1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
|
#!@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 makeGlobalGrid
from Tasmanian import makeSequenceGrid
from Tasmanian import loadNeededPoints
import numpy
def example_02():
print("\n---------------------------------------------------------------------------------------------------\n")
print("EXAMPLE 2: set the inference problem: identify model parameters x_0 and x_1")
print(" from data (noise free example)")
print(" model: f(x) = sin(x_0*M_PI*t + x_1), data: d = sin(M_PI*t + 0.3*M_PI)")
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 likelihood")
print(" NOTE: See the comments in the C++ DREAM Example 2\n")
iNumDimensions = 2;
iNumChains = 100;
iNumBurnupIterations = 3000;
iNumCollectIterations = 100;
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])
def likelihood(aY, aData):
# using log-form likelihood
# numpy.ones((1,)) converts the scalar to a 1D numpy array
return - 0.5 * len(aData) * numpy.sum((aY - aData)**2) * numpy.ones((1,))
aData = model([1.0, 0.3 * numpy.pi])
domain_lower = numpy.array([0.5, -0.1])
domain_upper = numpy.array([8.0, 1.7])
grid = makeGlobalGrid(iNumDimensions, 1, 10, 'iptotal', 'clenshaw-curtis')
grid.setDomainTransform(numpy.column_stack([domain_lower, domain_upper]))
loadNeededPoints(lambda x, tid : likelihood(model(x), aData), grid, iNumThreads = 2)
state = DREAM.State(iNumChains, grid)
state.setState(DREAM.genUniformSamples(domain_lower, domain_upper, state.getNumChains()))
DREAM.Sample(iNumBurnupIterations, iNumCollectIterations,
lambda x : grid.evaluateBatch(x).reshape((x.shape[0],)), # link to the SparseGrid
DREAM.Domain(grid),
state,
DREAM.IndependentUpdate("uniform", 0.5),
DREAM.DifferentialUpdate(90),
typeForm = DREAM.typeLogform)
aMean, aVariance = state.getHistoryMeanVariance()
print("Inferred values (using 10th order polynomial sparse grid):")
print(" frequency:{0:13.6f} error:{1:14.6e}".format(aMean[0],
numpy.abs(aMean[0] - 1.0)))
print(" correction:{0:13.6f} error:{1:14.6e}\n".format(aMean[1],
numpy.abs(aMean[0] - 0.3 * numpy.pi)))
# repeat the example using the faster Sequence grid and 30th order polynomials
grid = makeSequenceGrid(iNumDimensions, 1, 30, 'iptotal', 'leja')
grid.setDomainTransform(numpy.column_stack([domain_lower, domain_upper]))
loadNeededPoints(lambda x, tid : likelihood(model(x), aData), grid, iNumThreads = 2)
state = DREAM.State(iNumChains, grid)
state.setState(DREAM.genUniformSamples(domain_lower, domain_upper, state.getNumChains()))
DREAM.Sample(iNumBurnupIterations, iNumCollectIterations,
lambda x : grid.evaluateBatch(x).reshape((x.shape[0],)), # link to the SparseGrid
DREAM.Domain(grid),
state,
DREAM.IndependentUpdate("uniform", 0.5),
DREAM.DifferentialUpdate(90),
typeForm = DREAM.typeLogform)
aMean, aVariance = state.getHistoryMeanVariance()
print("Inferred values (using 30th order polynomial sparse grid):")
print(" frequency:{0:13.6f} error:{1:14.6e}".format(aMean[0],
numpy.abs(aMean[0] - 1.0)))
print(" correction:{0:13.6f} error:{1:14.6e}".format(aMean[1],
numpy.abs(aMean[0] - 0.3 * numpy.pi)))
if __name__ == "__main__":
example_02()
|
