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
|
##############################################################################################################################################################################
# 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.
##############################################################################################################################################################################
import numpy as np
import Tasmanian
def example_10():
print("\n---------------------------------------------------------------------------------------------------\n")
print("Example 10: comparison between local polynomial and wavelet grids\n")
iNumInputs = 2 # using two inputs for testing
# test the error on a uniform dense grid with 10K points
iTestGridSize = 100
dx = np.linspace(-1.0, 1.0, iTestGridSize) # sample on a uniform grid
aMeshX, aMeshY = np.meshgrid(dx, dx)
aTestPoints = np.column_stack([aMeshX.reshape((iTestGridSize**2, 1)),
aMeshY.reshape((iTestGridSize**2, 1))])
def get_error(grid, model, aTestPoints):
aGridResult = grid.evaluateBatch(aTestPoints)
aModelResult = np.empty((aTestPoints.shape[0], 1), np.float64)
for i in range(aTestPoints.shape[0]):
aModelResult[i,:] = model(aTestPoints[i,:])
return np.max(np.abs(aModelResult[:,0] - aGridResult[:,0]))
def sharp_model(aX):
return np.ones((1,)) * aX[0] / (1.0 + 100.0 * np.exp(-10.0 * aX[1]))
grid_poly = Tasmanian.makeLocalPolynomialGrid(iNumInputs, 1, 3,
iOrder = 1, sRule = "localp")
grid_wavelet = Tasmanian.makeWaveletGrid(iNumInputs, 1, 1, 1)
print(" polynomial wavelet")
print(" points error points error")
fTolerance = 1.E-5;
while((grid_poly.getNumNeeded() > 0) or (grid_wavelet.getNumNeeded() > 0)):
Tasmanian.loadNeededValues(lambda x, tid: sharp_model(x), grid_poly, 4);
Tasmanian.loadNeededValues(lambda x, tid: sharp_model(x), grid_wavelet, 4);
# print the results at this stage
print("{0:>8d}{1:>14.4e}{2:>8d}{3:>14.4e}".format(
grid_poly.getNumLoaded(), get_error(grid_poly, sharp_model, aTestPoints),
grid_wavelet.getNumLoaded(), get_error(grid_wavelet, sharp_model, aTestPoints)))
# setting refinement for each grid
grid_poly.setSurplusRefinement(fTolerance, 0, "fds");
grid_wavelet.setSurplusRefinement(fTolerance, 0, "fds");
if (__name__ == "__main__"):
example_10()
|
