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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_04():
print("\n---------------------------------------------------------------------------------------------------\n")
print("Example 4: interpolate f(x,y) = exp(-x^2) * cos(y), using clenshaw-curtis iptotal rule")
iNumInputs = 2
iNumOutputs = 1
aPointOfInterest = np.array([0.3, 0.7])
aReferenceSolution = np.exp(-aPointOfInterest[0]**2) * np.cos(aPointOfInterest[1])
for prec in [6, 12]:
grid = Tasmanian.makeGlobalGrid(iNumInputs, iNumOutputs, prec,
"iptotal", "clenshaw-curtis")
aPoints = grid.getNeededPoints()
aModelValues = np.exp(-aPoints[:,0]**2) * np.cos(aPoints[:,1])
grid.loadNeededValues(aModelValues.reshape((aModelValues.shape[0], iNumOutputs)))
# when using multiple points at once, evaluateBatch() is more efficient
aResult = grid.evaluate(aPointOfInterest)
fError = np.abs(aResult[0] - aReferenceSolution)
print("\n using total degree polynomials: {0:>2d}th degree".format(prec))
print(" the grid has: {0:1d} points".format(grid.getNumPoints()))
print(" interpolant at (0.3,0.7): {0:1.5e}".format(aResult[0]))
print(" error: {0:1.5e}".format(fError))
if (__name__ == "__main__"):
example_04()
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