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##############################################################################################################################################################################
# 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_08():
print("\n---------------------------------------------------------------------------------------------------\n")
print("Example 8: interpolate different functions demonstrating the different")
print(" local polynomial rules\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 smooth_model(aX):
return np.ones((1,)) * np.exp(-aX[0]**2) * np.cos(aX[1])
iOrder = 2
grid_localp = Tasmanian.makeLocalPolynomialGrid(iNumInputs, 1, 7, iOrder, "localp")
grid_semilocalp = Tasmanian.makeLocalPolynomialGrid(iNumInputs, 1, 7, iOrder, "semi-localp")
Tasmanian.loadNeededValues(lambda x, tid : smooth_model(x), grid_localp, 4)
Tasmanian.loadNeededValues(lambda x, tid : smooth_model(x), grid_semilocalp, 4)
print("Using smooth model: f(x, y) = exp(-x*x) * cos(y)")
print(" rule_localp, points = {0:1d} error = {1:1.4e}".format(
grid_localp.getNumPoints(), get_error(grid_localp, smooth_model, aTestPoints)))
print(" rule_semilocalp, points = {0:1d} error = {1:1.4e}".format(
grid_semilocalp.getNumPoints(), get_error(grid_semilocalp, smooth_model, aTestPoints)))
print(" If the model is smooth, rule_semilocalp has an advantage.\n")
def zero_model(aX):
return np.ones((1,)) * np.cos(0.5 * np.pi * aX[0]) * np.cos(0.5 * np.pi * aX[1])
grid_localp0 = Tasmanian.makeLocalPolynomialGrid(iNumInputs, 1, 6, iOrder, "localp-zero")
Tasmanian.reloadLoadedPoints(lambda x, tid : zero_model(x), grid_localp, 4)
Tasmanian.loadNeededValues(lambda x, tid : zero_model(x), grid_localp0, 4)
print("Using homogeneous model: f(x, y) = cos(pi * x / 2) * cos(pi * y / 2)")
print(" rule_localp, points = {0:1d} error = {1:1.4e}".format(
grid_localp.getNumPoints(), get_error(grid_localp, zero_model, aTestPoints)))
print(" rule_localp0, points = {0:1d} error = {1:1.4e}".format(
grid_localp0.getNumPoints(), get_error(grid_localp0, zero_model, aTestPoints)))
print(" The rule_localp0 uses basis tuned for models with zero boundary.")
if (__name__ == "__main__"):
example_08()
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