def calc_model_evidence(self):
vval = 0
mp.mp.dps = 50
for action in range(self.hparams.num_actions):
# val=1
# aa = self.a[action]
# for i in xrange(int(self.a[action]-self.a0)):
# aa-=1
# val*=aa
# val/=(2.0*math.pi)
# val/=self.b[action]
# val*=gamma(aa)
# val/=(self.b[action]**aa)
# val *= np.sqrt(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)) / np.linalg.det(self.precision[action]))
# val *= (self.b0 ** self.a0)
# val/= gamma(self.a0)
# vval += val
#val= 1/float((2.0 * math.pi) ** (self.a[action]-self.a0))
#val*= (float(gamma(self.a[action]))/float(gamma(self.a0)))
#val*= np.sqrt(float(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))/float(np.linalg.det(self.precision[action])))
#val*= (float(self.b0**self.a0)/float(self.b[action]**self.a[action]))
val= mp.mpf(mp.fmul(mp.fneg(mp.log(mp.fmul(2.0 , mp.pi))) , mp.fsub(self.a[action],self.a0)))
val+= mp.loggamma(self.a[action])
val-= mp.loggamma(self.a0)
val+= 0.5*mp.log(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))
val -= 0.5*mp.log(np.linalg.det(self.precision[action]))
val+= mp.fmul(self.a0,mp.log(self.b0))
val-= mp.fmul(self.a[action],mp.log(self.b[action]))
vval+=mp.exp(val)
vval/=float(self.hparams.num_actions)
return vval
def findPoissonChangePoint( data, factorial ): # data is a list of counts in each time period, uniformly spaced # the denominator (including both P(D|H1) and constant parts of P(D|H2) ) C = data.sum() N = mpf(len(data)) denominator = factorial[C-1] * pi / ( 2 * N**C ) # the numerator (trickier) # this needs to be averaged over the possible change points weights = zeros(N,dtype=object) CA = 0 CB = C for i in range(1,N) : # points up through i are in data set A; the rest are in B datapoint = data[i-1] NA = mpf(i) ; CA += datapoint NB = mpf(N-i) ; CB -= datapoint fraction_num = factorial[CA] * factorial[CB] fraction_den = NA**(CA+1) * NB**(CB+1) * ( (CA/NA)**2 + (CB/NB)**2 ) #weights.append( fraction_num/fraction_den ) weights[i-1] = mpf(fraction_num)/fraction_den numerator = weights.mean() lognum= inv_log10 * log( numerator ) logden= inv_log10 * log( denominator ) logodds = lognum - logden print "num:",numerator, "log num:", lognum, "| denom:", denominator, "log denom:", logden, "|| log odds:", logodds # If there is a change point, then logodds will be greater than 0 if logodds < 0 : return None return ( weights.argmax(), logodds )
def polyfit_erfc(nroots, x, low):
t = x
if t > 19682.99:
t = 19682.99
if t > 1.0:
tt = mpmath.log(t) / mpmath.log(3) + 1.0 # log3(t) + 1
else:
tt = mpmath.sqrt(t)
it = int(tt)
tt = tt - it
tt = 2.0 * tt - 1.0 # map [0, 1] to [-1, 1]
u = low * 2 - 1 # map [0, 1] to [-1, 1]
tab_rs, tab_ws = tabulate_erfc(nroots, it)
im = clenshaw_d1(tab_rs.astype(float), u, nroots)
rr = clenshaw_d1(im, tt, nroots)
rr = [r / (1 - r) for r in rr]
im = clenshaw_d1(tab_ws.astype(float), u, nroots)
ww = clenshaw_d1(im, tt, nroots)
if x * low**2 < DECIMALS * .7:
factor = mpmath.exp(-x * low**2)
ww = [w * factor for w in ww]
return rr, ww
def cplot_in_terminal(expr, *args, prec=None, logname=None, color=lambda i:
-mpmath.floor(mpmath.log(abs(i), 10))/(30 -
mpmath.floor(mpmath.log(abs(i), 10))), points=1000000, **kwargs):
"""
Run mpmath.cplot() but show in terminal if possible
"""
kwargs['color'] = color
kwargs['points'] = points
from mpmath import cplot
if prec:
mpmath.mp.dps = prec
f = lambdify(t, expr, mpmath)
try:
from iterm2_tools.images import display_image_bytes
except ImportError:
if logname:
os.makedirs('plots', exist_ok=True)
file = 'plots/%s.png' % logname
else:
file = None
cplot(f, *args, file=file, **kwargs)
else:
from io import BytesIO
b = BytesIO()
cplot(f, *args, **kwargs, file=b)
if logname:
os.makedirs('plots', exist_ok=True)
with open('plots/%s.png' % logname, 'wb') as f:
f.write(b.getvalue())
print(display_image_bytes(b.getvalue()))
def pdf_bb_ratio(a1, a2, b1, b2, w):
lnA = mpmath.log(mpmath.beta(a1, b1)) + mpmath.log(mpmath.beta(a2, b2))
def pdf_calc(wi):
if wi < 0:
print('Ratio below Zero! Not reasonable!')
exit(1)
elif wi == 0:
resulti = 0
elif wi < 1:
resulti = mpmath.exp(
mpmath.log(mpmath.beta(a1 + a2, b2)) +
(a1 - 1.0) * mpmath.log(wi) +
log_hyper_2F1(a1 + a2, 1 - b1, a1 + a2 + b2, wi) - lnA)
else:
resulti = mpmath.exp(
mpmath.log(mpmath.beta(a1 + a2, b1)) -
(1.0 + a2) * mpmath.log(wi) +
log_hyper_2F1(a1 + a2, 1 - b2, a1 + a2 + b1, (1 / wi)) - lnA)
return resulti
if isinstance(w, int) or isinstance(w, float) or isinstance(w, mpmath.mpf):
result = pdf_calc(w)
else:
result = np.zeros(len(w))
for i in range(len(w)):
wi = w[i]
result[i] = pdf_calc(wi)
return result
def cMLE(self, ip, **kwargs):
"""
Estimation of c
"""
c = ip
if len(kwargs.keys()) != 0:
a = kwargs['a']
b = kwargs['b']
else:
a = self.arule[self.j + 1]
b = self.brule[self.j + 1]
tVec = self.tVec
tn = tVec[-1]
exp_tn = exp(-b * pow(tn, c))
n = np.size(tVec)
sum_k = 0
for i in range(n):
tVeci = tVec[i]
tVeci1 = tVec[i - 1]
if i > 0:
numer = (pow(tVeci, c) * self.expo(i, b, c) * log(tVeci) -
pow(tVeci1, c) * self.expo(i - 1, b, c) * log(tVeci1))
denom = (self.expo(i - 1, b, c) - self.expo(i, b, c))
else:
numer = (pow(tVeci, c) * self.expo(i, b, c) * log(tVeci))
denom = (1 - self.expo(i, b, c))
sum_k += self.kVec[i] * b * (numer / denom)
cprime = sum_k - a * b * pow(self.tn, c) * self.expo(-1, b, c) * log(
self.tn)
return cprime
def findGaussianChangePoint( data ): # the denominator. This is the easy part. N = len( data ) if N<6 : return None # can't find a cp in data this small # set up gamma function table #for i in range(N): s2 = mpf(data.var()) gpart = gamma( mpf(N)/2.0 - 1 ) denom = (pi**1.5) * mpf((N*s2))**( -N/2.0 + 0.5 ) * gpart # the numerator. A little trickier. # calc_twostate_weights() already deals with ts<3 and ts>N-2. weights=calc_twostate_weights( data ) if weights is None: return None num = 2.0**2.5 * abs(data.mean()) * weights.mean() logodds = log( num ) - log( denom ) print "num:", num, "log num:", log(num), "| denom:", denom, "log denom:", log(denom), "|| log odds:", logodds # If there is a change point, then logodds will be greater than 0 if logodds < 0 : return None return ( weights.argmax(), logodds )
def mobility(self, z=1000, E=0, T=300, pn=None):
if pn is None:
Eg = self.band_gap(T, symbolic=False, electron_volts=False)
# print Eg, self.__to_numeric(-Eg/(k*T)), mp.exp(self.__to_numeric(-Eg/(k*T)))
pn = self.Nc(T, symbolic=False) * self.Nv(T, symbolic=False) * mp.exp(
self.__to_numeric(-Eg / (k * T))) * 1e-12
# print pn
N = 0
for dopant in self.dopants:
N += dopant.concentration(z)
N *= 1e-6
# print N
mobility = {'mobility_e': {'mu_L': 0, 'mu_I': 0, 'mu_ccs': 0, 'mu_tot': 0},
'mobility_h': {'mu_L': 0, 'mu_I': 0, 'mu_ccs': 0, 'mu_tot': 0}}
for key in mobility.keys():
mu_L = self.reference[key]['mu_L0'] * (T / 300.0) ** (-self.reference[key]['alpha'])
mu_I = (self.reference[key]['A'] * (T ** (3 / 2)) / N) / (
mp.log(1 + self.reference[key]['B'] * (T ** 2) / N) - self.reference[key]['B'] * (T ** 2) / (
self.reference[key]['B'] * (T ** 2) + N))
try:
mu_ccs = (2e17 * (T ** (3 / 2)) / mp.sqrt(pn)) / (mp.log(1 + 8.28e8 * (T ** 2) * (pn ** (-1 / 3))))
X = mp.sqrt(6 * mu_L * (mu_I + mu_ccs) / (mu_I * mu_ccs))
except:
mu_ccs = np.nan
X = 0
# print X
mu_tot = mu_L * (1.025 / (1 + ((X / 1.68) ** (1.43))) - 0.025)
Field_coeff = (1 + (mu_tot * E * 1e-2 / self.reference[key]['v_s']) ** self.reference[key]['beta']) ** (
-1 / self.reference[key]['beta'])
mobility[key]['mu_L'] = mu_L * 1e-4
mobility[key]['mu_I'] = mu_I * 1e-4
mobility[key]['mu_ccs'] = mu_ccs * 1e-4
mobility[key]['mu_tot'] = mu_tot * 1e-4 * Field_coeff
return mobility
def generate_log_moments(N, max_lambda, noise_scale, lot_size):
# print('generating log moments')
L = lot_size
q = 1.0 * L / N
# these moments are a function of q, noise_scale and max_lambda
# generate pdfs which are to be integrated numerically
pdf1 = lambda x: pdf_gauss(x, noise_scale, mp.mpf(0))
pdf2 = lambda x: (1 - q) * pdf_gauss(x, noise_scale, mp.mpf(0)) + \
q * pdf_gauss(x, noise_scale, mp.mpf(1))
# placeholder for alpha_M(lambda) for each iteration
alpha_M_lambda = np.zeros(max_lambda)
for lambda_val in range(1, max_lambda + 1):
# it isn't defined which dataset is D and which is D' - thus consider both and take the maximum
I1_func, I2_func = get_I1_I2_lambda(lambda_val, pdf1, pdf2)
I1_val = integral_inf_mp(I1_func)
I2_val = integral_inf_mp(I2_func)
if I1_val > I2_val:
alpha_M_lambda[lambda_val - 1] = to_np_float_64(mp.log(I1_val))
else:
alpha_M_lambda[lambda_val - 1] = to_np_float_64(mp.log(I2_val))
return alpha_M_lambda
def BrunTerms(m, n, d, a, x0):
result = (d / m) / (2 * (exp(d / m) - 1)) * X0(m, d, a, x0)**(-2) + w / (
exp(d / m) - 1) * X0(m, d, a, x0)**(-1 / 2) + 2 * vf1(m, n, a) * (
1 + d * a) * (d / m + log(X0(m, d, a, x0) * (1 + d))) / log(
(exp(d / m) - 1) * X0(m, d, a, x0))
#print(round(result,1))
return result
def get_apparent_activation_energy(self,rxn_parameters,epsilon=1e-10):
"""
returns apparent Arrhenius activation energies (in units of R)
for production/consumption of each gas phase species.
Calculated as
E_app = T^2(dlnr_+/dT)=(T^2/r_+)(dr_+/dT), where r+ is the TOF
:param rxn_parameters: reaction paramenters, see solver-base
:param epsilon: degree of pertubation in temperature
:type epsilon: float, optional
"""
current_tofs = self.get_turnover_frequency(rxn_parameters)
current_T = self.temperature
new_T = current_T*(1+epsilon)
dT = new_T-current_T
self.temperature = new_T
descriptors = list(self._rxm.mapper._descriptors) #don't overwrite them, if temperature is a descriptor
if 'temperature' in self._rxm.descriptor_names:
index = self._rxm.descriptor_names.index('temperature')
descriptors[index] = new_T
rxn_parameters_newT = self._rxm.scaler.get_rxn_parameters(descriptors)
new_tofs = self.get_turnover_frequency(rxn_parameters_newT)
E_apps = []
R = 8.31447e-3/96.485307#units of eV
for i,gas in enumerate(self.gas_names):
barriers_i = []
dlnTOF = mp.log(new_tofs[i])-mp.log(current_tofs[i]) #this will fail if any of the TOFs are 0.
E_app = R*float(dlnTOF.real)/dT*(current_T**2)
E_apps.append(E_app)
self.temperature = current_T
self._apparent_activation_energy = E_apps
#self.get_turnover_frequency(rxn_parameters)
print E_apps
return E_apps
def gaussian_logx_given_r(r, sigma, n_dim):
"""
Returns logx coordinate corresponding to r values for a Gaussian prior with
the specificed standard deviation and dimension
Uses mpmath package for arbitary precision.
Parameters
----------
r: float or numpy array
Radial coordinates at which to evaluate logx.
sigma: float
Standard deviation of Gaussian.
n_dim: int
Number of dimensions.
Returns
-------
logx: float or numpy array
Logx coordinates corresponding to input radial coordinates.
"""
exponent = 0.5 * (r / sigma) ** 2
if isinstance(r, np.ndarray): # needed to ensure output is numpy array
logx = np.zeros(r.shape)
for i, expo in enumerate(exponent):
logx[i] = float(mpmath.log(mpmath.gammainc(n_dim / 2., a=0, b=expo,
regularized=True)))
return logx
else:
return float(mpmath.log(mpmath.gammainc(n_dim / 2., a=0, b=exponent,
regularized=True)))
def jamieson_hb():
max_iter = 1121 # maximum iterations/epochs per configuration
eta = 3 # defines downsampling rate (default=3)
logeta = lambda x: mpmath.log(x) / mpmath.log(eta)
s_max = int(
logeta(max_iter)
) # number of unique executions of Successive Halving (minus one)
B = (
s_max + 1
) * max_iter # total number of iterations (without reuse) per execution of Succesive Halving (n,r)
#### Begin Finite Horizon Hyperband outlerloop. Repeat indefinetely.
for s in reversed(range(s_max + 1)):
n = int(ceil(int(B / max_iter / (s + 1)) *
eta**s)) # initial number of configurations
r = max_iter * eta**(
-s) # initial number of iterations to run configurations for
#### Begin Finite Horizon Successive Halving with (n,r)
T = [get_random_hyperparameter_configuration() for i in range(n)]
print(
f"{'=' * 90}\n>> Generated {n} arms and evaluated with TPE for {r} resources\n"
)
for i in range(s + 1):
# Run each of the n_i configs for r_i iterations and keep best n_i/eta
n_i = n * eta**(-i)
r_i = r * eta**(i)
val_losses = [
run_then_return_val_loss(num_iters=r_i, hyperparameters=t)
for t in T
]
print(
f"** Evaluated {len(val_losses)} arms (n_i is {n_i}), each with {r_i:.2f} resources"
)
T = [T[i] for i in np.argsort(val_losses)[0:int(n_i / eta)]]
def getRobbinsConstant( ):
robbins = fsub( fsub( fadd( 4, fmul( 17, sqrt( 2 ) ) ), fmul( 6, sqrt( 3 ) ) ), fmul( 7, pi ) )
robbins = fdiv( robbins, 105 )
robbins = fadd( robbins, fdiv( log( fadd( 1, sqrt( 2 ) ) ), 5 ) )
robbins = fadd( robbins, fdiv( fmul( 2, log( fadd( 2, sqrt( 3 ) ) ) ), 5 ) )
return robbins
def pdf(x, df, nc):
"""
Probability density function of the noncentral t distribution.
The infinite series is estimated with `mpmath.nsum`.
"""
with mpmath.extradps(5):
x = mpmath.mpf(x)
df = mpmath.mpf(df)
nc = mpmath.mpf(nc)
if x == 0:
logp = (-nc**2 / 2 - mpmath.log(mpmath.pi) / 2 -
mpmath.log(df) / 2 + mpmath.loggamma(
(df + 1) / 2) - mpmath.loggamma(df / 2))
p = mpmath.exp(logp)
else:
logc = (df * mpmath.log(df) / 2 - nc**2 / 2 -
mpmath.loggamma(df / 2) - mpmath.log(mpmath.pi) / 2 -
(df + 1) / 2 * mpmath.log(df + x**2))
c = mpmath.exp(logc)
def _pdf_term(i):
logterm = (mpmath.loggamma(
(df + i + 1) / 2) + i * mpmath.log(x * nc) +
i * mpmath.log(2 / (df + x**2)) / 2 -
mpmath.loggamma(i + 1))
return mpmath.exp(logterm).real
s = mpmath.nsum(_pdf_term, [0, mpmath.inf])
p = c * s
return p
def polyfit_erfc(nroots, x, low):
t = x
if t > 19682.99:
t = 19682.99
if t > 1.0:
tt = mpmath.log(t) / mpmath.log(3) + 1.0 # log3(t) + 1
else:
tt = mpmath.sqrt(t)
it = int(tt)
tt = tt - it
tt = 2.0 * tt - 1.0 # map [0, 1] to [-1, 1]
u = low * 2 - 1 # map [0, 1] to [-1, 1]
tab_rs, tab_ws = tabulate_erfc(nroots, it)
im = clenshaw_d1(tab_rs.astype(float), u, nroots)
imc = intermediate(im)
rr = clenshaw_d1(imc, tt, nroots)
rr = [r / (1 - r) for r in rr]
im = clenshaw_d1(tab_ws.astype(float), u, nroots)
imc = intermediate(im)
ww = clenshaw_d1(imc, tt, nroots)
return rr, ww
def custom_logsumexp_mpmath(logs, signs):
positive_mask = signs > 0
positive_logs = np.array(logs)[positive_mask]
negative_logs = np.array(logs)[positive_mask == False]
res_pos = mpmath.mpf(0.0)
res_neg = None
if (len(positive_logs) > 0):
res_pos = max(positive_logs) + mpmath.log(
sum([mpmath.exp(i - max(positive_logs)) for i in positive_logs]))
if (len(negative_logs) > 0):
res_neg = max(negative_logs) + mpmath.log(
sum([mpmath.exp(i - max(negative_logs)) for i in negative_logs]))
if (res_neg is None):
return res_pos, 1.0
if (res_pos == res_neg):
print("not enough precision!!!...")
exit(-1)
return None, None
elif (res_pos == res_neg and res_pos == 0):
print("0?!")
print(logs)
exit(-1)
if (res_neg < res_pos):
return res_neg + mpmath.log(mpmath.exp(res_pos - res_neg) - 1), 1.0
else:
return res_pos + mpmath.log(mpmath.exp(res_neg - res_pos) - 1), -1.0
def findGaussianChangePoint(data):
# the denominator. This is the easy part.
N = len(data)
if N < 6: return None # can't find a cp in data this small
# set up gamma function table
#for i in range(N):
s2 = mpf(data.var())
gpart = gamma(mpf(N) / 2.0 - 1)
denom = (pi**1.5) * mpf((N * s2))**(-N / 2.0 + 0.5) * gpart
# the numerator. A little trickier.
# calc_twostate_weights() already deals with ts<3 and ts>N-2.
weights = calc_twostate_weights(data)
if weights is None: return None
num = 2.0**2.5 * abs(data.mean()) * weights.mean()
logodds = log(num) - log(denom)
print "num:", num, "log num:", log(
num), "| denom:", denom, "log denom:", log(
denom), "|| log odds:", logodds
# If there is a change point, then logodds will be greater than 0
if logodds < 0:
return None
return (weights.argmax(), logodds)
def mp_fast_logsumexp(X, coeffs=None):
"""fast_logsumexp for high precision numbers using mpmath.
Parameters
----------
X : ndarray
Terms inside logs.
coeffs : ndarray
Factors in front of exponentials.
Returns
-------
float
Value of magnitude of quantity inside log (the sum of exponentials).
float
Sign.
"""
Xmx = max(X)
if coeffs is None:
y = sum(map(mp.exp, X - Xmx))
else:
y = np.array(coeffs).dot(list(map(mp.exp, X - Xmx)))
if y < 0:
return mp.log(abs(y)) + Xmx, -1.
return mp.log(y) + Xmx, 1.
def log_likelihood(self,
data,
shape,
loc,
scale,
dx='1e-10',
precision=100):
"""
Calculates log-likelihood.
Parameters
----------
data : float or array_like
shape : float
loc : float
scale : float
dx : str, optional
precision : int, optional
"""
with mpmath.workdps(precision):
# Make sure passed values are valid
data = self.check_support(data, shape, loc, scale, dx, precision)
if np.isscalar(data):
return mpmath.log(
self.pdf(data, shape, loc, scale, dx, precision))
else:
return mpmath.fsum([
mpmath.log(self.pdf(_x, shape, loc, scale, dx, precision))
for _x in data
])
def set_precision_parameters(self):
r = numpy.min(self.shape)
m, n = self.shape
zeta = float(
(2*numpy.sqrt(-m*n*log(self.delta))) -
(2*log(self.delta)) + (m*n)
)
printd('r: {r}\nm: {m}\nn: {n}\nzeta: {z}',
level=6, r=r, m=m, n=n, z=zeta)
self.precision_parameters = dict()
''' Alpha as defined in Theorm 2. p8. equation 1
'''
self.precision_parameters['alpha'] = (
(generalised_harmonic_sum(r)+generalised_harmonic_sum(r, 0.5)
)*pow(self.query_sup, 2) +
2*generalised_harmonic_sum(r)*self.query_sup*self.sensitivity
)
''' Beta as defined in Theorm 2. p8. equation 1
'''
self.precision_parameters['beta'] = (
2*pow(n*m, 0.25)*zeta*generalised_harmonic_sum(r)*self.sensitivity
)
''' Omega as defined in Theorm 3. p12. equation 8
'''
self.precision_parameters['omega'] = (
4*generalised_harmonic_sum(r)*self.query_sup*self.sensitivity
)
def dpint(f,snr): '''Integrand of the detection probability of single sources. Since it contains a modified Bessel function, which gets very big values, it has to be defined in a special way.''' big=mpmath.log(mpmath.besseli(1,snr*np.sqrt(2.*f))) small=mpmath.mpf(-f-0.5*snr**2.) normal=mpmath.log(np.sqrt(2.*f)*1./snr) result=mpmath.exp(mpmath.fsum([big,small,normal])) return float(result) #In the end the result should be between 0 and some sizeable number, so a float should be enough.
def _w_tilde(self, u_bar):
"""Compute w_tilde, the threshold for the word-length w such that
MSB = computeNaiveMSB if w >= w_tilde
MSB = computeNaiveMSB+1 if w < w_tilde
(this doesn't count into account the roundoff error, as in FxPF)
See ARITH26 paper
Parameters:
- u_bar: vector of bounds on the inputs of the system
Returns: a vector of thresholds w_tilde
We use: w_tilde = 1 + ceil(log2(zeta_bar)) - floor(log2( 2^ceil(log2(zeta_bar)) - zeta_bar ))
with zeta_bar = <<Hzeta>>.u_bar
"""
#TODO: test if zeta_bar is a power of 2 (should be +Inf in that case)
zeta_bar = self.Hzeta.WCPG() * u_bar
with mpmath.workprec(500): # TODO: compute how many bit we need !!
wtilde = [
int(1 + mpmath.ceil(mpmath.log(x[0], 2)) - mpmath.floor(
mpmath.log(
mpmath.power(2, mpmath.ceil(mpmath.log(x[0], 2))) -
x[0], 2))) for x in zeta_bar.tolist()
]
return wtilde
def getSuperRootsOperator(n, k):
'''Returns all the super-roots of n, not just the nice, positive, real one.'''
k = fsub(k, 1)
factors = [fmul(i, root(k, k)) for i in unitroots(int(k))]
base = root(fdiv(log(n), lambertw(fmul(k, log(n)))), k)
return [fmul(i, base) for i in factors]
def genenergies(fnR,fnQ,seqsR,seqsQ,gamma,sQ,sR,R0): #Parses seqs and model type then calculates and returns energies R is transcription factor, Q is RNAP
ematR = np.genfromtxt(fnR,skiprows=1)
ematQ = np.genfromtxt(fnQ,skiprows=1)
fR = open(fnR)
fQ = open(fnQ)
mattype = fR.read()[:6] #mattype must be the same
#mattypeQ = fQ.read()[:6]
energies = np.zeros(len(seqsQ))
N = len(seqsQ)
mut_region_lengthQ = len(seqsQ[0])
mut_region_lengthR = len(seqsR[0])
if mattype == '1Point':
for i,s in enumerate(seqsR):
seq_matR = seq2mat(s)
seq_matQ = seq2mat(seqsQ[i])
RNAP = (seq_matQ*ematQ).sum()*sQ
TF = (seq_matR*ematR).sum()*sR + R0
energies[i] = -RNAP + mp.log(1 + mp.exp(-TF - gamma)) - mp.log(1 + mp.exp(-TF))
'''
elif mattype == '2Point':
for i,s in enumerate(seqs):
seq_mat = np.zeros(round(sp.misc.comb(mut_region_length,2))*16)
seq_mat[seq2mat2(s)] = 1
energies[i] = (seq_mat*(emat.ravel())).sum()
elif mattype == '3Point':
for i,s in enumerate(seqs):
seq_mat = np.zeros(round(sp.misc.comb(mut_region_length,3))*64)
seq_mat[seq2mat3(s)] = 1
energies[i] = (seq_mat*(emat.ravel())).sum()
'''
return energies
def get_apparent_activation_energy(self,rxn_parameters,epsilon=1e-10):
"""
returns apparent Arrhenius activation energies (in units of R)
for production/consumption of each gas phase species.
Calculated as
E_app = T^2(dlnr_+/dT)=(T^2/r_+)(dr_+/dT), where r+ is the TOF
:param rxn_parameters: reaction paramenters, see solver-base
:param epsilon: degree of pertubation in temperature
:type epsilon: float, optional
"""
current_tofs = self.get_turnover_frequency(rxn_parameters)
current_T = self.temperature
new_T = current_T*(1+epsilon)
dT = new_T-current_T
self.temperature = new_T
descriptors = list(self._rxm.mapper._descriptors) #don't overwrite them, if temperature is a descriptor
if 'temperature' in self._rxm.descriptor_names:
index = self._rxm.descriptor_names.index('temperature')
descriptors[index] = new_T
rxn_parameters_newT = self._rxm.scaler.get_rxn_parameters(descriptors)
new_tofs = self.get_turnover_frequency(rxn_parameters_newT)
E_apps = []
R = 8.31447e-3/96.485307#units of eV
for i,gas in enumerate(self.gas_names):
barriers_i = []
dlnTOF = mp.log(new_tofs[i])-mp.log(current_tofs[i]) #this will fail if any of the TOFs are 0.
E_app = R*float(dlnTOF.real)/dT*(current_T**2)
E_apps.append(E_app)
self.temperature = current_T
self._apparent_activation_energy = E_apps
#self.get_turnover_frequency(rxn_parameters)
print(E_apps)
return E_apps
def lnProb_rhoA2rhoB2_given_rhoA2orhoB2o( rhoA2, rhoB2, rhoA2o, rhoB2o ):
'''
return ln( p(rhoA2,rhoB2|rhoA2o,rhoB2o) )
NOTE: essentially 2 independent chi2 distributions
'''
types = (int,float)
if isinstance(rhoA2, types) and isinstance(rhoB2, types) \
and isinstance(rhoA2o, types) and isinstance(rhoB2o, types):
return np.log(0.25) - 0.5*(rhoA2 + rhoB2 + rhoA2o + rhoB2o) \
+ float(mpmath.log(mpmath.besseli(0, (rhoA2*rhoA2o)**0.5))) \
+ float(mpmath.log(mpmath.besseli(0, (rhoB2*rhoB2o)**0.5)))
else:
N = len(rhoA2)
assert N==len(rhoB2), 'rhoA2 and rhoB2 do not have the same length'
assert N==len(rhoA2o), 'rhoA2 and rhoA2o do not have the same length'
assert N==len(rhoB2o), 'rhoA2 and rhoB2o do not have the same length'
log25 = np.log(0.25)
ans = [log25 - 0.5*(rhoa2 + rhob2 + rhoa2o + rhob2o) \
+ float(mpmath.log(mpmath.besseli(0, (rhoa2*rhoa2o)**0.5))) \
+ float(mpmath.log(mpmath.besseli(0, (rhob2*rhob2o)**0.5))) \
for rhoa2, rhob2, rhoa2o, rhob2o in zip(rhoA2, rhoB2, rhoA2o, rhoB2o)
]
if isinstance(rhoA2, np.ndarray) or isinstance(rhoB2, np.ndarray) or isinstance(rhoA2o, np.ndarray) or isinstance(rhoB2o, np.ndarray):
ans = np.array(ans)
ans[ans!=ans] = -np.infty ### get rid of nans
### FIXME we may want to be smarter about this and
### prevent nans from showing up in the first place
return ans
def getRobbinsConstant( ):
robbins = fsub( fsub( fadd( 4, fmul( 17, sqrt( 2 ) ) ), fmul( 6, sqrt( 3 ) ) ), fmul( 7, pi ) )
robbins = fdiv( robbins, 105 )
robbins = fadd( robbins, fdiv( log( fadd( 1, sqrt( 2 ) ) ), 5 ) )
robbins = fadd( robbins, fdiv( fmul( 2, log( fadd( 2, sqrt( 3 ) ) ) ), 5 ) )
return robbins
def _compute_eps(lam):
session = WolframLanguageSession(wlpath)
session.evaluate(
wlexpr('''
randomgamma[alpha_, beta_, gamma_, samples_] := RandomVariate[GammaDistribution[alpha, beta, gamma, 0], samples];
'''))
random_gamma = session.function(wlexpr('randomgamma'))
session.evaluate(
wlexpr('''
integrant[exponents_, beta_, dimension_, clippingbound_, lam_, r_, q_] := Mean[NIntegrate[
(Sin[x]^(dimension-2)*Gamma[dimension/2]/(Sqrt[Pi]*Gamma[(dimension-1)/2]))*(((1-q)*(1-q+
q*Exp[(r^exponents-(r^2+clippingbound^2-2*r*clippingbound*Cos[x])^(exponents/2))/beta])^(lam))
+(q*(1-q+q*Exp[((r^2+clippingbound^2+2*r*clippingbound*Cos[x])^(exponents/2)-r^exponents)/beta])^(lam))),{x,0,Pi}
]];
'''))
integrant_moment = session.function(wlexpr('integrant'))
samples = random_gamma(FLAGS.dimension / FLAGS.exponents,
beta**(1 / FLAGS.exponents), FLAGS.exponents,
FLAGS.num_samples)
moment = integrant_moment(FLAGS.exponents, beta, FLAGS.dimension,
FLAGS.clippingbound, lam, samples, FLAGS.q)
eps = (FLAGS.T * mp.log(moment) + mp.log(1 / FLAGS.delta)) / lam
session.terminate()
return eps
def integral(pos, shift, poles):
"""
Returns the inner product of two monic monomials with respect to the
positive measure prefactor that turns a `PolynomialVector` into a rational
approximation to a conformal block.
"""
single_poles = []
double_poles = []
ret = mpmath.mpf(0)
for p in poles:
p = mpmath.mpf(str(p))
if (p - shift) in single_poles:
single_poles.remove(p - shift)
double_poles.append(p - shift)
elif (p - shift) < 0:
single_poles.append(p - shift)
for i in range(0, len(single_poles)):
denom = mpmath.mpf(1)
pole = single_poles[i]
other_single_poles = single_poles[:i] + single_poles[i + 1:]
for p in other_single_poles:
denom *= pole - p
for p in double_poles:
denom *= (pole - p)**2
ret += (mpmath.mpf(1) / denom) * (rho_cross**pole) * (
(-pole)**pos) * mpmath.factorial(pos) * mpmath.gammainc(
-pos, a=pole * mpmath.log(rho_cross))
for i in range(0, len(double_poles)):
denom = mpmath.mpf(1)
pole = double_poles[i]
other_double_poles = double_poles[:i] + double_poles[i + 1:]
for p in other_double_poles:
denom *= (pole - p)**2
for p in single_poles:
denom *= pole - p
# Contribution of the most divergent part
ret += (mpmath.mpf(1) /
(pole * denom)) * ((-1)**(pos + 1)) * mpmath.factorial(pos) * (
(mpmath.log(rho_cross))**(-pos))
ret -= (mpmath.mpf(1) / denom) * (rho_cross**pole) * (
(-pole)**(pos - 1)) * mpmath.factorial(pos) * mpmath.gammainc(
-pos, a=pole *
mpmath.log(rho_cross)) * (pos + pole * mpmath.log(rho_cross))
factor = 0
for p in other_double_poles:
factor -= mpmath.mpf(2) / (pole - p)
for p in single_poles:
factor -= mpmath.mpf(1) / (pole - p)
# Contribution of the least divergent part
ret += (factor / denom) * (rho_cross**pole) * (
(-pole)**pos) * mpmath.factorial(pos) * mpmath.gammainc(
-pos, a=pole * mpmath.log(rho_cross))
return (rho_cross**shift) * ret
def eta(lam):
"""Function from DLMF 8.12.1 shifted to be centered at 0."""
if lam > 0:
return mp.sqrt(2*(lam - mp.log(lam + 1)))
elif lam < 0:
return -mp.sqrt(2*(lam - mp.log(lam + 1)))
else:
return 0
def S4(m, s):
dZD = lambda t: (
(5 - 2 * s) * A * log(t)**(4 - 2 * s) * t**
(8 / 3 * (1 - s) - 1) + A * log(t)**(5 - 2 * s) *
(8 / 3 * (1 - s)) * t**(8 / 3 *
(1 - s) - 1) + 2 * B * log(t) / t) / t**(m + 1)
#return 2*ZD(s, H)/H**(m + 1) #simplified expression for optimising with higher Riemann height
return ZD(s, H) / H**(m + 1) + sum(list(quad(dZD, H, inf)))
def wme_gen(f, pYs_p, pZs_p, X, alpha, g_p, delta=0):
# convert probabilities to mpmath.mpf
pYs = [{k: mpmath.mpmathify(pY[k]) for k in pY} for pY in pYs_p]
pZs = [{k: mpmath.mpmathify(pZ[k]) for k in pZ} for pZ in pZs_p]
g = {w: {y: mpmath.mpmathify(g_p[w][y]) for y in g_p[w]} for w in g_p}
delta = mpmath.mpmathify(delta)
# precondition
# bypass precondition if number of arguments == 0, i.e. if f is defined as a function of another function
if len(X) + len(pYs) + len(pZs) != len(inspect.getargspec(f)[0]) and len(
inspect.getargspec(f)[0]) != 0:
sys.exit(
"Aborted: Number of function arguments and inputs didn't match")
if len(inspect.getargspec(f)[0]) == 0:
try:
a = f(*((0, ) * (len(X) + len(pYs) + len(pZs))))
except KeyError:
# here we tolerate KeyError because merged functions might not recognise input (0, 0, ...)
pass
except:
sys.exit(
"Aborted: Number of function arguments and inputs didn't match"
)
# joint distribution for Output and Y
pOaY = dict()
for Y in itertools.product(*pYs):
for Z in itertools.product(*pZs):
o = f(*(X + Y + Z))
p_o = prod((pYZ[yz] for (yz, pYZ) in zip(Y + Z, pYs + pZs)))
# critical for distributions with a zero probability!
# next line ensures that only possible events appear in pO (the if)
if p_o > 0:
if o in pOaY:
if Y in pOaY[o]:
pOaY[o][Y] += p_o
else:
pOaY[o][Y] = p_o
else:
pOaY[o] = {Y: p_o}
# W[o] is the vector inside the norm (over guesses w)
W = dict()
for o in pOaY:
W[o] = [
sum(pOaY[o][Y] * g[w][Y] for Y in g[w] if Y in pOaY[o]) + delta
for w in g
]
if alpha == -1:
sum_o = sum(max(W[o]) for o in pOaY)
result = -mpmath.log(sum_o, b=2)
else:
sum_o = sum(p_norm(W[o], alpha) for o in pOaY)
result = (alpha / (1 - alpha)) * mpmath.log(sum_o, b=2)
return result
def redistill(distillate_filename, out_filename, expected_dps=60,
newton_steps=7,
min_model_digits=None):
"""Second-distills a distillate."""
if mpmath.mp.dps < expected_dps:
raise RuntimeError(
'Precision setting for mpmath is below the expected dps '
'for this calculation: %s < %s' % (mpmath.mp.dps, expected_dps))
# Tries to find out if there are further opportunities that reduce the number
# of parameters which have been missed in 1st distillation, and if so,
# performs the corresponding reduction.
# In any case, adds basic information about physics.
distillate_model = read_distillate_model(distillate_filename)
v70 = v70_from_model(distillate_model)
if expected_dps > 15:
sinfo0 = scalar_sector_mpmath.mpmath_scalar_manifold_evaluator(v70)
else:
sinfo0 = scalar_sector.numpy_scalar_manifold_evaluator(v70)
threshold_deviation = (max(3 * sinfo0.stationarity, 1e-7)
if expected_dps >= 40 else 1e-3)
# First-distillation produced a high-accuracy form of the numerical
# solution, so we should use a stricter check here.
def still_good(v70_trial):
sinfo = scalar_sector.numpy_scalar_manifold_evaluator(v70_trial)
return (abs(sinfo0.potential - sinfo.potential) < threshold_deviation and
sinfo.stationarity < threshold_deviation)
# This is strongly expected to work, given that we already had highly
# accurate data.
low_dim_model_take2 = iter(find_simple_low_dimensional_model(
[v70],
min_digits=max(3, min_model_digits or int(
-mpmath.log(sinfo0.stationarity, 10)) // 2 - 2),
still_good=still_good)).next()
if len(low_dim_model_take2.params) < len(distillate_model.params):
print('Note: Could further reduce the number of model parameters '
'({} -> {}).'.format(distillate_model.params,
low_dim_model_take2.params))
model_take2, mdnewton_ok = distill_model(
low_dim_model_take2,
newton_steps=newton_steps,
still_good=still_good,
target_digits_position=expected_dps)
v70_accurate = v70_from_model(model_take2)
sinfo_accurate = scalar_sector_mpmath.mpmath_scalar_manifold_evaluator(
v70_accurate)
stationarity = sinfo_accurate.stationarity
log10_stationarity = math.floor(mpmath.log(stationarity, 10))
approx_stationarity_str = (
'%.3fe%d' %
(float(stationarity *
mpmath.mpf(10)**(-log10_stationarity)),
log10_stationarity))
with open(out_filename, 'w') as h:
write_model(h, model_take2,
dict(mdnewton_ok=mdnewton_ok,
potential=str(sinfo_accurate.potential),
stationarity=approx_stationarity_str))
def mpmsb(value, signed):
if isinstance(value, Interval):
return np.max([mpmsb(value.lower_bound, signed=signed),
mpmsb(value.upper_bound, signed=signed)])
if value > 0:
return int(mpmath.floor(mpmath.log(value, 2))) + int(signed)
if value < 0:
return int(mpmath.ceil(mpmath.log(-value, 2)))
return -np.inf
def compute_similarity(partitions_themes, similarity='KLDivergence'):
"""
Third step of the Temporal Text Mining algorithm. Receives the distribution of all themes in two partitions.
Computes and returns the similarity between all the themes.
:param partitions_themes: Contains the distribution of all themes in the partitions.
:type list
:param similarity: Specifies which similarity measure to use
:type str
:return: Returns the computed similarities between all the themes.
:rtype: list
"""
# Declare the similarity matrix to store the computed similarities
similarity_matrix = []
# Compute the similarities between all the themes
for theme1_index, theme1 in enumerate(partitions_themes[0]):
# Creates a new line in the matrix
similarity_matrix.append([])
for theme2_index, theme2 in enumerate(partitions_themes[1]):
# If the similarity is KL-Divergence
if similarity == 'KLDivergence':
vocabulary_size = len(theme1)
klDivergence = 0
for word_index in range(vocabulary_size):
klDivergence += theme2[word_index]*math.log(theme2[word_index]/theme1[word_index])
similarity_matrix[theme1_index].append(1/klDivergence)
# If the similarity is Jensen-Shanon Divergence (JSD)
if similarity == 'JSDivergence':
vocabulary_size = len(theme1)
jsDivergence = 0
for word_index in range(vocabulary_size):
jsDivergence += (0.5*theme1[word_index]*math.log(theme1[word_index]/theme2[word_index]) +
0.5*theme2[word_index]*math.log(theme2[word_index]/theme1[word_index]))
similarity_matrix[theme1_index].append(1/jsDivergence)
# If the similarity is the support of the distributions
if similarity == 'support':
# Compute the support of each theme distribution
threshold = 0.001
theme1_support = (theme1 > threshold)
theme2_support = (theme2 > threshold)
# Compute and store the similarity between the distributions' support
support_similarity = sum((theme1_support & theme2_support))
similarity_matrix[theme1_index].append(support_similarity)
# Returns the computed similarities between all the themes.
return similarity_matrix
def pqCandidates(z, w = w):
PiI = mpmath.pi * 1j
if abs(1 - z) < globalsettings.getSetting("maximalError"):
return (z, 0, 0), 1
p = mpmathRoundToInt( (w.w0 - mpmath.log( z)) / PiI)
q = mpmathRoundToInt( (w.w1 + mpmath.log(1-z)) / PiI)
err = abs(w.w2 + mpmath.log(z) - mpmath.log(1-z) + p * PiI + q * PiI)
return (z, p, q), err
def logOfSquare(c):
return mpmath.log(c)
csquare = c * c
maxErr = globalsettings.getSetting("maximalError")
if not ((csquare.real > 0 or
abs(csquare.imag) > maxErr)):
raise NumericalError(c, msg = "logOfSqaure near branch cut")
return mpmath.log(csquare) / 2
def my_secant(eq, p1, p2, debug=False):
tol = mp.mpf(0.1)
max_count = 10000
sol = 0
for count in range(max_count):
if debug: print (count + 1), ''
if p1 == p2:
sol = p1
break
y1 = eq(p1)
y2 = eq(p2)
if debug: print '-->', p1, '->', y1
if debug: print '-->', p2, '->', y2
if abs(y1) < abs(y2):
sol = p1
err = abs(y1)
else:
sol = p2
err = abs(y2)
if err < tol:
break
if mp.sign(y1) * mp.sign(y2) < 0:
# p3 = (p1+p2)/mpf(2)
x1 = mp.log(p1)
x2 = mp.log(p2)
# x1 = p1
# x2 = p2
# x3 = (x2*y1 - x1*y2)/(y1-y2)
# if x3 == x1 or x3 == x2:
x3 = (x1 + x2) / mp.mpf(2)
p3 = mp.exp(x3)
# p3 = x3
if p3 == p1 or p3 == p2:
break
y3 = eq(p3)
if debug: print '--->', x1, x2, x3, p3, '->', y3
if mp.sign(y3) == mp.sign(y1):
p1 = p3
else:
p2 = p3
elif mp.sign(y1) * mp.sign(y2) == 0:
if y1 == 0:
sol = p1
elif y2 == 0:
sol = p2
else:
raise Exception('Strange: sign returns zero! without zeros $)')
break
else:
raise Exception('Functin has same sign on both ends')
if debug: print 'Solution:', sol
return sol
def energy(self, clustering):
energy = mpmath.mpf(0.0)
new_vertex_distributions = _combine_vertex_distributions_given_clustering(
self.vertex_distributions, clustering)
# likelihood
likelihood_energy = -self._log_likelihood(clustering, new_vertex_distributions)
# prior on similarity:
# We prefer the cluster whose minimum similarity is large.
# - the similarity of a pair of vertexes is measured by the similarity
# of top 10 words in the distribution. (measure each word type
# respectively and take average)
intra_cluster_energy = mpmath.mpf(0.0)
for cluster_id, cluster_vertex_set in enumerate(clustering):
min_similarity_within_cluster = self._min_similarity_within_cluster(cluster_vertex_set, new_vertex_distributions[cluster_id])
intra_cluster_energy += -mpmath.log(mpmath.exp(min_similarity_within_cluster - 1))
# Between cluster similarity:
# - For each pair of clusters, we want to find the pair of words with maximum similarity
# and prefer this similarity value to be small.
inter_cluster_energy = mpmath.mpf(0.0)
if len(clustering) > 1:
for i in range(0, len(clustering)-1):
for j in range(i+1, len(clustering)):
max_similarity_between_clusters = self._max_similarity_between_clusters(clustering[i], clustering[j])
inter_cluster_energy += -mpmath.log(mpmath.exp(-max_similarity_between_clusters))
# prior on clustering complexity: prefer small number of clusters.
length_energy = -mpmath.log(mpmath.exp(-len(clustering)))
# classification: prefer small number of categories.
class_energy = 0.0
if self._classifier is not None:
num_classes = self._calculate_num_of_categories(clustering, new_vertex_distributions)
class_energy = -mpmath.log(mpmath.exp(-(abs(num_classes-len(clustering)))))
# classification confidence: maximize the classification confidence
confidence_energy = 0.0
for cluster_id, cluster_vertex_set in enumerate(clustering):
(category, confidence) = self._predict_label(new_vertex_distributions[cluster_id])
confidence_energy += -mpmath.log(confidence)
energy += (0.5)*likelihood_energy + intra_cluster_energy + inter_cluster_energy + 30.0*length_energy + 20.0*class_energy + confidence_energy
logging.debug('ENERGY: {0:12.6f}\t{1:12.6f}\t{2:12.6f}\t{3:12.6f}\t{4:12.6f}\t{5:12.6f}'.format(
likelihood_energy.__float__(),
intra_cluster_energy.__float__(),
inter_cluster_energy.__float__(),
length_energy.__float__(),
class_energy.__float__(),
confidence_energy.__float__()))
return energy
def findGaussianChangePoint( data, gammatable ): N = len( data ) if N<6 : return None # can't find a cp in data this small # the denominator. This is the easy part. denom = (pi**1.5) * mpf(( N*data.var() ))**( -N/2.0 + 0.5 ) * gammatable[N] # BEGIN weight calculation # the numerator. A little trickier. weights=[0,0,0] # the change cannot have occurred in the last 3 points data2=data**2 #initialize dataA=data[0:3] ; dataA2=data2[0:3] ; NA = len(dataA) dataB=data[3:] ; dataB2=data2[3:] ; NB = len(dataB) sumA=dataA.sum() ; sumsqA=dataA2.sum() sumB=dataB.sum() ; sumsqB=dataB2.sum() # first data point--this could be done in the loop but it's okay here meanA=sumA/NA ; meansumsqA = sumsqA/NA ; meanA2 = meanA**2 ; sA2=meansumsqA-meanA2 meanB=sumB/NB ; meansumsqB = sumsqB/NB ; meanB2 = meanB**2 ; sB2=meansumsqB-meanB2 wnumf1 = mpf(NA)**(-0.5*NA + 0.5 ) * mpf(sA2)**(-0.5*NA + 1) * gammatable[NA] wnumf2 = mpf(NB)**(-0.5*NB + 0.5 ) * mpf(sB2)**(-0.5*NB + 1) * gammatable[NB] wdenom = (sA2 + sB2) * (meanA2*meanB2) weights.append( (wnumf1*wnumf2)/wdenom ) for i in range( 3, N-3 ): NA += 1 ; NB -= 1 next = data[i] sumA += next ; sumB -= next nextsq = data2[i] sumsqA += nextsq; sumsqB -= nextsq meanA=sumA/NA ; meansumsqA = sumsqA/NA ; meanA2 = meanA**2 ; sA2=meansumsqA-meanA2 meanB=sumB/NB ; meansumsqB = sumsqB/NB ; meanB2 = meanB**2 ; sB2=meansumsqB-meanB2 wnumf1 = mpf(NA)**(-0.5*NA + 0.5 ) * mpf(sA2)**(-0.5*NA + 1) * gammatable[NA] wnumf2 = mpf(NB)**(-0.5*NB + 0.5 ) * mpf(sB2)**(-0.5*NB + 1) * gammatable[NB] wdenom = (sA2 + sB2) * (meanA2*meanB2) weights.append( (wnumf1*wnumf2)/wdenom) weights.extend( [0,0] ) # the change cannot have occurred at the last 2 points weights=array(weights) # END weight calculation num = 2.0**2.5 * abs(data.mean()) * weights.mean() logodds = log( num ) - log( denom ) print "num:", num, "log num:", log(num), "| denom:", denom, "log denom:", log(denom), "|| log odds:", logodds # If there is a change point, then logodds will be greater than 0 if logodds < 0 : return None return ( weights.argmax(), logodds )
def L_function(self):
p = self.p
q = self.q
z = self.z
PiI = mpmath.pi * 1j
val= (
myDilog(z)
+ (mpmath.log(z) + p * PiI) * ( mpmath.log(1 - z) + q * PiI) / 2
- mpmath.pi ** 2 / 6)
if self.sign == -1:
return -val
else:
return val
def lnlhood(self, param):
""" This is the function that evaluates the likelihood at each point in NDIM space
Parameters
----------
param :
Returns
-------
"""
likeit=0
#loop over all the ions
for ii in range(self.nions):
#parity check : make sure data and models are aligned
if(self.data[ii][0] != self.mod_colm_tag[ii]):
raise ValueError('Mismtach between observables and models. This is a big mistake!!!')
#now call the interpolator for models given current ion
mod_columns=self.interpol[ii](param)
#check if upper limit
if(self.data[ii][3] == -1):
#integrate the upper limit of a Gaussian - cumulative distribution
arg=((self.data[ii][1]-mod_columns)/(np.sqrt(2)*self.data[ii][2]))[0]
thislike=mmath.log(0.5+0.5*mmath.erf(arg))
likeit=likeit+float(thislike)
#print self.data[ii][0], float(thislike), self.data[ii][1], mod_columns
#check if lower limit
elif(self.data[ii][3] == -2):
#integrate the lower limit of a Gaussian - Q function
arg=((self.data[ii][1]-mod_columns)/(np.sqrt(2)*self.data[ii][2]))[0]
thislike=mmath.log(0.5-0.5*mmath.erf(arg))
likeit=likeit+float(thislike)
#print self.data[ii][0], float(thislike), self.data[ii][1], mod_columns
#if value, just eval Gaussian
else:
#add the likelihood for this ion
thislike=-1*np.log(np.sqrt(2*np.pi)*self.data[ii][2])-(self.data[ii][1]-mod_columns)**2/(2*self.data[ii][2]**2)
likeit=likeit+thislike
return likeit
def getInvertedBits( n ):
value = real_int( n )
# determine how many groups of bits we will be looking at
if value == 0:
groupings = 1
else:
groupings = int( fadd( floor( fdiv( ( log( value, 2 ) ), g.bitwiseGroupSize ) ), 1 ) )
placeValue = mpmathify( 1 << g.bitwiseGroupSize )
multiplier = mpmathify( 1 )
remaining = value
result = mpmathify( 0 )
for i in range( 0, groupings ):
# Let's let Python do the actual inverting
group = fmod( ~int( fmod( remaining, placeValue ) ), placeValue )
result += fmul( group, multiplier )
remaining = floor( fdiv( remaining, placeValue ) )
multiplier = fmul( multiplier, placeValue )
return result
def kummer_log(a,b,x):
## First try using the funcion in the library.
## If it is 0 or inf then we try to use our own implementation with logs
## If it does not converge, then we return None !!
a = float(a); b = float(b); x = float(x)
# f_scipy = scipy_hyp1f1(a,b,x)
f_mpmath = mpmath.hyp1f1(a,b,x)
f_log = float(mpmath.log(f_mpmath))
if (np.isinf(f_log) == True):
# warnings.warn("hyp1f1() is 'inf', trying log version, (a,b,x) = (%f,%f,%f)" %(a,b,x),UserWarning, stacklevel=2)
f_log = kummer_own_log(a,b,x)
# print f_log
elif(f_mpmath == 0):
# warnings.warn("hyp1f1() is '0', trying log version, (a,b,x) = (%f,%f,%f)" %(a,b,x),UserWarning, stacklevel=2)
raise RuntimeError('Kummer function is 0. Kappa = %f', "Kummer_is_0", x)
# f_log = kummer_own_log(a,b,x) # TODO: We cannot do negative x, the functions is in log
else:
# f_log = np.log(f_scipy)
f_log = f_log
# print (a,b,x)
# print f_log
f_log = float(f_log)
return f_log
def run_gth_solve(A, verbose=0):
"""
gth_solve returns a stochastic vector x such that x A = 0
for an irreducible transition rate matrix A.
"""
if verbose > 1:
print("original matrix (gth_solve):\n", A)
x = mp.gth_solve(A)
if verbose > 1:
print("x\n", x)
eps = mp.exp(0.8 * mp.log(mp.eps)) # test_eigen.py
# x is a solution to x A = 0
err0 = mp.norm(x*A, p=1)
if verbose > 0:
print("|xA| (gth_solve):", err0)
assert err0 < eps
# x is a nonnegative vector
if verbose > 0:
print("min(x) (gth_solve):", min(x))
assert min(x) >= 0 - eps
# 1-norm of x is one
err1 = mp.fabs(mp.norm(x, p=1) - 1)
if verbose > 0:
print("||x| - 1| (gth_solve):", err1)
assert err1 < eps
def run_stoch_eig(P, verbose=0):
"""
stoch_eig returns a stochastic vector x such that x P = x
for an irreducible stochstic matrix P.
"""
if verbose > 1:
print("original matrix (stoch_eig):\n", P)
x = mp.stoch_eig(P)
if verbose > 1:
print("x\n", x)
eps = mp.exp(0.8 * mp.log(mp.eps)) # From test_eigen.py
# x is a left eigenvector of P with eigenvalue unity
err0 = mp.norm(x*P-x, p=1)
if verbose > 0:
print("|xP - x| (stoch_eig):", err0)
assert err0 < eps
# x is a nonnegative vector
if verbose > 0:
print("min(x) (stoch_eig):", min(x))
assert min(x) >= 0 - eps
# 1-norm of x is one
err1 = mp.fabs(mp.norm(x, p=1) - 1)
if verbose > 0:
print("||x| - 1| (stoch_eig):", err1)
assert err1 < eps
def base3int(x):
x = int(x)
exponents = range(int(log(x, 3)), -1, -1)
for e in exponents:
d = int(x // (3 ** e))
x -= d * (3 ** e)
yield d
def gauss_warp_arb(X, l1, l2, lw, x0):
r"""Warps the `X` coordinate with a Gaussian-shaped divot.
.. math::
l = l_1 - (l_1 - l_2) \exp\left ( -4\ln 2\frac{(X-x_0)^2}{l_{w}^{2}} \right )
Parameters
----------
X : :py:class:`Array`, (`M`,) or scalar float
`M` locations to evaluate length scale at.
l1 : positive float
Global value of the length scale.
l2 : positive float
Pedestal value of the length scale.
lw : positive float
Width of the dip.
x0 : float
Location of the center of the dip in length scale.
Returns
-------
l : :py:class:`Array`, (`M`,) or scalar float
The value of the length scale at the specified point.
"""
if isinstance(X, scipy.ndarray):
if isinstance(X, scipy.matrix):
X = scipy.asarray(X, dtype=float)
return l1 - (l1 - l2) * scipy.exp(-4.0 * scipy.log(2.0) * (X - x0)**2.0 / (lw**2.0))
else:
return l1 - (l1 - l2) * mpmath.exp(-4.0 * mpmath.log(2.0) * (X - x0)**2.0 / (lw**2.0))
def makeMeasOneDot_lognorm(func, xdot, b:list, c:dict, Ve=[]):
"""
MPMATH+CAPABLE
:param func: векторная функция
:param expplan: план эксперимента (список значений вектора x)
:param b: вектор b
:param c: вектор c
:param Ve: ковариационная матрица (np.array)
:param n: объём выборки y
:param outfilename: имя выходного файла, куда писать план
:param listOfOutvars: список выносимых переменных
:return: список экспериментальных данных в формате списка словарей 'x':..., 'y':...
"""
y=func(xdot,b,c) #вернёт mpm.matrix
if y is None: #если функция вернула чушь, то в measdata её не записывать!
return None
#Внесём возмущения:
if Ve is not None:
ydisps=np.diag(Ve)
for k in range(len(y)):
#y[k]=random.normalvariate(y[k], math.sqrt(ydisps[k]))
y[k]=math.exp( random.normalvariate(np.longdouble ( mpm.log(y[k])), math.sqrt(ydisps[k])))
return y
def test_beta():
np.random.seed(1234)
b = np.r_[np.logspace(-200, 200, 4),
np.logspace(-10, 10, 4),
np.logspace(-1, 1, 4),
-1, -2.3, -3, -100.3, -10003.4]
a = b
ab = np.array(np.broadcast_arrays(a[:,None], b[None,:])).reshape(2, -1).T
old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
try:
mpmath.mp.dps = 400
assert_func_equal(sc.beta,
lambda a, b: float(mpmath.beta(a, b)),
ab,
vectorized=False,
rtol=1e-10)
assert_func_equal(
sc.betaln,
lambda a, b: float(mpmath.log(abs(mpmath.beta(a, b)))),
ab,
vectorized=False,
rtol=1e-10)
finally:
mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
def log_likelihood(self, document):
log_likelihood = mpmath.mpf(0.0)
for word_type in WORD_TYPES:
for word_id in document.word_ids[word_type]:
if word_id in self._vertex_distribution[word_type]:
log_likelihood += mpmath.log(self._vertex_distribution[word_type][word_id] + 1e-100)
return log_likelihood
def compute_MI_origemcee(seq_matQ,seq_matR,batches,ematQ,ematR,gamma,R_0):
# preliminaries
n_seqs = len(batches)
n_batches = int(batches.max()) + 1 # assumes zero indexed batches
n_bins = 1000
#energies = sp.zeros(n_seqs)
f = sp.zeros((n_batches,n_seqs))
# compute energies
# for i in range(n_seqs):
# energies[i] = sp.sum(seqs[:,:,i]*emat)
# alternate way
energies = np.zeros(n_seqs)
for i in range(n_seqs):
RNAP = (seq_matQ[:,:,i]*ematQ).sum()
TF = (seq_matR[:,:,i]*ematR).sum() + R_0
energies[i] = -RNAP + mp.log(1 + mp.exp(-TF - gamma)) - mp.log(1 + mp.exp(-TF))
# sort energies
inds = sp.argsort(energies)
for i,ind in enumerate(inds):
f[batches[ind],i] = 1.0/n_seqs # batches aren't zero indexed
# bin and convolve with Gaussian
f_binned = sp.zeros((n_batches,n_bins))
for i in range(n_batches):
f_binned[i,:] = sp.histogram(f[i,:].nonzero()[0],bins=n_bins,range=(0,n_seqs))[0]
#f_binned = f_binned/f_binned.sum()
f_reg = sp.ndimage.gaussian_filter1d(f_binned,0.04*n_bins,axis=1)
f_reg = f_reg/f_reg.sum()
# compute marginal probabilities
p_b = sp.sum(f_reg,axis=1)
p_s = sp.sum(f_reg,axis=0)
# finally sum to compute the MI
MI = 0
for i in range(n_batches):
for j in range(n_bins):
if f_reg[i,j] != 0:
MI = MI + f_reg[i,j]*sp.log2(f_reg[i,j]/(p_b[i]*p_s[j]))
print MI
return MI,f_reg
def volume(self):
z = self.z
val = ( mpmath.arg(1 - z) * mpmath.log(abs(z))
+ myDilog(z).imag)
if self.sign == -1:
return -val
else:
return val
def get_prob_poisson(events, length, rate):
""" P(k, lambda = t * rate) = """
avg_events = mpmath.fmul(rate, length) # lambda
prob = mpmath.fmul((-1), avg_events)
for i in range(1, events + 1):
prob = mpmath.fadd(prob, mpmath.log(mpmath.fdiv(avg_events, i)))
prob = mpmath.exp(prob)
return prob
def test_stoch_eig_fp():
P = mp.fp.matrix([[0.9 , 0.075, 0.025],
[0.15, 0.8 , 0.05 ],
[0.25, 0.25 , 0.5 ]])
x_expected = mp.fp.matrix([[0.625, 0.3125, 0.0625]])
x = mp.fp.stoch_eig(P)
eps = mp.exp(0.8 * mp.log(mp.eps)) # test_eigen.py
err0 = mp.norm(x-x_expected, p=1)
assert err0 < eps
def test_gth_solve_fp():
P = mp.fp.matrix([[-0.1, 0.075, 0.025],
[0.15, -0.2 , 0.05 ],
[0.25, 0.25 , -0.5 ]])
x_expected = mp.fp.matrix([[0.625, 0.3125, 0.0625]])
x = mp.fp.gth_solve(P)
eps = mp.exp(0.8 * mp.log(mp.eps)) # test_eigen.py
err0 = mp.norm(x-x_expected, p=1)
assert err0 < eps
