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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 2009-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
#######################################################################
# scaling and mpi info; also optimizer configuration parameters
# hard-wired: use DE solver, don't use mpi, F-F' calculation
# (similar to concentration.in)
#######################################################################
scale = 1.0
#XXX: <mpi config goes here>
npop = 20
maxiter = 500
maxfun = 1e+6
convergence_tol = 1e-4
crossover = 0.9
percent_change = 0.9
#######################################################################
# the model function
# (similar to Simulation.cpp)
#######################################################################
def function(x):
"""a simple model function
f = x1*x2 + x3 + 2.0
Input:
- x -- 1-d array of coefficients [x1,x2,x3]
Output:
- f -- function result
"""
return x[0]*x[1] + x[2] + 2.0
#######################################################################
# the subdiameter calculation
# (similar to driver.sh)
#######################################################################
def costFactory(i):
"""a cost factory for the cost function"""
def cost(rv):
"""compute the diameter as a calculation of cost
Input:
- rv -- 1-d array of model parameters
Output:
- diameter -- scale * | F(x) - F(x')|**2
"""
# prepare x and xprime
params = rv[:-1] #XXX: assumes Xi' is at rv[-1]
params_prime = rv[:i]+rv[-1:]+rv[i+1:-1] #XXX: assumes Xi' is at rv[-1]
# get the F(x) response
Fx = function(params)
# get the F(x') response
Fxp = function(params_prime)
# compute diameter
return -scale * (Fx - Fxp)**2
return cost
#######################################################################
# the differential evolution optimizer
# (replaces the call to dakota)
#######################################################################
def dakota(cost,lb,ub):
from mystic.solvers import DifferentialEvolutionSolver2
from mystic.termination import CandidateRelativeTolerance as CRT
from mystic.strategy import Best1Exp
from mystic.monitors import VerboseMonitor, Monitor
from mystic.tools import getch, random_seed
random_seed(123)
#stepmon = VerboseMonitor(100)
stepmon = Monitor()
evalmon = Monitor()
ndim = len(lb) # [(1 + RVend) - RVstart] + 1
solver = DifferentialEvolutionSolver2(ndim,npop)
solver.SetRandomInitialPoints(min=lb,max=ub)
solver.SetStrictRanges(min=lb,max=ub)
solver.SetEvaluationLimits(maxiter,maxfun)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
tol = convergence_tol
solver.Solve(cost,termination=CRT(tol,tol),strategy=Best1Exp, \
CrossProbability=crossover,ScalingFactor=percent_change)
print(solver.bestSolution)
diameter = -solver.bestEnergy / scale
func_evals = solver.evaluations
return diameter, func_evals
#######################################################################
# loop over model parameters to calculate concentration of measure
# (similar to main.cc)
#######################################################################
def UQ(start,end,lower,upper):
diameters = []
function_evaluations = []
total_func_evals = 0
total_diameter = 0.0
for i in range(start,end+1):
lb = lower[start:end+1] + [lower[i]]
ub = upper[start:end+1] + [upper[i]]
#construct cost function and run optimizer
cost = costFactory(i)
subdiameter, func_evals = dakota(cost,lb,ub) #XXX: no initial conditions
function_evaluations.append(func_evals)
diameters.append(subdiameter)
total_func_evals += function_evaluations[-1]
total_diameter += diameters[-1]
print("subdiameters (squared): %s" % diameters)
print("diameter (squared): %s" % total_diameter)
print("func_evals: %s => %s" % (function_evaluations, total_func_evals))
return
#######################################################################
# rank, bounds, and restart information
# (similar to concentration.variables)
#######################################################################
if __name__ == '__main__':
RVstart = 0; RVend = 2
lower_bounds = [1.0,2.0,3.0]
upper_bounds = [1.1,2.2,3.3]
print(" function: f = x1*x2 + x3 + 2.0")
print(" parameters: ['x1', 'x2', 'x3']")
print(" lower bounds: %s" % lower_bounds)
print(" upper bounds: %s" % upper_bounds)
print(" ...")
UQ(RVstart,RVend,lower_bounds,upper_bounds)
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