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clean3.py
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clean3.py
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# Load libraries
import numpy as np
import matplotlib.pyplot as plt
import multiprocessing as mp
import scipy.integrate
import scipy.optimize as opt
# Use Gaussian process from scikit-learn
from sklearn.gaussian_process import GaussianProcessRegressor as GPR
from sklearn.gaussian_process import kernels
# suppression warning messages
import warnings
warnings.filterwarnings('ignore')
# Make Changes Here #
pairList = np.array([(8, 8192), (16, 4096), (32, 2048), (64, 1024), (128, 512), (256, 256),
(512, 128), (1024, 64), (2048, 32)])
folderName = "./3de5/"
emulatorGraphs = False
posteriorGraphs = False
# Feel free to change the integration method on line 190)
# DO NOT MAKE CHANGES BELOW (except line 190 and print statements) #
####################################################################
def do_something(bb):
# Storage: [data file names], amount of Design Points, [parameter names], [parameter min values],
# [parameter max values], [parameter truths], [observable names], [observable truths],
# number of trento runs per design point
savedValues = np.load("" + folderName + str(pairList[bb][0]) + "dp"
+ str(pairList[bb][1]) + "tr.npy", allow_pickle=True)
totDesPoints = savedValues[1]
paramNames = savedValues[2]
paramMins = savedValues[3]
paramMaxs = savedValues[4]
paramTruths = savedValues[5]
obsNames = savedValues[6]
obsTruths = savedValues[7][0]
truthUncert = savedValues[7][1]
nTrento = savedValues[8]
# datum: np.array([[design_points], [observables]])
desPts = np.load(str(savedValues[0][0]) + ".npy", allow_pickle=True)
observables = np.load(str(savedValues[0][1]) + ".npy", allow_pickle=True)
### Make emulator for each observable ###
emul_d = {}
for nn in range(len(obsTruths)):
# Kernels
k0 = 1. * kernels.RBF(
# length_scale=(param1_paramspace_length / 2., param2_paramspace_length / 2.)
# length_scale_bounds=(
# (param1_paramspace_length / param1_nb_design_pts, 3. * param1_paramspace_length),
# (param2_paramspace_length / param2_nb_design_pts, 3. * param2_paramspace_length)
# )
)
k2 = 1. * kernels.WhiteKernel(
noise_level=truthUncert[nn],
# noise_level_bounds='fixed'
noise_level_bounds=(truthUncert[nn] / 4., 4 * truthUncert[nn])
)
kernel = (k0 + k2)
nrestarts = 10
emulator_design_pts_value = np.array(desPts)
emulator_obs_mean_value = np.array(observables[:, nn])
# Fit a GP (optimize the kernel hyperparameters) to each PC.
gaussian_process = GPR(
kernel=kernel,
alpha=0.0001,
n_restarts_optimizer=nrestarts,
copy_X_train=True
).fit(emulator_design_pts_value, emulator_obs_mean_value)
"""
# https://github.com/keweiyao/JETSCAPE2020-TRENTO-BAYES/blob/master/trento-bayes.ipynb
print('Information on emulator for observable ' + obs_label)
print('RBF: ', gaussian_process.kernel_.get_params()['k1'])
print('White: ', gaussian_process.kernel_.get_params()['k2'])
"""
emul_d[obsNames[nn]] = {
'gpr': gaussian_process
# 'mean':scipy.interpolate.interp2d(calc_d[obs_name]['x_list'], calc_d[obs_name]['y_list'], np.transpose(
# calc_d[obs_name]['mean']), kind='linear', copy=True, bounds_error=False, fill_value=None),
# 'uncert':scipy.interpolate.interp2d(calc_d[obs_name]['x_list'], calc_d[obs_name]['y_list'], np.transpose(
# calc_d[obs_name]['uncert']), kind='linear', copy=True, bounds_error=False, fill_value=None)
}
#####################
# Plot the emulator #
#####################
if emulatorGraphs:
# Label for the observable
obs_label = obsNames[nn]
# observable vs value of one parameter (with the other parameter fixed)
for pl in range(len(paramTruths)):
plt.figure(1)
plt.xscale('linear')
plt.yscale('linear')
plt.xlabel(paramNames[pl])
plt.ylabel(obs_label)
# Compute the posterior for a range of values of the parameter "x"
ranges = np.zeros(50).reshape((1, 50))
for rr in range(0, len(paramMins)):
if rr != pl:
val = (paramMins[rr] + paramMaxs[rr]) / 2
ranges = np.append(ranges, np.linspace(val, val, 50).reshape((1, 50)), axis=0)
else:
ranges = np.append(ranges, np.linspace(paramMins[rr],
paramMaxs[rr], 50).reshape((1, 50)), axis=0)
param_value_array = np.transpose(ranges[1:, :])
z_list, z_list_uncert = gaussian_process.predict(param_value_array, return_std=True)
# Plot design points
plt.errorbar(desPts[:, pl], np.array(observables[:, nn]),
yerr=np.array(truthUncert)[nn], fmt='D', color='orange', capsize=4)
# Plot interpolator
plt.plot(ranges[pl + 1], z_list, color='blue')
plt.fill_between(ranges[pl + 1], z_list - z_list_uncert, z_list + z_list_uncert, color='blue', alpha=.4)
# Plot the truth
plt.plot(paramTruths[pl], obsTruths[nn], "D", color='black')
plt.ticklabel_format(axis='y', style='sci', scilimits=(0, 0))
plt.tight_layout()
plt.show()
print(str(pairList[bb]) + " emulators trained")
### Compute the Posterior ###
# We assume uniform priors (integral across the whole parameter space should = 1)
dims = np.array([paramMaxs[vv] - paramMins[vv] for vv in range(len(paramMins))])
area = np.prod(dims)
height = 1.0/area
def prior():
return height
# Under the approximations that we're using, the posterior is
# Likelihood = exp((-1/2)ln((2 pi)^n\prod_n{modelErr(observable, pT)^2 + dataErr(observable, pT)^2})
# - (1/2)\sum_{observables, pT}(model(observable, pT) - data(observable, pT))^2
# / (modelErr(observable, pT)^2 + dataErr(observable, pT)^2))
def likelihood(params):
res = 0.0
norm = (2*np.pi)**len(obsTruths)
# Sum over observables
for xx in range(len(obsTruths)):
# Function that returns the value of an observable
data_mean2 = obsTruths[xx]
data_uncert2 = truthUncert[xx]
tmp_data_mean, tmp_data_uncert = data_mean2, data_uncert2
emulator = emul_d[obsNames[xx]]['gpr']
tmp_model_mean, tmp_model_uncert = emulator.predict(np.atleast_2d(np.transpose(params)), return_std=True)
cov = (tmp_model_uncert * tmp_model_uncert + tmp_data_uncert * tmp_data_uncert)
res += np.power(tmp_model_mean - tmp_data_mean, 2) / cov
norm *= cov
res *= -0.5
return (norm ** -0.5) * (np.e ** res)
def posterior(*params):
return prior() * likelihood(np.array([*params]))
# Compute the posterior, evidence, and AIC #
div = totDesPoints
if totDesPoints < 50:
div = 50
param_ranges = np.zeros((len(paramMins), div))
for qq in range(len(paramMins)):
param_ranges[qq] = np.arange(paramMins[qq], paramMaxs[qq], (paramMaxs[qq] - paramMins[qq])/div)
paramTruthPost = float(posterior(*paramTruths))
ranges = np.zeros((len(paramMins), 2))
for dex in range(len(paramMins)):
ranges[dex][0] = paramMins[dex]
ranges[dex][1] = paramMaxs[dex]
vol1 = scipy.integrate.nquad(posterior, [*ranges], opts={'epsrel': 0.01})[0]
normish = paramTruthPost / vol1
print(vol1)
def minPost(*params):
return -1*posterior(*params[0])
maxPostPar = opt.fmin(minPost, paramTruths)
maxLike = float(likelihood(maxPostPar))
AIC = -2 * np.log(maxLike) + 2*len(paramMins)
subtitle = "NormP: " + str(normish) + ", AIC: " + str(AIC)
print(str(pairList[bb]) + " normP(truth): " + str(normish))
print(str(pairList[bb]) + " AIC: " + str(AIC))
###############################
# Plotting marginal posterior #
###############################
if posteriorGraphs:
for i in range(len(paramNames)):
plt.figure()
plt.xscale('linear')
plt.yscale('linear')
plt.xlabel(paramNames[i])
plt.ylabel(r'Posterior')
plt.title("Number of design points: " + str(totDesPoints) + ", Number of trento runs: " + str(nTrento))
plt.figtext(.5, 0.01, subtitle, ha='center')
# The marginal posterior for a parameter is obtained by integrating over a subset of other model parameters
# Compute the posterior for a range of values of the parameter "param_1"
posterior_list = np.array([])
param_vals = np.array([*paramTruths])
for ee in param_ranges[i]:
param_vals[i] = ee
posterior_list = np.append(posterior_list, posterior(*param_vals))
plt.plot(param_ranges[i], posterior_list, "-", color='black', lw=4)
plt.axvline(x=paramTruths[i], color='red')
plt.tight_layout()
plt.show()
# Use multiprocessing to make the script run faster
pool = mp.Pool()
pool.map(do_something, range(len(pairList)))