def test_cuboids(lb, ub, RVstart, RVend, cuboid_volume):
probmass = []
subdiams = []
tot_diam = []
solved_p = []
# subdivisions
for i in range(len(lb)):
if DEBUG:
print("\n")
print(" lower bounds: %s" % lb[i])
print(" upper bounds: %s" % ub[i])
if i in NEW_SLICES or not NEW_SLICES:
subcuboid_volume = volume(lb[i], ub[i])
sub_prob_mass = prob_mass(subcuboid_volume, cuboid_volume)
probmass.append(sub_prob_mass)
if DEBUG: print(" probability mass: %s" % sub_prob_mass)
solved, diameter, subdiameters = UQ(RVstart, RVend, lb[i], ub[i])
solved_p.append(solved)
subdiams.append(subdiameters)
tot_diam.append(diameter)
else:
probmass.append(PROBABILITY_MASS[i])
if DEBUG: print(" probability mass: %s" % PROBABILITY_MASS[i])
solved_p.append(SOLVED_PARAMETERS[i])
subdiams.append(SUB_DIAMETERS[i])
tot_diam.append(TOTAL_DIAMETERS[i])
return solved_p, subdiams, tot_diam, probmass
def test_cuboids(lb, ub, RVstart, RVend, cuboid_volume):
probmass = []
subdiams = []
tot_diam = []
solved_p = []
# subdivisions
for i in range(len(lb)):
if DEBUG:
print "\n"
print " lower bounds: %s" % lb[i]
print " upper bounds: %s" % ub[i]
if i in NEW_SLICES or not NEW_SLICES:
subcuboid_volume = volume(lb[i], ub[i])
sub_prob_mass = prob_mass(subcuboid_volume, cuboid_volume)
probmass.append(sub_prob_mass)
if DEBUG:
print " probability mass: %s" % sub_prob_mass
solved, diameter, subdiameters = UQ(RVstart, RVend, lb[i], ub[i])
solved_p.append(solved)
subdiams.append(subdiameters)
tot_diam.append(diameter)
else:
probmass.append(PROBABILITY_MASS[i])
if DEBUG:
print " probability mass: %s" % PROBABILITY_MASS[i]
solved_p.append(SOLVED_PARAMETERS[i])
subdiams.append(SUB_DIAMETERS[i])
tot_diam.append(TOTAL_DIAMETERS[i])
return solved_p, subdiams, tot_diam, probmass
def monte_carlo_integrate(f, lb, ub, n=10000): #XXX ok default for n?
"""
Returns the integral of an m-dimensional function f from lb to ub
using a Monte Carlo integration of n points
Inputs:
f -- a function that takes a list and returns a number.
lb -- a list of lower bounds
ub -- a list of upper bounds
n -- the number of points to sample [Default is n=10000]
References:
This code is adapted from A Primer on Scientific Programming with Python
by Hans Petter Langtangen, page 443-445.
Also, see http://en.wikipedia.org/wiki/Monte_Carlo_integration
and http://math.fullerton.edu/mathews/n2003/MonteCarloMod.html
"""
from mystic.math.stats import volume
from mystic.math.samples import random_samples
vol = volume(lb, ub)
x = [random_samples(lb, ub, npts=1) for k in range(1, n + 1)]
r = map(f, x) #FIXME: , nnodes=nnodes, launcher=launcher)
s = sum(r)[0]
I = (vol / k) * s
return float(I)
def monte_carlo_integrate(f, lb, ub, n=10000): #XXX ok default for n?
"""
Returns the integral of an m-dimensional function f from lb to ub
using a Monte Carlo integration of n points
Inputs:
f -- a function that takes a list and returns a number.
lb -- a list of lower bounds
ub -- a list of upper bounds
n -- the number of points to sample [Default is n=10000]
References:
1. "A Primer on Scientific Programming with Python", by Hans Petter
Langtangen, page 443-445, 2014.
2. http://en.wikipedia.org/wiki/Monte_Carlo_integration
3. http://math.fullerton.edu/mathews/n2003/MonteCarloMod.html
"""
from mystic.math.stats import volume
from mystic.math.samples import random_samples
vol = volume(lb, ub)
x = [random_samples(lb, ub, npts=1) for k in range(1, n+1)]
r = map(f, x) #FIXME: , nnodes=nnodes, launcher=launcher)
s = sum(r)[0]
I = (vol/n)*s
return float(I)
def integrated_mean(f, lb, ub):
"""
calculate the integrated mean of a function f
Inputs:
f -- a function that takes a list and returns a number
lb -- a list of lower bounds
ub -- a list of upper bounds
"""
expectation = integrate(f, lb, ub)
from mystic.math.stats import mean, volume
vol = volume(lb, ub)
return mean(expectation, vol)
def integrated_mean(f, lb, ub):
"""
calculate the integrated mean of a function f
Inputs:
f -- a function that takes a list and returns a number
lb -- a list of lower bounds
ub -- a list of upper bounds
"""
expectation = integrate(f, lb, ub)
from mystic.math.stats import mean,volume
vol = volume(lb, ub)
return mean(expectation, vol)
print(" model: f(x) = %s(x)" % function_name)
RVmax = len(lower_bounds)
param_string = "["
for i in range(RVmax):
param_string += "'x%s'" % str(i + 1)
if i == (RVmax - 1):
param_string += "]"
else:
param_string += ", "
print(" parameters: %s" % param_string)
# get diameter for entire cuboid
lb, ub = [lower_bounds], [upper_bounds]
cuboid_volume = volume(lb[0], ub[0])
params0, subdiams0, diam0, probmass0 = test_cuboids(lb,ub,RVstart,RVend,\
cuboid_volume)
SOLVED_PARAMETERS, SUB_DIAMETERS = params0, subdiams0
TOTAL_DIAMETERS, PROBABILITY_MASS = diam0, probmass0
if not DEBUG:
failure, success = sample(model, lb[0], ub[0])
pof = float(failure) / float(failure + success)
print("Exact PoF: %s" % pof)
for i in range(len(lb)):
print("\n")
print(" lower bounds: %s" % lb[i])
print(" upper bounds: %s" % ub[i])
for solved in params0[0]:
print " model: f(x) = %s(x)" % function_name
RVmax = len(lower_bounds)
param_string = "["
for i in range(RVmax):
param_string += "'x%s'" % str(i + 1)
if i == (RVmax - 1):
param_string += "]"
else:
param_string += ", "
print " parameters: %s" % param_string
# get diameter for entire cuboid
lb, ub = [lower_bounds], [upper_bounds]
cuboid_volume = volume(lb[0], ub[0])
params0, subdiams0, diam0, probmass0 = test_cuboids(lb, ub, RVstart, RVend, cuboid_volume)
SOLVED_PARAMETERS, SUB_DIAMETERS = params0, subdiams0
TOTAL_DIAMETERS, PROBABILITY_MASS = diam0, probmass0
if not DEBUG:
failure, success = sample(model, lb[0], ub[0])
pof = float(failure) / float(failure + success)
print "Exact PoF: %s" % pof
for i in range(len(lb)):
print "\n"
print " lower bounds: %s" % lb[i]
print " upper bounds: %s" % ub[i]
for solved in params0[0]:
print "solved: %s" % solved
print(" model: f(x) = %s(x)" % function_name)
param_string = "["
for i in range(RVmax):
param_string += "'x%s'" % str(i + 1)
if i == (RVmax - 1):
param_string += "]"
else:
param_string += ", "
print(" parameters: %s" % param_string)
print(" lower bounds: %s" % lower_bounds)
print(" upper bounds: %s" % upper_bounds)
# print(" ...")
#cuboid_volume = volume(lower_bounds,upper_bounds)
cuboid_volume = volume(lbounds, ubounds)
probability_mass = prob_mass(cuboid_volume, cuboid_volume)
print(" probability mass: %s" % probability_mass)
expectation = expectation_value(model, lower_bounds, upper_bounds)
print(" expectation: %s" % expectation)
mean_value = mean(expectation, cuboid_volume)
print(" mean value: %s" % mean_value)
diameter = UQ(RVstart, RVend, lower_bounds, upper_bounds)
mcdiarmid = mcdiarmid_bound(mean_value, sqrt(diameter))
print("McDiarmid bound: %s" % mcdiarmid)
#if RVstart != 0 or RVend != 2: # abort when not a 3-D problem
# break #FIXME: break? or exit? or pass/else? or ???
weighted_bound = []
sanity = []
print " model: f(x) = %s(x)" % function_name
param_string = "["
for i in range(RVmax):
param_string += "'x%s'" % str(i+1)
if i == (RVmax - 1):
param_string += "]"
else:
param_string += ", "
print " parameters: %s" % param_string
print " lower bounds: %s" % lower_bounds
print " upper bounds: %s" % upper_bounds
# print " ..."
#cuboid_volume = volume(lower_bounds,upper_bounds)
cuboid_volume = volume(lbounds,ubounds)
probability_mass = prob_mass(cuboid_volume,cuboid_volume)
print " probability mass: %s" % probability_mass
expectation = expectation_value(model,lower_bounds,upper_bounds)
print " expectation: %s" % expectation
mean_value = mean(expectation,cuboid_volume)
print " mean value: %s" % mean_value
diameter = UQ(RVstart,RVend,lower_bounds,upper_bounds)
mcdiarmid = mcdiarmid_bound(mean_value,sqrt(diameter))
print "McDiarmid bound: %s" % mcdiarmid
#if RVstart != 0 or RVend != 2: # abort when not a 3-D problem
# break #FIXME: break? or exit? or pass/else? or ???
weighted_bound = []
sanity = []