def yonas_3(self):
a, b = 0, 3
x_sim = np.linspace(truncnorm.ppf(0.01, a, b),
truncnorm.ppf(0.99, a, b), self.n_intervals)
x = np.arange(self.n_intervals)
y = np.exp(truncnorm.pdf(x_sim, a, b) * 1.35)
return y
def late(self):
a, b = 2, 3
y = np.linspace(truncnorm.ppf(0.01, a, b), truncnorm.ppf(0.99, a, b),
self.n_intervals)
y = np.exp(truncnorm.pdf(y, a, b))
y = y[::-1] / 13 + 1
y -= y[0] - 1
return y
def late(self):
a, b = 2, 100
x_sim = np.linspace(truncnorm.ppf(0.01, a, b),
truncnorm.ppf(0.99, a, b), self.n_intervals)
x = np.arange(50)
y = np.exp(truncnorm.pdf(x_sim, a, b))
y = y[::-1] / 15 + 1
y -= y[0] - 1
return y
def gen_model(mean=0.0,
std=1.0,
num_sigma=6.0,
order=1,
numel=512,
real_type=RealType.FixedPoint):
# create mixed-signal model
model = MixedSignalModel('model', build_dir=BUILD_DIR, real_type=real_type)
model.add_digital_input('clk')
model.add_digital_input('rst')
model.add_analog_output('real_out')
# compute the inverse CDF of the distribution (truncated to 0, 1 domain)
inv_cdf = lambda x: truncnorm.ppf(
x, -num_sigma, +num_sigma, loc=mean, scale=std)
# create the function object
inv_cdf_func = model.make_function(inv_cdf,
domain=[0.0, 1.0],
order=order,
numel=numel)
model.set_this_cycle(
model.real_out,
model.arbitrary_noise(inv_cdf_func, clk=model.clk, rst=model.rst))
# write the model
return model.compile_to_file(VerilogGenerator())
def test_pdf(self):
pdf = PDF(norm)
# even if it's really far out it's still a valid value
assert_equal(pdf.valid(1003), 1003)
# logp
assert_equal(pdf.logp(0), norm.logpdf(0))
# examine dist with finite support
pdf = PDF(truncnorm(-1, 1))
assert_equal(pdf.logp(-2), -np.inf)
assert_equal(pdf.logp(-0.5), truncnorm.logpdf(-0.5, -1, 1))
# obtain a random value of a bounds instance
vals = pdf.rvs(size=1000)
assert_(np.min(vals) >= -1)
assert_(np.min(vals) <= 1)
# test a uniform distribution
pdf = PDF(uniform(1, 9))
assert_equal(pdf.logp(2), np.log(1.0 / 9.0))
assert_equal(pdf.logp(10.0), np.log(1.0 / 9.0))
# test the invcdf
rando = np.random.uniform(size=10)
pdf = PDF(truncnorm(-1, 1))
assert_equal(pdf.invcdf(rando), truncnorm.ppf(rando, -1, 1))
def LOS_clouds_priortransform(u,
rlims=(0., 6.),
dlims=(4., 19.),
pb_params=(-3., 0.7, -np.inf, 0.)):
"""
The "prior transform" for the LOS fit that converts from draws on the
N-dimensional unit cube to samples from the prior. Used in nested sampling
methods. Assumes uniform priors for distance and reddening
and a (truncated) log-normal in outlier fraction.
Parameters
----------
u : `~numpy.ndarray` of shape `(Nparams)`
The `2 + 2 * Nclouds` values drawn from the unit cube.
Contains the portion of outliers `P_b`, followed by the foreground
reddening `fred`, followed by a series of `(dist, red)` pairs for
each "cloud" along the LOS.
rlims : 2-tuple, optional
The reddening bounds within which we'd like to sample. Default is
`(0., 6.)`, which also assumes reddening is in units of Av.
dlims : 2-tuple, optional
The distance bounds within which we'd like to sample. Default is
`(4., 19.)`, which also assumes distance is in units of distance
modulus.
pb_params : 4-tuple, optional
Mean, standard deviation, lower bound, and upper bound for a
truncated log-normal distribution. The default is
`(-3., 0.7, -np.inf, 0.)`, which corresponds to a mean of 0.05, a
standard deviation of a factor of 2, a lower bound of 0, and an
upper bound of 1.
Returns
-------
x : `~numpy.ndarray` of shape `(Nparams)`
The transformed parameters.
"""
# Initialize values.
x = u[:]
# pb (outlier fraction)
pb_mean, pb_std, pb_low, pb_high = pb_params
a = (pb_low - pb_mean) / pb_std # set normalized lower bound
b = (pb_high - pb_mean) / pb_std # set normalized upper bound
x[0] = np.exp(truncnorm.ppf(u[0], a, b, loc=pb_mean, scale=pb_std))
# reddening
x[1::2] = np.sort(u[1::2]) * (rlims[1] - rlims[0]) + rlims[0]
# distances
x[2::2] = np.sort(u[2::2]) * (dlims[1] - dlims[0]) + dlims[0]
return x
def prior(cube, ndim, nparams):
# NOTE: You may want to adjust this for your case!
# truncated normal prior
cube[0] = truncnorm.ppf(cube[0], a_A, b_A, loc=mu_A, scale=sigma_A)
# log-uniform prior
# if alpha = 1e2, it's between 1e1 and 1e3
cube[1] = 10**(cube[1] * 2 + (alpha_exponent - 1))
# log-uniform prior
# if T = 1e2, it's between 1e1 and 1e3
cube[2] = 10**(cube[2] * 2 + (T_exponent - 1))
# truncated normal prior
cube[3] = truncnorm.ppf(cube[3],
a_Eshift,
b_Eshift,
loc=mu_Eshift,
scale=sigma_Eshift)
if np.isinf(cube[3]):
self.LOG.debug("Encountered inf in cube[3]:\n%s", cube[3])
def createBall(frow, fline, fminRad, fmaxRad, fgsdFunction, fprobability, fx,
fmean, fstd, finterval, fa, fb):
# print('\ncreating next ball now !!!')
fGrainSize = {
2: awGrainSize(fprobability, fx, fmean, fstd, finterval, fa, fb),
1: truncnorm.ppf(random.random(), fa, fb, fmean, fstd),
0: random.uniform(fminRad, fmaxRad)
}[fgsdFunction]
return random.uniform(
0,
fline), frow + fGrainSize, fGrainSize #random.uniform(fminRad,fmaxRad)
def truncnorm_ppf(x, a, b,loc=0., scale=1.):
"""
Approximate Percentile function of the truncated normal. Particularly in
the tail regions (where the standard SciPy function may be undefined.
"""
thres = truncnorm.ppf(x,(a-loc)/scale,(b-loc)/scale,loc=loc, scale=scale)
if np.any(np.isnan(thres)) or np.any(np.isinf(thres)):
logging.info("Threshold is Nan using approximations.")
thres = loc+scale*quantile_tn(x,(a-loc)/scale,(b-loc)/scale)
return thres
def print_O2_confint(self, t, T, O2conv, save_path=None):
dX, sigmas = self.get_rate_and_var(T, O2conv)
if self.constrained:
lb = truncnorm.ppf(0.025, 0, np.inf, dX, sigmas)
ub = truncnorm.ppf(0.975, 0, np.inf, dX, sigmas)
else:
lb = dX - 2 * sigmas
ub = dX + 2 * sigmas
plt.figure()
plt.plot(t, dX)
plt.fill_between(t, lb, ub)
plt.xlabel('Time (min)')
plt.ylabel('Consumption (% mol)')
plt.title('Conversion Rate with Uncertainty Bounds')
if isinstance(save_path, str):
plt.savefig(save_path)
plt.show()
def ppf(self,u):
'''
Evaluates the percentile function (inverse c.d.f.) for a given array of quantiles.
:param u: Percentiles for which the ppf will be computed.
:type u: numpy.array
:returns: A Data object containing the values of the ppf.
:rtype: natter.DataModule.Data
'''
a,b = (self.param['a']-self.param['mu'])/self.param['sigma'],(self.param['b']-self.param['mu'])/self.param['sigma']
return Data(truncnorm.ppf(u,a,b,loc=self.param['mu'],scale=self.param['sigma']), 'Percentiles from a %s' % (self.name,))
def priortrans_spec(self,upars):
# calcuate transformation from prior volume to parameter for all modeled parameters
outdict = {}
for namepar in ['Teff','log(g)','[Fe/H]','[a/Fe]','Vrad','Vrot','Inst_R','CarbonScale']:
if namepar in upars.keys():
upars_i = upars[namepar]
if namepar in self.priordict['uniform'].keys():
par_i = (
(max(self.priordict['uniform'][namepar])-min(self.priordict['uniform'][namepar]))*upars_i +
min(self.priordict['uniform'][namepar])
)
elif namepar in self.priordict['gaussian'].keys():
par_i = norm.ppf(upars_i,loc=self.priordict['gaussian'][namepar][0],scale=self.priordict['gaussian'][namepar][1])
elif namepar in self.priordict['tgaussian'].keys():
a = (self.priordict['tgaussian'][namepar][0] - self.priordict['tgaussian'][namepar][2]) / self.priordict['tgaussian'][namepar][3]
b = (self.priordict['tgaussian'][namepar][1] - self.priordict['tgaussian'][namepar][2]) / self.priordict['tgaussian'][namepar][3]
par_i = truncnorm.ppf(upars_i,a,b,loc=self.priordict['tgaussian'][namepar][2],scale=self.priordict['tgaussian'][namepar][3])
if par_i == np.inf:
par_i = self.priordict['tgaussian'][namepar][1]
elif namepar in self.priordict['exp'].keys():
par_i = expon.ppf(upars_i,loc=self.priordict['exp'][namepar][0],scale=self.priordict['exp'][namepar][1])
elif namepar in self.priordict['texp'].keys():
b = (self.priordict['texp'][namepar][1] - self.priordict['texp'][namepar][0]) / self.priordict['texp'][namepar][2]
par_i = truncexpon.ppf(upars_i,b,loc=self.priordict['texp'][namepar][0],scale=self.priordict['texp'][namepar][2])
if par_i == np.inf:
par_i = self.priordict['texp'][namepar][1]
else:
par_i = (self.defaultpars[namepar][1]-self.defaultpars[namepar][0])*upars_i + self.defaultpars[namepar][0]
outdict[namepar] = par_i
# if fitting a blaze function, do transformation for polycoef
pcarr = [x_i for x_i in upars.keys() if 'pc' in x_i]
if len(pcarr) > 0:
for pc_i in pcarr:
if pc_i == 'pc_0':
uspec_scale = upars['pc_0']
outdict['pc_0'] = (1.25 - 0.75)*uspec_scale + 0.75
else:
pcind = int(pc_i.split('_')[-1])
pcmax = self.polycoefarr[pcind][0]+5.0*self.polycoefarr[pcind][1]
pcmin = self.polycoefarr[pcind][0]-5.0*self.polycoefarr[pcind][1]
outdict[pc_i] = (pcmax-pcmin)*upars[pc_i] + pcmin
return outdict
def dndx(W,t0,epsilon,mu,sig,d00,d10,d01,d11,l):
"""
W[0]: Enviornmental state measure `n'
W[1]: Fraction of high effort harvesters `x'
"""
"Gradient of selection"
g = (1-W[0])*(d10*W[1]+d00*(1-W[1]))-W[0]*(d11*W[1]+d01*(1-W[1]))
f = truncnorm.ppf(W[0],a,b,mu,sig)
h = norm.ppf(W[0],mu,sig)
theta=1/mu - 1
"dynamical equations"
dx = W[1]*(1-W[1])*(g)
dn = [ epsilon*W[0]*(1-W[0])*(-1+(1+theta)*W[1]) , epsilon*W[0]*(1-W[0])*(W[1]-mu) , epsilon*W[0]*(1-W[0])*(W[1]-mu+sig/2-sig*W[0]), epsilon*W[0]*(1-W[0])*(W[1]-h) , epsilon*W[0]*(1-W[0])*(W[1]-f) , epsilon*(W[1]-f) ]
return([dn[l], dx])
def inverse_sample(self, hypercube):
""" Draw sample uniformly from the distribution via inverse sampling. """
p = super(CustomPrior, self).inverse_sample(hypercube)
# distance
p[0] = truncnorm.ppf(hypercube[0], -2.0, 7.0, loc=0.3, scale=0.1)
# phase of primary hot region
if p[10] > 0.5:
p[10] -= 1.0
# phase of secondary hot region
if p[11] > 0.5:
p[11] -= 1.0
return p
def priortrans_mist(self, upars):
outdict = {}
for namepar in [
'EEP', 'initial_Mass', 'initial_[Fe/H]', 'initial_[a/Fe]'
]:
if namepar in upars.keys():
upars_i = upars[namepar]
if namepar in self.priordict['uniform'].keys():
par_i = (
(max(self.priordict['uniform'][namepar]) -
min(self.priordict['uniform'][namepar])) * upars_i +
min(self.priordict['uniform'][namepar]))
elif namepar in self.priordict['gaussian'].keys():
par_i = norm.ppf(
upars_i,
loc=self.priordict['gaussian'][namepar][0],
scale=self.priordict['gaussian'][namepar][1])
elif namepar in self.priordict['tgaussian'].keys():
a = (self.priordict['tgaussian'][namepar][0] -
self.priordict['tgaussian'][namepar][2]
) / self.priordict['tgaussian'][namepar][3]
b = (self.priordict['tgaussian'][namepar][1] -
self.priordict['tgaussian'][namepar][2]
) / self.priordict['tgaussian'][namepar][3]
par_i = truncnorm.ppf(
upars_i,
a,
b,
loc=self.priordict['tgaussian'][namepar][2],
scale=self.priordict['tgaussian'][namepar][3])
if par_i == np.inf:
par_i = self.priordict['tgaussian'][namepar][1]
else:
par_i = (self.defaultpars[namepar][1] -
self.defaultpars[namepar][0]
) * upars_i + self.defaultpars[namepar][0]
outdict[namepar] = par_i
return outdict
def inverse_sample(self, hypercube):
""" Draw sample uniformly from the distribution via inverse sampling.
:param hypercube: A pseudorandom point in an n-dimensional hypercube.
:return: A parameter ``list``.
"""
p = super(CustomPrior, self).inverse_sample(hypercube)
# distance
p[0] = truncnorm.ppf(hypercube[0], -2.0, 7.0, loc=0.3, scale=0.1)
if p[10] > 0.5:
p[10] -= 1.0
if p[11] > 0.5:
p[11] -= 1.0
return p
def _ppf(self, q, a, b, mu, sigma):
return truncnorm.ppf(q, a, b, loc=mu, scale=sigma)
def FittedISMIP_project_icesheets(nsamps, pyear_start, pyear_end, pyear_step,
cyear_start, cyear_end, baseyear,
pipeline_id, rngseed):
# Load the data file
datafilename = "{}_data.pkl".format(pipeline_id)
datafile = os.path.join(os.path.dirname(__file__), datafilename)
with open(datafile, 'rb') as f:
my_data = pickle.load(f)
years = my_data["years"]
temp_data = my_data["temp_data"]
scenario = my_data["scenario"]
# Load the fit file
datafilename = "{}_fit.pkl".format(pipeline_id)
datafile = os.path.join(os.path.dirname(__file__), datafilename)
with open(datafile, 'rb') as f:
my_data = pickle.load(f)
groups_dict = my_data["groups_dict"]
models_dict = my_data["models_dict"]
betas_dict = my_data["betas_dict"]
sigmas_dict = my_data["sigmas_dict"]
trend_mean = my_data["trend_mean"]
trend_sd = my_data["trend_sd"]
# Extract the ice sources from the fitted dictionaries
icesources = betas_dict.keys()
# Define the target projection years
targyears = np.arange(pyear_start, pyear_end + 1, pyear_step)
# Find the data years that overlap with the target projection years
(_, datayr_idx, targyear_idx) = np.intersect1d(years,
targyears,
return_indices=True)
# Zero out the temperature data to the base year (Fitted models have 0-forced intercept)
baseyear_idx = np.flatnonzero(years == baseyear)
if baseyear_idx.size == 0:
raise Exception(
"baseyear is not found in temperature data. baseyear = {}".format(
baseyear))
temp_data = temp_data - temp_data[:, baseyear_idx]
# Set the seed for the RNG
np.random.seed(rngseed)
# Initialize the samples dictionary to pass to the post-processing stage
samps_dict = {}
# Generate the indices for the temperature samples
temp_sample_idx = np.random.choice(np.arange(temp_data.shape[0]), nsamps)
# Generate a list of quantiles for the trend samples
trend_q = np.random.random_sample(nsamps)
# Loop over the ice sources
#for icesource in icesources:
for icesource in ["GIS"]:
# Calculate the trend contributions over time for this ice sheet component
ice_trend = truncnorm.ppf(trend_q,
a=0.0,
b=99999.9,
loc=trend_mean[icesource],
scale=trend_sd[icesource])[:, np.newaxis] * (
targyears - baseyear)[np.newaxis, :]
# Which model parameters do we need
betas = betas_dict[icesource]
sigmas = sigmas_dict[icesource]
# Generate the indices for the model samples
model_sample_idx = np.random.choice(np.arange(betas.shape[0]), nsamps)
# Loop over the number of samples we need
samps = []
temp_samps = []
time_samps = []
const_samps = []
for tidx, midx in zip(temp_sample_idx, model_sample_idx):
# Generate a sample
(this_sample, samp_temp, samp_time, samp_const) = my_model(temp_data[tidx,datayr_idx], \
betas[midx,:], sigmas[midx], \
targyears - baseyear, pyear_step)
samps.append(this_sample)
#temp_samps.append(samp_temp)
#time_samps.append(samp_time)
#const_samps.append(samp_const)
# Convert the sample array into a numpy array
samps = np.array(samps)
#temp_samps = np.array(temp_samps)
#time_samps = np.array(time_samps)
#const_samps = np.array(const_samps)
# Add the trend to the samples
samps = samps + ice_trend
# If the user wants to extrapolate projections based on rates, do so here
if cyear_start or cyear_end:
for i in np.arange(nsamps):
samps[i, :] = ExtrapolateRate(samps[i, :], targyears,
cyear_start, cyear_end)
# Add the total samples to the samples dictionary
samps_dict[icesource] = samps
# Write the global projections to output netCDF files
WriteNetCDF(samps, icesource, targyears[targyear_idx], scenario,
pipeline_id, baseyear)
#WriteNetCDF(temp_samps, "{}TEMP".format(icesource), targyears[targyear_idx], scenario, pipeline_id)
#WriteNetCDF(time_samps, "{}TIME".format(icesource), targyears[targyear_idx], scenario, pipeline_id)
#WriteNetCDF(const_samps, "{}CONST".format(icesource), targyears[targyear_idx], scenario, pipeline_id)
# Write the combined AIS projections to netcdf
#ais_samps = samps_dict["WAIS"] + samps_dict["EAIS"] + samps_dict["PEN"]
#WriteNetCDF(ais_samps, "AIS", targyears[targyear_idx], scenario, pipeline_id, baseyear)
# Store the variables in a pickle
output = {
'samps_dict': samps_dict,
'scenario': scenario,
'targyears': targyears[targyear_idx],
'baseyear': baseyear
}
outfilename = "{}_projections.pkl".format(pipeline_id)
outfile = open(os.path.join(os.path.dirname(__file__), outfilename), 'wb')
pickle.dump(output, outfile)
outfile.close()
return (None)
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return super(TruncatedNormal, self).log_prob(
self._to_std_rv(value)) - self._log_scale
if __name__ == '__main__':
from scipy.stats import truncnorm
loc, scale, a, b = 1., 2., 1., 2.
tn_pt = TruncatedNormal(loc, scale, a, b)
mean_pt, var_pt = tn_pt.mean.item(), tn_pt.variance.item()
alpha, beta = (a - loc) / scale, (b - loc) / scale
mean_sp, var_sp = truncnorm.stats(alpha,
beta,
loc=loc,
scale=scale,
moments='mv')
print('mean', mean_pt, mean_sp)
print('var', var_pt, var_sp)
print('cdf',
tn_pt.cdf(1.4).item(),
truncnorm.cdf(1.4, alpha, beta, loc=loc, scale=scale))
print('icdf',
tn_pt.icdf(0.333).item(),
truncnorm.ppf(0.333, alpha, beta, loc=loc, scale=scale))
print('logpdf',
tn_pt.log_prob(1.5).item(),
truncnorm.logpdf(1.5, alpha, beta, loc=loc, scale=scale))
print('entropy', tn_pt.entropy.item(),
truncnorm.entropy(alpha, beta, loc=loc, scale=scale))
def transform_truncated_normal(x, hyperparameters):
mu, sigma, a, b = hyperparameters
ar, br = (a - mu) / sigma, (b - mu) / sigma
return truncnorm.ppf(x, ar, br, loc=mu, scale=sigma)
from msdsl import *
from scipy.stats import truncnorm
m = MixedSignalModel('model')
y = m.add_analog_output('y')
inv_cdf = lambda x: truncnorm.ppf(x, -8, +8)
inv_cdf_func = m.make_function(inv_cdf, domain=[0.0, 1.0])
m.set_this_cycle(y, m.arbitrary_noise(inv_cdf_func))
m.compile_and_print(VerilogGenerator())
def normal_truncated_ppf(self, xvalue):
return truncnorm.ppf(
xvalue, (self.lower_limit - self.prior_estimate) / self.spread,
(self.upper_limit - self.prior_estimate) / self.spread,
loc=self.prior_estimate,
scale=self.spread)
# -*- coding: utf-8 -*- """ Created on Fri Jan 10 14:22:02 2020 @author: Paul Vincent Nonat """ from scipy.stats import truncnorm import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) a, b = 0, np.inf mean, var, skew, kurt = truncnorm.stats(a, b, moments='mvsk') x = np.linspace(truncnorm.ppf(0, a, b), truncnorm.ppf(0.99, a, b), 100) ax.plot(x, truncnorm.pdf(x, a, b), 'r-', lw=5, alpha=1, label='truncnorm pdf') mean = 2 rv = truncnorm(a, b) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') vals = truncnorm.ppf([0.1, 0.1, b], a, b) np.allclose([0.0001, 1.5, 2], truncnorm.cdf(vals, a, b)) r = truncnorm.rvs(a, b, size=1000) ax.hist(r, density=True, histtype='stepfilled', alpha=1) ax.legend(loc='best', frameon=False)
def get_truncated_lognormal_example_exact_quantities(lb, ub, mu, sigma):
f = lambda x: np.exp(x).T
#lb,ub passed to truncnorm_rv are defined for standard normal.
#Adjust for mu and sigma using
alpha, beta = (lb - mu) / sigma, (ub - mu) / sigma
denom = normal_rv.cdf(beta) - normal_rv.cdf(alpha)
#truncated_normal_cdf = lambda x: (
# normal_rv.cdf((x-mu)/sigma)-normal_rv.cdf(alpha))/denom
truncated_normal_cdf = lambda x: truncnorm_rv.cdf(
x, alpha, beta, loc=mu, scale=sigma)
truncated_normal_pdf = lambda x: truncnorm_rv.pdf(
x, alpha, beta, loc=mu, scale=sigma)
truncated_normal_ppf = lambda p: truncnorm_rv.ppf(
p, alpha, beta, loc=mu, scale=sigma)
# CDF of output variable (log truncated normal PDF)
def f_cdf(y):
vals = np.zeros_like(y)
II = np.where((y > np.exp(lb)) & (y < np.exp(ub)))[0]
vals[II] = truncated_normal_cdf(np.log(y[II]))
JJ = np.where((y >= np.exp(ub)))[0]
vals[JJ] = 1.
return vals
# PDF of output variable (log truncated normal PDF)
def f_pdf(y):
vals = np.zeros_like(y)
II = np.where((y > np.exp(lb)) & (y < np.exp(ub)))[0]
vals[II] = truncated_normal_pdf(np.log(y[II])) / y[II]
return vals
# Analytic VaR of model output
VaR = lambda p: np.exp(truncated_normal_ppf(p))
const = np.exp(mu + sigma**2 / 2)
# Analytic VaR of model output
CVaR = lambda p: -0.5 / denom * const / (1 - p) * (erf(
(mu + sigma**2 - ub) / (np.sqrt(2) * sigma)) - erf(
(mu + sigma**2 - np.log(VaR(p))) / (np.sqrt(2) * sigma)))
def cond_exp_le_eta(y):
vals = np.zeros_like(y)
II = np.where((y > np.exp(lb)) & (y < np.exp(ub)))[0]
vals[II] = -0.5 / denom * const * (erf(
(mu + sigma**2 - np.log(y[II])) / (np.sqrt(2) * sigma)) - erf(
(mu + sigma**2 - lb) / (np.sqrt(2) * sigma))) / f_cdf(y[II])
JJ = np.where((y >= np.exp(ub)))[0]
vals[JJ] = mean
return vals
ssd = lambda y: f_cdf(y) * (y - cond_exp_le_eta(y))
mean = CVaR(np.zeros(1))
def cond_exp_y_ge_eta(y):
vals = np.ones_like(y) * mean
II = np.where((y > np.exp(lb)) & (y < np.exp(ub)))[0]
vals[II] = -0.5 / denom * const * (erf(
(mu + sigma**2 - ub) / (np.sqrt(2) * sigma)) - erf(
(mu + sigma**2 - np.log(y[II])) /
(np.sqrt(2) * sigma))) / (1 - f_cdf(y[II]))
JJ = np.where((y > np.exp(ub)))[0]
vals[JJ] = 0
return vals
ssd_disutil = lambda eta: (1 - f_cdf(-eta)) * (eta + cond_exp_y_ge_eta(-eta
))
return f, f_cdf, f_pdf, VaR, CVaR, ssd, ssd_disutil
def sample(self, *args):
x = np.asarray(args)
self.last_sampled = truncnorm.ppf(x, self.xmin, self.xmax, self.mu,
self.sd)
return self.last_sampled
def priortrans_phot(self, upars):
outdict = {}
# if only fitting the SED, pull Teff/logg/FeH and do prior transformation
if not self.spec_bool:
for namepar in ['Teff', 'log(g)', '[Fe/H]', '[a/Fe]']:
if namepar in upars.keys():
upars_i = upars[namepar]
if namepar in self.priordict['uniform'].keys():
par_i = ((max(self.priordict['uniform'][namepar]) -
min(self.priordict['uniform'][namepar])) *
upars_i +
min(self.priordict['uniform'][namepar]))
elif namepar in self.priordict['gaussian'].keys():
par_i = norm.ppf(
upars_i,
loc=self.priordict['gaussian'][namepar][0],
scale=self.priordict['gaussian'][namepar][1])
elif namepar in self.priordict['tgaussian'].keys():
loc = self.priordict['tgaussian'][namepar][2]
scale = self.priordict['tgaussian'][namepar][3]
a = (self.priordict['tgaussian'][namepar][0] -
loc) / scale
b = (self.priordict['tgaussian'][namepar][1] -
loc) / scale
par_i = truncnorm.ppf(upars_i,
a,
b,
loc=loc,
scale=scale)
if par_i == np.inf:
par_i = self.priordict['tgaussian'][namepar][1]
elif namepar in self.priordict['beta'].keys():
a = self.priordict['beta'][namepar][0]
b = self.priordict['beta'][namepar][1]
loc = self.priordict['beta'][namepar][2]
scale = self.priordict['beta'][namepar][3]
par_i = beta.ppf(upars_i, a, b, loc=loc, scale=scale)
elif namepar in self.priordict['exp'].keys():
par_i = expon.ppf(
upars_i,
loc=self.priordict['exp'][namepar][0],
scale=self.priordict['exp'][namepar][1])
else:
par_i = (self.defaultpars[namepar][1] -
self.defaultpars[namepar][0]
) * upars_i + self.defaultpars[namepar][0]
outdict[namepar] = par_i
isopars = ['log(A)', 'log(R)', 'Av', 'Rv', 'Dist']
if self.gal_bool:
if 'Dist' in upars.keys():
outdict['Dist'] = 1000.0 * self.AP.gal_ppf(upars['Dist'])
isopars.remove('Dist')
for namepar in isopars:
if namepar in upars.keys():
upars_i = upars[namepar]
if namepar in self.priordict['uniform'].keys():
par_i = (
(max(self.priordict['uniform'][namepar]) -
min(self.priordict['uniform'][namepar])) * upars_i +
min(self.priordict['uniform'][namepar]))
elif namepar in self.priordict['gaussian'].keys():
par_i = norm.ppf(
upars_i,
loc=self.priordict['gaussian'][namepar][0],
scale=self.priordict['gaussian'][namepar][1])
elif namepar in self.priordict['exp'].keys():
par_i = expon.ppf(upars_i,
loc=self.priordict['exp'][namepar][0],
scale=self.priordict['exp'][namepar][1])
elif namepar in self.priordict['tgaussian'].keys():
loc = self.priordict['tgaussian'][namepar][2]
scale = self.priordict['tgaussian'][namepar][3]
a = (self.priordict['tgaussian'][namepar][0] - loc) / scale
b = (self.priordict['tgaussian'][namepar][1] - loc) / scale
par_i = truncnorm.ppf(upars_i, a, b, loc=loc, scale=scale)
if par_i == np.inf:
par_i = self.priordict['tgaussian'][namepar][1]
elif namepar in self.priordict['texp'].keys():
loc = self.priordict['texp'][namepar][2]
scale = self.priordict['texp'][namepar][3]
a = (self.priordict['texp'][namepar][0] - loc) / scale
b = (self.priordict['texp'][namepar][1] - loc) / scale
par_i = truncexpon.ppf(upars_i, a, b, loc=loc, scale=scale)
if par_i == np.inf:
par_i = self.priordict['texp'][namepar][1]
elif namepar in self.priordict['beta'].keys():
a = self.priordict['beta'][namepar][0]
b = self.priordict['beta'][namepar][1]
loc = self.priordict['beta'][namepar][2]
scale = self.priordict['beta'][namepar][3]
par_i = beta.ppf(upars_i, a, b, loc=loc, scale=scale)
elif namepar in self.priordict['loguniform'].keys():
par_i = reciprocal.ppf(
upars_i, self.priordict['loguniform'][namepar][0],
self.priordict['loguniform'][namepar][1])
else:
par_i = (self.defaultpars[namepar][1] -
self.defaultpars[namepar][0]
) * upars_i + self.defaultpars[namepar][0]
outdict[namepar] = par_i
return outdict
def inv_cdf(x):
return truncnorm.ppf(x, -8, 8)
import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm # using msdsl from scipy.stats import truncnorm from msdsl import Function inv_cdf = lambda x: truncnorm.ppf(x, -6, +6) func = Function(inv_cdf, domain=[0.0, 0.5], order=1, numel=512, log_bits=5) # print(func.get_samp_points_spline()) # for elem in func.get_samp_points_spline(): # print(elem) # print(func.calc_addr(elem)) # compare results test_pts = np.linspace(0, 0.5, 1000) plt.plot(test_pts, inv_cdf(test_pts)) plt.plot(test_pts, func.eval_on(test_pts)) plt.show()
def transform_truncated_normal(x,mu,sigma,a=0.,b=1.):
ar, br = (a - mu) / sigma, (b - mu) / sigma
return truncnorm.ppf(x,ar,br,loc=mu,scale=sigma)
def priortrans_spec(self, upars):
# calcuate transformation from prior volume to parameter for all modeled parameters
outdict = {}
for namepar in [
'Teff', 'log(g)', '[Fe/H]', '[a/Fe]', 'Vrad', 'Vrot', 'Vmic',
'Inst_R'
]:
if namepar in upars.keys():
upars_i = upars[namepar]
if namepar in self.priordict['uniform'].keys():
par_i = (
(max(self.priordict['uniform'][namepar]) -
min(self.priordict['uniform'][namepar])) * upars_i +
min(self.priordict['uniform'][namepar]))
elif namepar in self.priordict['gaussian'].keys():
par_i = norm.ppf(
upars_i,
loc=self.priordict['gaussian'][namepar][0],
scale=self.priordict['gaussian'][namepar][1])
elif namepar in self.priordict['tgaussian'].keys():
loc = self.priordict['tgaussian'][namepar][2]
scale = self.priordict['tgaussian'][namepar][3]
a = (self.priordict['tgaussian'][namepar][0] - loc) / scale
b = (self.priordict['tgaussian'][namepar][1] - loc) / scale
par_i = truncnorm.ppf(upars_i, a, b, loc=loc, scale=scale)
if par_i == np.inf:
par_i = self.priordict['tgaussian'][namepar][1]
elif namepar in self.priordict['beta'].keys():
a = self.priordict['beta'][namepar][0]
b = self.priordict['beta'][namepar][1]
loc = self.priordict['beta'][namepar][2]
scale = self.priordict['beta'][namepar][3]
par_i = beta.ppf(upars_i, a, b, loc=loc, scale=scale)
elif namepar in self.priordict['exp'].keys():
par_i = expon.ppf(upars_i,
loc=self.priordict['exp'][namepar][0],
scale=self.priordict['exp'][namepar][1])
else:
par_i = (self.defaultpars[namepar][1] -
self.defaultpars[namepar][0]
) * upars_i + self.defaultpars[namepar][0]
outdict[namepar] = par_i
# if fitting a blaze function, do transformation for polycoef
pcarr = [x_i for x_i in upars.keys() if 'pc' in x_i]
if len(pcarr) > 0:
for pc_i in pcarr:
if pc_i == 'pc_0':
uspec_scale = upars['pc_0']
outdict['pc_0'] = (2.0 - 0.5) * uspec_scale + 0.5
else:
pcind = int(pc_i.split('_')[-1])
# pcmax = self.polycoefarr[pcind][0]+3.0*self.polycoefarr[pcind][1]
# pcmin = self.polycoefarr[pcind][0]-3.0*self.polycoefarr[pcind][1]
# outdict[pc_i] = (pcmax-pcmin)*upars[pc_i] + pcmin
# outdict[pc_i] = norm.ppf(upars[pc_i],loc=self.polycoefarr[pcind][0],scale=self.polycoefarr[pcind][1])
loc = self.polycoefarr[pcind][0]
scale = self.polycoefarr[pcind][1]
minval = loc - 5.0 * scale
maxval = loc + 5.0 * scale
a = (minval - loc) / scale
b = (maxval - loc) / scale
outdict[pc_i] = truncnorm.ppf(upars[pc_i],
a,
b,
loc=loc,
scale=scale)
return outdict