.
In general, we need to use a function F(x), where x = (adjusted - avg)/avg
1. which is bounded between 0 and 1, so that ultimately reweight_urgency will also be bounded.
2. A larger value of x, should imply more urgency to reweight.
3. Also, the difference between F(x) when x is large, should be minimal.
4. The value of F(x) should get close to 1 (highest urgency to reweight) with steeply.
Could have used F(x) = (1 - e^(-x)). But that had slower convergence to 1, compared to the one currently in use.
cdf of standard normal distribution: https://stackoverflow.com/a/29273201
'''
score += target[k] * (math.erf(((adjusted - avg)/avg) / math.sqrt(2.0)))
sum_weight += target[k]
dev += (avg - adjusted) * (avg - adjusted)
stddev = math.sqrt(dev / float(max(num - 1, 1)))
score = score / max(sum_weight, 1)
r[t] = {
'avg': avg,
'stddev': stddev,
'sum_weight': sum_weight,
'score': score,
}
return r
def CDF(self, x):
if (self.sigma == 0.0) and (x < self.mu):
return 0.0
elif (self.sigma == 0.0) and (x >= self.mu):
return 1.0
else:
return 0.5 * (1.0 + math.erf((x - self.mu)/(self.sigma * math.sqrt(2.0))))
def gammainc_halfint(s, x):
""" Lower incomplete gamma function =
integral from 0 to x of t ** (s-1) exp(-t) dt divided by gamma(s),
i.e., the fraction of gamma that you get if you integrate only until
x instead of all the way to infinity.
Implemented here only if s is a positive multiple of 0.5.
"""
# scipy equivalent: scipy.special.gammainc(s,x)
if s <= 0:
raise ValueError('%s is not positive' % s)
if x < 0:
raise ValueError('%s < 0' % x)
if s * 2 != int(s * 2):
raise NotImplementedError('%s is not a multiple of 0.5' % s)
# Handle integers analytically
if s == int(s):
term = 1
total = 1
for k in range(1, int(s)):
term *= x / k
total += term
return 1 - exp(-x) * total
# Otherwise s is integer + 0.5. Decrease to 0.5 using recursion formula:
result = 0.0
while s > 1:
result -= x ** (s - 1) * exp(-x) / gamma(s)
s = s - 1
# Then use gammainc(0.5, x) = erf(sqrt(x))
result += erf(sqrt(x))
return result
def main():
iIndex = 0
for line in sys.stdin:
Coh,z,grain_size,tm,a,x1,x2,length,width,thick,strike,dip,zs= map(float, line.split())
n = 1.0
A = 1e6
#Coh = 2000
r = 1.0
Ea = 335e3
p = 3330 * 9.8 * z * 1000
Va = 4e-6
R = 8.3144
G = 30e3
pp = 3
d = grain_size
Tm = tm
Rm = 3330 # mantle density (kg/m^3)
Cp = 1171 # specific heat (J/kg/K)
k = 3.138
kappa = k / (Rm * Cp)
T = (Tm * math.erf ((z-zs) / math.sqrt ( 4 * kappa * a * 3.15e7)))+273
gamma0=((G**n)*A*(Coh**r)*(d**(-pp))* math.exp (-(Ea + p*Va)/(R*T)))
if (not math.isnan(gamma0)):
iIndex+=1
print("%d %.6f %.2f %.2f %.2f %.2f %.2f %.2f %.2f %.2f" % (iIndex,gamma0,x1,x2,z,length,width,thick,strike,dip))
def sort_key(self):
"""Returns 1.0 for a ratio of 1, falling to 0.0 for extremely small
or large values."""
score = math.log10(self.score)
cdf = (1.0 + math.erf(score / math.sqrt(2.0))) / 2.0
return 1 - 2*math.fabs(0.5 - cdf)
def finite_mixture_model(fined_predictions, function_type):
'''
function_type: 0 pdf, 1 cdf
note:
mu and sigma is not mean and variance.
return:
plotxy:[plotx,ploty]
'''
#假设每个prediction都包含了均值和方差, mean variance
#利用含变量的lambda表达式的自动变化特性
mu = lambda :math.log(mean) - math.log(1+var/(mean**2))/2
sigma2 = lambda :math.log(1+var/(mean**2))
if function_type == 0:
log_normal = lambda x:math.exp( -(math.log(x) - mu())**2/(2*sigma2()))/(x*math.sqrt(sigma2())*math.sqrt(2*math.pi))
else:
log_normal = lambda x:(1+math.erf((math.log(x) - mu())/(math.sqrt(sigma2()*2))))/2
fined_prediction_tuple=[(fp['prior'], fp['mean'], fp['var']) for fp in fined_predictions]
plotxy = [[0.01*i for i in range(1,101)]]
#for x in plotxy[0]:
# #[prior*log_normal(x) for (prior,mean,var) in fined_prediction_tuple]
# for (prior,mean,var) in fined_prediction_tuple:
# print prior,mean,var,mu(),sigma2()
plotxy.append([sum([prior*log_normal(x) for (prior,mean,var) in fined_prediction_tuple]) for x in plotxy[0]])
return plotxy
def main():
iIndex = 0
for line in sys.stdin:
Coh,z,a,x1,x2,length,width,thick,strike,dip,zs= map(float, line.split())
n = 3.5
A = 90
#Coh = 2000
r = 1.2
Ea = 462e3
p = 3300 * 9.8 * z * 1000
Va = 11e-6
R = 8.3144
G = 30e3
Tm = 1350 # in K ( K = c + 273)
Rm = 3300 # mantle density (kg/m^3)
Cp = 1171 # specific heat (J/kg/K)
k = 3.138
corr=3.14e7/((1e3)**(n-1))
kappa = k / (Rm * Cp)
T = (Tm * math.erf ((z-zs) / math.sqrt ( 4 * kappa * a * 3.15e7)))+273
gamma0=corr*((G**n)*A*(Coh**r)* math.exp (-(Ea + p*Va)/(R*T)))
if (not math.isnan(gamma0)):
iIndex+=1
#print(iIndex,gamma0,x1,x2,z,length,width,thick,strike,dip)
print(x1,z,a)
def diffusion_percentage(length, diffusion_coefficient, time):
L = length
D = diffusion_coefficient
t = time
a = math.sqrt(D*t)
return 1/L * (-2*math.pi*math.pow(a,2)*L*math.erf(L/(2*a))+2*math.pi*math.pow(a,2)*L-4*math.sqrt(math.pi)*
math.pow(a,3) * math.exp(-1*math.pow(L,2)/(4*math.pow(a,2))) - (-4*math.sqrt(math.pi)*math.pow(a,3)))
def test_save_output():
filename = "function_values"
x = np.arange(0, 100, 1)
y = np.exp(x)
y1 = y*math.erf(0.5)
output.save_output(x, y, filename, q_or_2theta="Q", err=None,
dir_path=None)
output.save_output(x, y, filename, q_or_2theta="2theta", ext=".dat",
err=None, dir_path=None)
output.save_output(x, y, filename, q_or_2theta="2theta", ext=".xye",
err=y1, dir_path=None)
Data_chi = np.loadtxt("function_values.chi", skiprows=7)
Data_dat = np.loadtxt("function_values.dat", skiprows=7)
Data_xye = np.loadtxt("function_values.xye", skiprows=7)
assert_array_almost_equal(x, Data_chi[:, 0])
assert_array_almost_equal(y, Data_chi[:, 1])
assert_array_almost_equal(x, Data_dat[:, 0])
assert_array_almost_equal(y, Data_dat[:, 1])
assert_array_almost_equal(x, Data_xye[:, 0])
assert_array_almost_equal(y, Data_xye[:, 1])
assert_array_almost_equal(y1, Data_xye[:, 2])
os.remove("function_values.chi")
os.remove("function_values.dat")
os.remove("function_values.xye")
def normal_cdf(x, mu=0, sigma=1): # cumulative distribution function
return (1 + math.erf((x - mu) / math.sqrt(2) / sigma)) / 2
def cdfnorm(x, mu, sigma):
return 0.5 * (1 + math.erf((x - mu) / (sigma * (2**1 / 2))))
def g(self, x):
#return np.tanh(x)
return math.erf(x)
def norm_score(self):
"""Return 1.0 for a ratio of 1, falling to 0.0 for extremely small
or large values."""
score = math.log10(self.score)
cdf = (1.0 + math.erf(score / math.sqrt(2.0))) / 2.0
return 1 - 2 * math.fabs(0.5 - cdf)
def normal_cdf(x, mu=0, sigma=1):
return (1 + math.erf((x - mu) / math.sqrt(2) / sigma)) / 2
import math
if __name__ == '__main__':
mean, std = 70, 10
cdf = lambda x: 0.5 * (1 + math.erf((x - mean) / (std * (2**0.5))))
print(round((1 - cdf(80)) * 100, 2))
print(round((1 - cdf(60)) * 100, 2))
print(round((cdf(60)) * 100, 2))
def comp_source_time_function(t, hdur):
# quasi Heaviside, small Gaussian moment-rate tensor with hdur
# (according to SPECFEM definition)
val = 0.5 * (1.0 + erf(t / hdur))
return val
def __init__(
self,
galaxy_pdf_list: List[Galaxy],
grid: aa.Grid2D,
mat_plot_1d: MatPlot1D = MatPlot1D(),
visuals_1d: Visuals1D = Visuals1D(),
include_1d: Include1D = Include1D(),
mat_plot_2d: MatPlot2D = MatPlot2D(),
visuals_2d: Visuals2D = Visuals2D(),
include_2d: Include2D = Include2D(),
sigma: Optional[float] = 3.0,
):
"""
Plots the attributes of a list of `GalaxyProfile` objects using the matplotlib methods `plot()` and `imshow()`
and many other matplotlib functions which customize the plot's appearance.
Figures plotted by this object average over a list galaxy profiles to computed the average value of each
attribute with errors, where the 1D regions within the errors are plotted as a shaded region to show the range
of plausible models. Therefore, the input list of galaxies is expected to represent the probability density
function of an inferred model-fit.
The `mat_plot_1d` and `mat_plot_2d` attributes wrap matplotlib function calls to make the figure. By default,
the settings passed to every matplotlib function called are those specified in
the `config/visualize/mat_wrap/*.ini` files, but a user can manually input values into `MatPlot2D` to
customize the figure's appearance.
Overlaid on the figure are visuals, contained in the `Visuals1D` and `Visuals2D` objects. Attributes may be
extracted from the `GalaxyProfile` and plotted via the visuals object, if the corresponding entry is `True` in
the `Include1D` or `Include2D` object or the `config/visualize/include.ini` file.
Parameters
----------
galaxy_profile_pdf_list
The list of galaxy profiles whose mean and error values the plotter plots.
grid
The 2D (y,x) grid of coordinates used to evaluate the galaxy profile quantities that are plotted.
mat_plot_1d
Contains objects which wrap the matplotlib function calls that make 1D plots.
visuals_1d
Contains 1D visuals that can be overlaid on 1D plots.
include_1d
Specifies which attributes of the `GalaxyProfile` are extracted and plotted as visuals for 1D plots.
mat_plot_2d
Contains objects which wrap the matplotlib function calls that make 2D plots.
visuals_2d
Contains 2D visuals that can be overlaid on 2D plots.
include_2d
Specifies which attributes of the `GalaxyProfile` are extracted and plotted as visuals for 2D plots.
sigma
The confidence interval in terms of a sigma value at which the errors are computed (e.g. a value of
sigma=3.0 uses confidence intevals at ~0.01 and 0.99 the PDF).
"""
super().__init__(
galaxy=None,
grid=grid,
mat_plot_2d=mat_plot_2d,
include_2d=include_2d,
visuals_2d=visuals_2d,
mat_plot_1d=mat_plot_1d,
include_1d=include_1d,
visuals_1d=visuals_1d,
)
self.galaxy_pdf_list = galaxy_pdf_list
self.sigma = sigma
self.low_limit = (1 - math.erf(sigma / math.sqrt(2))) / 2
def calculate_pair(snp1, snp2, pop, web, request=None):
# trim any whitespace
snp1 = snp1.lower().strip()
snp2 = snp2.lower().strip()
# Set data directories using config.yml
with open('config.yml', 'r') as f:
config = yaml.load(f)
env = config['env']
api_mongo_addr = config['api']['api_mongo_addr']
dbsnp_version = config['data']['dbsnp_version']
pop_dir = config['data']['pop_dir']
vcf_dir = config['data']['vcf_dir']
mongo_username = config['database']['mongo_user_readonly']
mongo_password = config['database']['mongo_password']
mongo_port = config['database']['mongo_port']
tmp_dir = "./tmp/"
# Ensure tmp directory exists
if not os.path.exists(tmp_dir):
os.makedirs(tmp_dir)
# Create JSON output
output = {}
# Connect to Mongo snp database
if env == 'local':
mongo_host = api_mongo_addr
else:
mongo_host = 'localhost'
if web:
client = MongoClient('mongodb://' + mongo_username + ':' + mongo_password + '@' + mongo_host+'/admin', mongo_port)
else:
if env == 'local':
client = MongoClient('mongodb://' + mongo_username + ':' + mongo_password + '@' + mongo_host+'/admin', mongo_port)
else:
client = MongoClient('localhost', mongo_port)
db = client["LDLink"]
def get_coords(db, rsid):
rsid = rsid.strip("rs")
query_results = db.dbsnp151.find_one({"id": rsid})
query_results_sanitized = json.loads(json_util.dumps(query_results))
return query_results_sanitized
# Query genomic coordinates
def get_rsnum(db, coord):
temp_coord = coord.strip("chr").split(":")
chro = temp_coord[0]
pos = temp_coord[1]
query_results = db.dbsnp151.find({"chromosome": chro.upper() if chro == 'x' or chro == 'y' else chro, "position": pos})
query_results_sanitized = json.loads(json_util.dumps(query_results))
return query_results_sanitized
# Replace input genomic coordinates with variant ids (rsids)
def replace_coord_rsid(db, snp):
if snp[0:2] == "rs":
return snp
else:
snp_info_lst = get_rsnum(db, snp)
print("snp_info_lst")
print(snp_info_lst)
if snp_info_lst != None:
if len(snp_info_lst) > 1:
var_id = "rs" + snp_info_lst[0]['id']
ref_variants = []
for snp_info in snp_info_lst:
if snp_info['id'] == snp_info['ref_id']:
ref_variants.append(snp_info['id'])
if len(ref_variants) > 1:
var_id = "rs" + ref_variants[0]
if "warning" in output:
output["warning"] = output["warning"] + \
". Multiple rsIDs (" + ", ".join(["rs" + ref_id for ref_id in ref_variants]) + ") map to genomic coordinates " + snp
else:
output["warning"] = "Multiple rsIDs (" + ", ".join(["rs" + ref_id for ref_id in ref_variants]) + ") map to genomic coordinates " + snp
elif len(ref_variants) == 0 and len(snp_info_lst) > 1:
var_id = "rs" + snp_info_lst[0]['id']
if "warning" in output:
output["warning"] = output["warning"] + \
". Multiple rsIDs (" + ", ".join(["rs" + ref_id for ref_id in ref_variants]) + ") map to genomic coordinates " + snp
else:
output["warning"] = "Multiple rsIDs (" + ", ".join(["rs" + ref_id for ref_id in ref_variants]) + ") map to genomic coordinates " + snp
else:
var_id = "rs" + ref_variants[0]
return var_id
elif len(snp_info_lst) == 1:
var_id = "rs" + snp_info_lst[0]['id']
return var_id
else:
return snp
else:
return snp
return snp
snp1 = replace_coord_rsid(db, snp1)
snp2 = replace_coord_rsid(db, snp2)
# Find RS numbers in snp database
# SNP1
snp1_coord = get_coords(db, snp1)
if snp1_coord == None:
output["error"] = snp1 + " is not in dbSNP build " + dbsnp_version + "."
return(json.dumps(output, sort_keys=True, indent=2))
# SNP2
snp2_coord = get_coords(db, snp2)
if snp2_coord == None:
output["error"] = snp2 + " is not in dbSNP build " + dbsnp_version + "."
return(json.dumps(output, sort_keys=True, indent=2))
# Check if SNPs are on the same chromosome
if snp1_coord['chromosome'] != snp2_coord['chromosome']:
output["warning"] = snp1 + " and " + \
snp2 + " are on different chromosomes"
# Select desired ancestral populations
pops = pop.split("+")
pop_dirs = []
for pop_i in pops:
if pop_i in ["ALL", "AFR", "AMR", "EAS", "EUR", "SAS", "ACB", "ASW", "BEB", "CDX", "CEU", "CHB", "CHS", "CLM", "ESN", "FIN", "GBR", "GIH", "GWD", "IBS", "ITU", "JPT", "KHV", "LWK", "MSL", "MXL", "PEL", "PJL", "PUR", "STU", "TSI", "YRI"]:
pop_dirs.append(pop_dir + pop_i + ".txt")
else:
output["error"] = pop_i + " is not an ancestral population. Choose one of the following ancestral populations: AFR, AMR, EAS, EUR, or SAS; or one of the following sub-populations: ACB, ASW, BEB, CDX, CEU, CHB, CHS, CLM, ESN, FIN, GBR, GIH, GWD, IBS, ITU, JPT, KHV, LWK, MSL, MXL, PEL, PJL, PUR, STU, TSI, or YRI."
return(json.dumps(output, sort_keys=True, indent=2))
get_pops = "cat " + " ".join(pop_dirs)
proc = subprocess.Popen(get_pops, shell=True, stdout=subprocess.PIPE)
pop_list = [x.decode('utf-8') for x in proc.stdout.readlines()]
ids = [i.strip() for i in pop_list]
pop_ids = list(set(ids))
# Extract 1000 Genomes phased genotypes
# SNP1
vcf_file1 = vcf_dir + snp1_coord['chromosome'] + ".phase3_shapeit2_mvncall_integrated_v5.20130502.genotypes.vcf.gz"
tabix_snp1_offset = "tabix {0} {1}:{2}-{2} | grep -v -e END".format(
vcf_file1, snp1_coord['chromosome'], snp1_coord['position'])
proc1_offset = subprocess.Popen(
tabix_snp1_offset, shell=True, stdout=subprocess.PIPE)
vcf1_offset = [x.decode('utf-8') for x in proc1_offset.stdout.readlines()]
# SNP2
vcf_file2 = vcf_dir + snp2_coord['chromosome'] + ".phase3_shapeit2_mvncall_integrated_v5.20130502.genotypes.vcf.gz"
tabix_snp2_offset = "tabix {0} {1}:{2}-{2} | grep -v -e END".format(
vcf_file2, snp2_coord['chromosome'], snp2_coord['position'])
proc2_offset = subprocess.Popen(
tabix_snp2_offset, shell=True, stdout=subprocess.PIPE)
vcf2_offset = [x.decode('utf-8') for x in proc2_offset.stdout.readlines()]
vcf1_pos = snp1_coord['position']
vcf2_pos = snp2_coord['position']
vcf1 = vcf1_offset
vcf2 = vcf2_offset
# Import SNP VCF files
# SNP1
if len(vcf1) == 0:
output["error"] = snp1 + " is not in 1000G reference panel."
return(json.dumps(output, sort_keys=True, indent=2))
elif len(vcf1) > 1:
geno1 = []
for i in range(len(vcf1)):
if vcf1[i].strip().split()[2] == snp1:
geno1 = vcf1[i].strip().split()
if geno1 == []:
output["error"] = snp1 + " is not in 1000G reference panel."
return(json.dumps(output, sort_keys=True, indent=2))
else:
geno1 = vcf1[0].strip().split()
if geno1[2] != snp1:
if "warning" in output:
output["warning"] = output["warning"] + \
". Genomic position for query variant1 (" + snp1 + \
") does not match RS number at 1000G position (chr" + \
geno1[0]+":"+geno1[1]+")"
else:
output["warning"] = "Genomic position for query variant1 (" + snp1 + \
") does not match RS number at 1000G position (chr" + \
geno1[0]+":"+geno1[1]+")"
snp1 = geno1[2]
if "," in geno1[3] or "," in geno1[4]:
output["error"] = snp1 + " is not a biallelic variant."
return(json.dumps(output, sort_keys=True, indent=2))
if len(geno1[3]) == 1 and len(geno1[4]) == 1:
snp1_a1 = geno1[3]
snp1_a2 = geno1[4]
elif len(geno1[3]) == 1 and len(geno1[4]) > 1:
snp1_a1 = "-"
snp1_a2 = geno1[4][1:]
elif len(geno1[3]) > 1 and len(geno1[4]) == 1:
snp1_a1 = geno1[3][1:]
snp1_a2 = "-"
elif len(geno1[3]) > 1 and len(geno1[4]) > 1:
snp1_a1 = geno1[3][1:]
snp1_a2 = geno1[4][1:]
allele1 = {"0|0": [snp1_a1, snp1_a1], "0|1": [snp1_a1, snp1_a2], "1|0": [snp1_a2, snp1_a1], "1|1": [
snp1_a2, snp1_a2], "0": [snp1_a1, "."], "1": [snp1_a2, "."], "./.": [".", "."], ".": [".", "."]}
# SNP2
if len(vcf2) == 0:
output["error"] = snp2 + " is not in 1000G reference panel."
return(json.dumps(output, sort_keys=True, indent=2))
elif len(vcf2) > 1:
geno2 = []
for i in range(len(vcf2)):
if vcf2[i].strip().split()[2] == snp2:
geno2 = vcf2[i].strip().split()
if geno2 == []:
output["error"] = snp2 + " is not in 1000G reference panel."
return(json.dumps(output, sort_keys=True, indent=2))
else:
geno2 = vcf2[0].strip().split()
if geno2[2] != snp2:
if "warning" in output:
output["warning"] = output["warning"] + \
". Genomic position for query variant2 (" + snp2 + \
") does not match RS number at 1000G position (chr" + \
geno2[0]+":"+geno2[1]+")"
else:
output["warning"] = "Genomic position for query variant2 (" + snp2 + \
") does not match RS number at 1000G position (chr" + \
geno2[0]+":"+geno2[1]+")"
snp2 = geno2[2]
if "," in geno2[3] or "," in geno2[4]:
output["error"] = snp2 + " is not a biallelic variant."
return(json.dumps(output, sort_keys=True, indent=2))
if len(geno2[3]) == 1 and len(geno2[4]) == 1:
snp2_a1 = geno2[3]
snp2_a2 = geno2[4]
elif len(geno2[3]) == 1 and len(geno2[4]) > 1:
snp2_a1 = "-"
snp2_a2 = geno2[4][1:]
elif len(geno2[3]) > 1 and len(geno2[4]) == 1:
snp2_a1 = geno2[3][1:]
snp2_a2 = "-"
elif len(geno2[3]) > 1 and len(geno2[4]) > 1:
snp2_a1 = geno2[3][1:]
snp2_a2 = geno2[4][1:]
allele2 = {"0|0": [snp2_a1, snp2_a1], "0|1": [snp2_a1, snp2_a2], "1|0": [snp2_a2, snp2_a1], "1|1": [
snp2_a2, snp2_a2], "0": [snp2_a1, "."], "1": [snp2_a2, "."], "./.": [".", "."], ".": [".", "."]}
if geno1[1] != vcf1_pos:
output["error"] = "VCF File does not match variant coordinates for SNP1."
return(json.dumps(output, sort_keys=True, indent=2))
if geno2[1] != vcf2_pos:
output["error"] = "VCF File does not match variant coordinates for SNP2."
return(json.dumps(output, sort_keys=True, indent=2))
# Get headers
tabix_snp1_h = "tabix -H {0} | grep CHROM".format(vcf_file1)
proc1_h = subprocess.Popen(
tabix_snp1_h, shell=True, stdout=subprocess.PIPE)
head1 = [x.decode('utf-8') for x in proc1_h.stdout.readlines()][0].strip().split()
tabix_snp2_h = "tabix -H {0} | grep CHROM".format(vcf_file2)
proc2_h = subprocess.Popen(
tabix_snp2_h, shell=True, stdout=subprocess.PIPE)
head2 = [x.decode('utf-8') for x in proc2_h.stdout.readlines()][0].strip().split()
# Combine phased genotypes
geno = {}
for i in range(9, len(head1)):
geno[head1[i]] = [allele1[geno1[i]], ".."]
for i in range(9, len(head2)):
if head2[i] in geno:
geno[head2[i]][1] = allele2[geno2[i]]
# Extract haplotypes
hap = {}
for ind in pop_ids:
if ind in geno:
hap1 = geno[ind][0][0] + "_" + geno[ind][1][0]
hap2 = geno[ind][0][1] + "_" + geno[ind][1][1]
if hap1 in hap:
hap[hap1] += 1
else:
hap[hap1] = 1
if hap2 in hap:
hap[hap2] += 1
else:
hap[hap2] = 1
# Remove missing haplotypes
keys = list(hap.keys())
for key in keys:
if "." in key:
hap.pop(key, None)
# Check all haplotypes are present
if len(hap) != 4:
snp1_a = [snp1_a1, snp1_a2]
snp2_a = [snp2_a1, snp2_a2]
haps = [snp1_a[0] + "_" + snp2_a[0], snp1_a[0] + "_" + snp2_a[1],
snp1_a[1] + "_" + snp2_a[0], snp1_a[1] + "_" + snp2_a[1]]
for i in haps:
if i not in hap:
hap[i] = 0
# Sort haplotypes
A = hap[sorted(hap)[0]]
B = hap[sorted(hap)[1]]
C = hap[sorted(hap)[2]]
D = hap[sorted(hap)[3]]
N = A + B + C + D
tmax = max(A, B, C, D)
hap1 = sorted(hap, key=hap.get, reverse=True)[0]
hap2 = sorted(hap, key=hap.get, reverse=True)[1]
hap3 = sorted(hap, key=hap.get, reverse=True)[2]
hap4 = sorted(hap, key=hap.get, reverse=True)[3]
delta = float(A * D - B * C)
Ms = float((A + C) * (B + D) * (A + B) * (C + D))
if Ms != 0:
# D prime
if delta < 0:
D_prime = abs(delta / min((A + C) * (A + B), (B + D) * (C + D)))
else:
D_prime = abs(delta / min((A + C) * (C + D), (A + B) * (B + D)))
# R2
r2 = (delta**2) / Ms
# P-value
num = (A + B + C + D) * (A * D - B * C)**2
denom = Ms
chisq = num / denom
p = 2 * (1 - (0.5 * (1 + math.erf(chisq**0.5 / 2**0.5))))
else:
D_prime = "NA"
r2 = "NA"
chisq = "NA"
p = "NA"
# Find Correlated Alleles
if str(r2) != "NA" and float(r2) > 0.1:
Ac=hap[sorted(hap)[0]]
Bc=hap[sorted(hap)[1]]
Cc=hap[sorted(hap)[2]]
Dc=hap[sorted(hap)[3]]
if ((Ac*Dc) / max((Bc*Cc), 0.01) > 1):
corr1 = snp1 + "(" + sorted(hap)[0].split("_")[0] + ") allele is correlated with " + snp2 + "(" + sorted(hap)[0].split("_")[1] + ") allele"
corr2 = snp1 + "(" + sorted(hap)[3].split("_")[0] + ") allele is correlated with " + snp2 + "(" + sorted(hap)[3].split("_")[1] + ") allele"
corr_alleles = [corr1, corr2]
else:
corr1 = snp1 + "(" + sorted(hap)[1].split("_")[0] + ") allele is correlated with " + snp2 + "(" + sorted(hap)[1].split("_")[1] + ") allele"
corr2 = snp1 + "(" + sorted(hap)[2].split("_")[0] + ") allele is correlated with " + snp2 + "(" + sorted(hap)[2].split("_")[1] + ") allele"
corr_alleles = [corr1, corr2]
else:
corr_alleles = [snp1 + " and " + snp2 + " are in linkage equilibrium"]
# Create JSON output
snp_1 = {}
snp_1["rsnum"] = snp1
snp_1["coord"] = "chr" + snp1_coord['chromosome'] + ":" + \
vcf1_pos
snp_1_allele_1 = {}
snp_1_allele_1["allele"] = sorted(hap)[0].split("_")[0]
snp_1_allele_1["count"] = str(A + B)
snp_1_allele_1["frequency"] = str(round(float(A + B) / N, 3))
snp_1["allele_1"] = snp_1_allele_1
snp_1_allele_2 = {}
snp_1_allele_2["allele"] = sorted(hap)[2].split("_")[0]
snp_1_allele_2["count"] = str(C + D)
snp_1_allele_2["frequency"] = str(round(float(C + D) / N, 3))
snp_1["allele_2"] = snp_1_allele_2
output["snp1"] = snp_1
snp_2 = {}
snp_2["rsnum"] = snp2
snp_2["coord"] = "chr" + snp2_coord['chromosome'] + ":" + \
vcf2_pos
snp_2_allele_1 = {}
snp_2_allele_1["allele"] = sorted(hap)[0].split("_")[1]
snp_2_allele_1["count"] = str(A + C)
snp_2_allele_1["frequency"] = str(round(float(A + C) / N, 3))
snp_2["allele_1"] = snp_2_allele_1
snp_2_allele_2 = {}
snp_2_allele_2["allele"] = sorted(hap)[1].split("_")[1]
snp_2_allele_2["count"] = str(B + D)
snp_2_allele_2["frequency"] = str(round(float(B + D) / N, 3))
snp_2["allele_2"] = snp_2_allele_2
output["snp2"] = snp_2
two_by_two = {}
cells = {}
cells["c11"] = str(A)
cells["c12"] = str(B)
cells["c21"] = str(C)
cells["c22"] = str(D)
two_by_two["cells"] = cells
two_by_two["total"] = str(N)
output["two_by_two"] = two_by_two
haplotypes = {}
hap_1 = {}
hap_1["alleles"] = hap1
hap_1["count"] = str(hap[hap1])
hap_1["frequency"] = str(round(float(hap[hap1]) / N, 3))
haplotypes["hap1"] = hap_1
hap_2 = {}
hap_2["alleles"] = hap2
hap_2["count"] = str(hap[hap2])
hap_2["frequency"] = str(round(float(hap[hap2]) / N, 3))
haplotypes["hap2"] = hap_2
hap_3 = {}
hap_3["alleles"] = hap3
hap_3["count"] = str(hap[hap3])
hap_3["frequency"] = str(round(float(hap[hap3]) / N, 3))
haplotypes["hap3"] = hap_3
hap_4 = {}
hap_4["alleles"] = hap4
hap_4["count"] = str(hap[hap4])
hap_4["frequency"] = str(round(float(hap[hap4]) / N, 3))
haplotypes["hap4"] = hap_4
output["haplotypes"] = haplotypes
statistics = {}
if Ms != 0:
statistics["d_prime"] = str(round(D_prime, 4))
statistics["r2"] = str(round(r2, 4))
statistics["chisq"] = str(round(chisq, 4))
if p >= 0.0001:
statistics["p"] = str(round(p, 4))
else:
statistics["p"] = "<0.0001"
else:
statistics["d_prime"] = D_prime
statistics["r2"] = r2
statistics["chisq"] = chisq
statistics["p"] = p
output["statistics"] = statistics
output["corr_alleles"] = corr_alleles
# Generate output file
ldpair_out = open(tmp_dir + "LDpair_" + request + ".txt", "w")
print("Query SNPs:", file=ldpair_out)
print(output["snp1"]["rsnum"] + \
" (" + output["snp1"]["coord"] + ")", file=ldpair_out)
print(output["snp2"]["rsnum"] + \
" (" + output["snp2"]["coord"] + ")", file=ldpair_out)
print("", file=ldpair_out)
print(pop + " Haplotypes:", file=ldpair_out)
print(" " * 15 + output["snp2"]["rsnum"], file=ldpair_out)
print(" " * 15 + \
output["snp2"]["allele_1"]["allele"] + " " * \
7 + output["snp2"]["allele_2"]["allele"], file=ldpair_out)
print(" " * 13 + "-" * 17, file=ldpair_out)
print(" " * 11 + output["snp1"]["allele_1"]["allele"] + " | " + output["two_by_two"]["cells"]["c11"] + " " * (5 - len(output["two_by_two"]["cells"]["c11"])) + " | " + output["two_by_two"]["cells"]["c12"] + " " * (
5 - len(output["two_by_two"]["cells"]["c12"])) + " | " + output["snp1"]["allele_1"]["count"] + " " * (5 - len(output["snp1"]["allele_1"]["count"])) + " (" + output["snp1"]["allele_1"]["frequency"] + ")", file=ldpair_out)
print(output["snp1"]["rsnum"] + " " * \
(10 - len(output["snp1"]["rsnum"])) + " " * 3 + "-" * 17, file=ldpair_out)
print(" " * 11 + output["snp1"]["allele_2"]["allele"] + " | " + output["two_by_two"]["cells"]["c21"] + " " * (5 - len(output["two_by_two"]["cells"]["c21"])) + " | " + output["two_by_two"]["cells"]["c22"] + " " * (
5 - len(output["two_by_two"]["cells"]["c22"])) + " | " + output["snp1"]["allele_2"]["count"] + " " * (5 - len(output["snp1"]["allele_2"]["count"])) + " (" + output["snp1"]["allele_2"]["frequency"] + ")", file=ldpair_out)
print(" " * 13 + "-" * 17, file=ldpair_out)
print(" " * 15 + output["snp2"]["allele_1"]["count"] + " " * (5 - len(output["snp2"]["allele_1"]["count"])) + " " * 3 + output["snp2"]["allele_2"]["count"] + " " * (
5 - len(output["snp2"]["allele_2"]["count"])) + " " * 3 + output["two_by_two"]["total"], file=ldpair_out)
print(" " * 14 + "(" + output["snp2"]["allele_1"]["frequency"] + ")" + " " * (5 - len(output["snp2"]["allele_1"]["frequency"])) + \
" (" + output["snp2"]["allele_2"]["frequency"] + ")" + \
" " * (5 - len(output["snp2"]["allele_2"]["frequency"])), file=ldpair_out)
print("", file=ldpair_out)
print(" " + output["haplotypes"]["hap1"]["alleles"] + ": " + \
output["haplotypes"]["hap1"]["count"] + \
" (" + output["haplotypes"]["hap1"]["frequency"] + ")", file=ldpair_out)
print(" " + output["haplotypes"]["hap2"]["alleles"] + ": " + \
output["haplotypes"]["hap2"]["count"] + \
" (" + output["haplotypes"]["hap2"]["frequency"] + ")", file=ldpair_out)
print(" " + output["haplotypes"]["hap3"]["alleles"] + ": " + \
output["haplotypes"]["hap3"]["count"] + \
" (" + output["haplotypes"]["hap3"]["frequency"] + ")", file=ldpair_out)
print(" " + output["haplotypes"]["hap4"]["alleles"] + ": " + \
output["haplotypes"]["hap4"]["count"] + \
" (" + output["haplotypes"]["hap4"]["frequency"] + ")", file=ldpair_out)
print("", file=ldpair_out)
print(" D': " + output["statistics"]["d_prime"], file=ldpair_out)
print(" R2: " + output["statistics"]["r2"], file=ldpair_out)
print(" Chi-sq: " + output["statistics"]["chisq"], file=ldpair_out)
print(" p-value: " + output["statistics"]["p"], file=ldpair_out)
print("", file=ldpair_out)
if len(output["corr_alleles"]) == 2:
print(output["corr_alleles"][0], file=ldpair_out)
print(output["corr_alleles"][1], file=ldpair_out)
else:
print(output["corr_alleles"][0], file=ldpair_out)
try:
output["warning"]
except KeyError:
www = "do nothing"
else:
print("WARNING: " + output["warning"] + "!", file=ldpair_out)
ldpair_out.close()
# Return output
return(json.dumps(output, sort_keys=True, indent=2))
def equation(d, x, t, cm, c):
return (c - cm*(1.-erf(x/2./np.sqrt(d*t))))
def cdf(self, x):
'Cumulative distribution function. P(X <= x)'
if not self.sigma:
raise StatisticsError('cdf() not defined when sigma is zero')
return 0.5 * (1.0 + erf((x - self.mu) / (self.sigma * sqrt(2.0))))
def cdf(x):
return 0.5 * (1 + math.erf((x - mean) / (std * (2**0.5))))
def standard_normal_cdf(x):
result = (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
return result
def math_erf(A, B):
i = cuda.grid(1)
B[i] = math.erf(A[i])
def normalcdf(x,m,sd):
return (1 + math.erf((x-m) / math.sqrt(2) / sd)) / 2
from math import erf, sqrt capacity = 9800 boxes = 49 mean = 205 * boxes sd = 15 * sqrt(boxes) val1 = (1 + erf((capacity - mean) / (sd * sqrt(2)))) / 2 print(round(val1, 4))
def cumul(x, m, std):
return 0.5 * (1 + math.erf((x - m) / (std * math.sqrt(2))))
def ufunc(x):
return math.erf(x)
def BPSO(prob_prams, pso_prams):
#================================Problem definition===========================================
nVar = prob_prams['nVar']
#varSize=[1,prob_prams['nVar']]
costFn = prob_prams['costFn']
#===========================================================================
#===================================Parameters of BPSO========================================
MaxIt = pso_prams['MaxIt'] # Maximum number of iteration
nPop = pso_prams['nPop'] # Number of particle
w = pso_prams['w']
#Inertia coefficient
wdamp = pso_prams['wdamp'] #Damping ratio
c1 = pso_prams['c1']
c2 = pso_prams['c2']
Vmax = pso_prams['Vmax']
trans_fn = pso_prams['trans_fn']
s = np.zeros(nVar)
#===========================================================================
#=================================Initialization==========================================
GlobalBest_Postion = []
GlobalBest_Cost = np.Infinity
p = [particle() for i in range(0, nPop)]
for i in range(0, nPop):
#Generate random position
p[i].Position = np.random.randint(2, size=nVar)
#Initialize velocity
p[i].Velocity = np.zeros(nVar)
#Update personal best
p[i].Best['Position'] = p[i].Position.copy()
p[i].Best['Cost'] = p[i].Cost
#Update Global Best
GlobalBest_Cost, GlobalBest_Postion = p[i].updateGbest(
GlobalBest_Cost, GlobalBest_Postion)
BestCosts = [0] * MaxIt
gbests = [0] * MaxIt
# ===========================Evaluation Iteration begins here==============================================
for it in range(MaxIt):
for i in range(nPop):
#Evaluate the cost function
p[i].Cost = costFn(p[i].Position)
if p[i].updatePbest():
GlobalBest_Cost, GlobalBest_Postion = p[i].updateGbest(
GlobalBest_Cost, GlobalBest_Postion)
#Update Velocity
p[i].updateVelocity(GlobalBest_Postion, c1, c2, w, nVar)
p[i].Velocity = tools.boundary(p[i].Velocity, -Vmax, Vmax)
#Update Position and Cost
#Transfer functions
for j in range(nVar):
if trans_fn == 1:
s[j] = 1 / (1 + exp(-2 * p[i].Velocity[j]))
if trans_fn == 2:
s[j] = 1 / (1 + exp(-p[i].Velocity[j]))
if trans_fn == 3:
s[j] = 1 / (1 + exp(-p[i].Velocity[j] / 2))
if trans_fn == 4:
s[j] = 1 / (1 + exp(-p[i].Velocity[j] / 3))
if trans_fn <= 4:
if random() < s[j]:
p[i].Position[j] = 1
else:
p[i].Position[j] = 0
if trans_fn == 5:
s[j] = abs(erf(((sqrt(pi) / 2) * p[i].Velocity[j])))
if trans_fn == 6:
s[j] = abs(tanh(p[i].Velocity[j]))
if trans_fn == 7:
s[j] = abs(p[i].Velocity[j] / sqrt(
(1 + p[i].Velocity[j]**2)))
if trans_fn == 8:
s[j] = abs((2 / pi) * atan((pi / 2) * p[i].Velocity[j]))
if trans_fn > 4:
if random() < s[j]:
p[i].Position[j] = tools.flip(p[i].Position[j])
BestCosts[it] = GlobalBest_Cost
gbests[it] = (GlobalBest_Postion, GlobalBest_Cost)
if pso_prams['showItr']:
print("Iteration", it, 'Best cost', BestCosts[it])
#Damping Inertia Coefficient
w = w * wdamp
#----------------------------------------------------------------------------------------------
out_pso = {
'BestCosts': BestCosts,
'GlobalBest': (GlobalBest_Postion, GlobalBest_Cost),
'gbests': gbests,
'particle': p
}
return out_pso
def Vfunction2(gamma):
val = (math.pi)**(0.5)
val /= 2
val *= gamma
val = math.erf(val)
return abs(val)
def h(self, z):
return 0.5 * z * np.sqrt(math.pi) * math.erf(z) + np.exp(-(z**2))
def set_initial_guess(self):
"""
Set the initial guess for the solution. The initial guess is generated
by assuming infinitely-fast chemistry.
"""
super(CounterflowDiffusionFlame, self).set_initial_guess()
moles = lambda el: (self.gas.elemental_mass_fraction(el) /
self.gas.atomic_weight(el))
# Compute stoichiometric mixture composition
Yin_f = self.fuel_inlet.Y
self.gas.TPY = self.fuel_inlet.T, self.P, Yin_f
mdotf = self.fuel_inlet.mdot
u0f = mdotf / self.gas.density
T0f = self.fuel_inlet.T
sFuel = moles('O')
if 'C' in self.gas.element_names:
sFuel -= 2 * moles('C')
if 'H' in self.gas.element_names:
sFuel -= 0.5 * moles('H')
Yin_o = self.oxidizer_inlet.Y
self.gas.TPY = self.oxidizer_inlet.T, self.P, Yin_o
mdoto = self.oxidizer_inlet.mdot
u0o = mdoto / self.gas.density
T0o = self.oxidizer_inlet.T
sOx = moles('O')
if 'C' in self.gas.element_names:
sOx -= 2 * moles('C')
if 'H' in self.gas.element_names:
sOx -= 0.5 * moles('H')
zst = 1.0 / (1 - sFuel / sOx)
Yst = zst * Yin_f + (1.0 - zst) * Yin_o
# get adiabatic flame temperature and composition
Tbar = 0.5 * (T0f + T0o)
self.gas.TPY = Tbar, self.P, Yst
self.gas.equilibrate('HP')
Teq = self.gas.T
Yeq = self.gas.Y
# estimate strain rate
zz = self.flame.grid
dz = zz[-1] - zz[0]
a = (u0o + u0f)/dz
kOx = (self.gas.species_index('O2') if 'O2' in self.gas.species_names else
self.gas.species_index('o2'))
f = np.sqrt(a / (2.0 * self.gas.mix_diff_coeffs[kOx]))
x0 = np.sqrt(mdotf*u0f) * dz / (np.sqrt(mdotf*u0f) + np.sqrt(mdoto*u0o))
nz = len(zz)
Y = np.zeros((nz, self.gas.n_species))
T = np.zeros(nz)
for j in range(nz):
x = zz[j] - zz[0]
zeta = f * (x - x0)
zmix = 0.5 * (1.0 - erf(zeta))
if zmix > zst:
Y[j] = Yeq + (Yin_f - Yeq) * (zmix - zst) / (1.0 - zst)
T[j] = Teq + (T0f - Teq) * (zmix - zst) / (1.0 - zst)
else:
Y[j] = Yin_o + zmix * (Yeq - Yin_o) / zst
T[j] = T0o + (Teq - T0o) * zmix / zst
T[0] = T0f
T[-1] = T0o
zrel = (zz - zz[0])/dz
self.set_profile('u', [0.0, 1.0], [u0f, -u0o])
self.set_profile('V', [0.0, x0/dz, 1.0], [0.0, a, 0.0])
self.set_profile('T', zrel, T)
for k,spec in enumerate(self.gas.species_names):
self.set_profile(spec, zrel, Y[:,k])
def CDF(x):
return 0.5 * (1 + math.erf((x - mean) / (sd * math.sqrt(2))))
import sys
import math
# def erf(x, z):
# return ((2/math.sqrt(math.pi)) * (integrate(exp(-x), (x, 0, z))))
ms = input('Enter mean and std dev: ')
l = input('Enter less than ')
between = input('Enter between ')
MS = list([int(i) for i in ms.split()])
less = float(l)
Between = list([int(i) for i in between.split()])
mean = MS[0]
std = MS[1]
lower = Between[0]
higher = Between[1]
#cdf1 = .5 * (1 + ((less - mean)/(std*math.sqrt(2))))
#cdf2 = 1 - (.5 * (1 + ((lower - mean)/(std*math.sqrt(2)))) + (1 - .5 * (1 + ((higher - mean)/(std*math.sqrt(2))))))
cdf1 = .5 * (1 + math.erf(((less - mean) / (std * math.sqrt(2)))))
cdf2 = 1 - (.5 * (1 + math.erf(
((lower - mean) / (std * math.sqrt(2))))) + (1 - .5 * (1 + math.erf(
((higher - mean) / (std * math.sqrt(2)))))))
print("{0:0.3f}".format(cdf1))
print("{0:0.3f}".format(cdf2))
def erf(x):
return math.erf(x)
import math
def cmf(case, mean, std):
z = (case - mean) / (std * (2**0.5))
error = math.erf(z)
return (1 + error) * 0.5
mean = 100 * 2.4
std = 10 * 2
case1 = 250
result1 = cmf(case1, mean, std)
print(round(result1, 4))
def g(self, z):
return 1.0 * z * np.sqrt(math.pi) * math.erf(z) + np.exp(-(z**2))
def cdf(x, u, o):
''' u: mean
o: standard deviation
'''
return (1 / 2) * (1 + erf((x - u) / (o * sqrt(2))))
def normal_cdf(x, mean=0, std_dev=1) -> float:
''' Returns the normal CDF (cumulative distribution function) of x
given the mean and standard deviation.
'''
return 0.5 * (1 + math.erf((x - mean) / (std_dev * math.sqrt(2))))
def norm_cdf(x):
# Computes standard normal cumulative distribution function
return (1. + math.erf(x / math.sqrt(2.))) / 2.
