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#!@Tasmanian_string_python_hashbang@
##############################################################################################################################################################################
# Copyright (c) 2017, Miroslav Stoyanov
#
# This file is part of
# Toolkit for Adaptive Stochastic Modeling And Non-Intrusive ApproximatioN: TASMANIAN
#
# Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions
# and the following disclaimer in the documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse
# or promote products derived from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
# INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
# IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
# OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
# OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# UT-BATTELLE, LLC AND THE UNITED STATES GOVERNMENT MAKE NO REPRESENTATIONS AND DISCLAIM ALL WARRANTIES, BOTH EXPRESSED AND IMPLIED.
# THERE ARE NO EXPRESS OR IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, OR THAT THE USE OF THE SOFTWARE WILL NOT INFRINGE ANY PATENT,
# COPYRIGHT, TRADEMARK, OR OTHER PROPRIETARY RIGHTS, OR THAT THE SOFTWARE WILL ACCOMPLISH THE INTENDED RESULTS OR THAT THE SOFTWARE OR ITS USE WILL NOT RESULT IN INJURY OR DAMAGE.
# THE USER ASSUMES RESPONSIBILITY FOR ALL LIABILITIES, PENALTIES, FINES, CLAIMS, CAUSES OF ACTION, AND COSTS AND EXPENSES, CAUSED BY, RESULTING FROM OR ARISING OUT OF,
# IN WHOLE OR IN PART THE USE, STORAGE OR DISPOSAL OF THE SOFTWARE.
##############################################################################################################################################################################
from Tasmanian import DREAM
from Tasmanian import SparseGrid
from Tasmanian import makeSequenceGrid
from Tasmanian import loadNeededPoints
import numpy
def example_03():
print("\n---------------------------------------------------------------------------------------------------\n")
print("EXAMPLE 3: set the inference problem: identify x_0 and x_1 model parameters")
print(" from data (noise free example)")
print(" model: f(x) = sin(x_0*M_PI*t + x_1),")
print(" data: d = sin(5*M_PI*t + 0.3*M_PI) + sin(10*M_PI*t + 0.1*M_PI)")
print(" compared to Example 2, the data is a superposition of two signals")
print(" and the posterior is multi-modal")
print(" -- problem setup --")
print(" t in [0,1], t is discretized with 32 equidistant nodes")
print(" the likelihood is exp(- 16 * (f(x) - d)^2)")
print(" using a sparse grid to interpolate the model\n")
iNumDimensions = 2
iNumOutputs = 32
iNumChains = 500
iNumBurnupIterations = 1000
iNumCollectIterations = 300
def model(aX):
# using 32 nodes in the interior of (0.0, 1.0)
t = numpy.linspace(1.0 / 64.0, 1.0 - 1.0 / 64.0, 32)
return numpy.sin(numpy.pi * aX[0] * t + aX[1])
aData = model([5.0, 0.3 * numpy.pi]) + model([10.0, 0.1 * numpy.pi])
grid = makeSequenceGrid(iNumDimensions, iNumOutputs, 30, 'iptotal', 'leja')
domain_lower = numpy.array([ 1.0, -0.1])
domain_upper = numpy.array([12.0, 1.7])
grid.setDomainTransform(numpy.column_stack([domain_lower, domain_upper]))
loadNeededPoints(lambda x, tid : model(x), grid, 2)
likely = DREAM.LikelihoodGaussIsotropic(1.0 / float(iNumOutputs), aData)
state = DREAM.State(iNumChains, grid)
state.setState(DREAM.genUniformSamples(domain_lower, domain_upper, state.getNumChains()))
DREAM.Sample(iNumBurnupIterations, iNumCollectIterations,
DREAM.Posterior(grid, likely, prior = "uniform", typeForm = DREAM.typeLogform),
DREAM.Domain(grid),
state,
DREAM.IndependentUpdate("gaussian", 0.01),
DREAM.DifferentialUpdate(90),
typeForm = DREAM.typeLogform)
aSamples = state.getHistory()
# split the frequencies into low and high for the two modes of the posterior
# here 6.5 is the mid-point of the domain
low_frequency = numpy.average(numpy.array(
[aSamples[i,0] for i in range(aSamples.shape[0]) if aSamples[i,0] < 6.5]
))
low_correction = numpy.average(numpy.array(
[aSamples[i,1] for i in range(aSamples.shape[0]) if aSamples[i,0] < 6.5]
))
high_frequency = numpy.average(numpy.array(
[aSamples[i,0] for i in range(aSamples.shape[0]) if aSamples[i,0] >= 6.5]
))
high_correction = numpy.average(numpy.array(
[aSamples[i,1] for i in range(aSamples.shape[0]) if aSamples[i,0] >= 6.5]
))
print("Inferred values:")
print(" low frequency:{0:13.6f} error:{1:14.6e}".format(low_frequency,
numpy.abs(low_frequency - 5.0)))
print(" low correction:{0:13.6f} error:{1:14.6e}\n".format(low_correction,
numpy.abs(low_correction - 0.3 * numpy.pi)))
print(" high frequency:{0:13.6f} error:{1:14.6e}".format(high_frequency,
numpy.abs(high_frequency - 10.0)))
print(" high correction:{0:13.6f} error:{1:14.6e}".format(high_correction,
numpy.abs(high_correction - 0.1 * numpy.pi)))
if __name__ == "__main__":
example_03()
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