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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_02():
print("\n---------------------------------------------------------------------------------------------------\n")
print("Example 2: integrate f(x,y) = exp(-x^2) * cos(y) over [-5,5] x [-2,3]")
print(" using Gauss-Patterson nodes and total degree polynomial space)")
iNumDimensions = 2
iExactness = 20
fExactIntegral = 1.861816427518323e+00
# the type_qptotal will guarantee exact integral for all polynomials with degree 20 or less
grid = Tasmanian.makeGlobalGrid(iNumDimensions, 0, iExactness, "qptotal", "gauss-patterson")
grid.setDomainTransform(np.array([[-5.0, 5.0], [-2.0, 3.0]])) # set the non-canonical domain
aPoints = grid.getPoints()
aWeights = grid.getQuadratureWeights()
fApproximateIntegral = np.sum(aWeights * np.exp(-aPoints[:,0]**2) * np.cos(aPoints[:,1]))
fError = np.abs(fApproximateIntegral - fExactIntegral)
print(" at polynomial exactness".format(iExactness))
print(" the grid has: {0:1d}".format(grid.getNumPoints()))
print(" integral: {0:1.14e}".format(fApproximateIntegral))
print(" error: {0:1.14e}\n".format(fError))
iExactness = 40
# the type_qptotal will guarantee exact integral for all polynomials with degree 20 or less
grid = Tasmanian.makeGlobalGrid(iNumDimensions, 0, iExactness, "qptotal", "gauss-patterson")
grid.setDomainTransform(np.array([[-5.0, 5.0], [-2.0, 3.0]])) # must reset the domain
aPoints = grid.getPoints()
aWeights = grid.getQuadratureWeights()
fApproximateIntegral = np.sum(aWeights * np.exp(-aPoints[:,0]**2) * np.cos(aPoints[:,1]))
fError = np.abs(fApproximateIntegral - fExactIntegral)
print(" at polynomial exactness".format(iExactness))
print(" the grid has: {0:1d}".format(grid.getNumPoints()))
print(" integral: {0:1.14e}".format(fApproximateIntegral))
print(" error: {0:1.14e}\n".format(fError))
if (__name__ == "__main__"):
example_02()
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