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// @HEADER
// ************************************************************************
//
// Intrepid2 Package
// Copyright (2007) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// 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 Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "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 SANDIA CORPORATION OR THE
// 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.
//
// Questions? Contact Kyungjoo Kim (kyukim@sandia.gov),
// Mauro Perego (mperego@sandia.gov), or
// Nate Roberts (nvrober@sandia.gov)
//
// ************************************************************************
// @HEADER
/** \file LegendreTests.cpp
\brief Tests to verify various implementations of Legendre polynomials.
\author Created by N.V. Roberts.
*/
#include "Teuchos_UnitTestHarness.hpp"
#include "Intrepid2_Polylib.hpp" // provides JacobiPolynomial implementation used for verification
#include "Intrepid2_Polynomials.hpp" // provides the Legendre polynomials under test
#include "Intrepid2_Types.hpp"
#include "Intrepid2_TestUtils.hpp"
#include "Kokkos_Core.hpp"
namespace
{
using namespace Intrepid2;
using DeviceType = DefaultTestDeviceType;
using ExecutionSpace = typename DeviceType::execution_space;
void testLegendreDerivatives(const double x, const int maxPolyOrder, const int derivativeOrder, const double tol,
Teuchos::FancyOStream &out, bool &success)
{
Kokkos::View<double*,DeviceType> legendreDerivatives("legendre derivatives",maxPolyOrder+1);
using Intrepid2::Polynomials::legendreDerivativeValues;
// wrap invocation in parallel_for just to ensure execution on device (for CUDA)
auto policy = Kokkos::RangePolicy<>(ExecutionSpace(),0,1);
Kokkos::parallel_for(policy, KOKKOS_LAMBDA(const int dummy_index)
{
legendreDerivativeValues(legendreDerivatives, maxPolyOrder, x, derivativeOrder);
});
auto legendreDerivativesHost = getHostCopy(legendreDerivatives);
// Polylib Jacobi computes a single function at potentially multiple points
const int numPoints = 1;
Kokkos::View<double*,DeviceType> inputPoints("x point", numPoints);
Kokkos::deep_copy(inputPoints,x);
Kokkos::View<double*,DeviceType> jacobiValue("jacobi value from Polynomials::JacobiPolynomial",numPoints);
for (int i=0; i<=maxPolyOrder; i++)
{
double expectedValue;
if (i <= derivativeOrder)
{
expectedValue = 0.0;
}
else
{
const Kokkos::View<double*,DeviceType> null;
const double alpha = 0;
const double beta = 0;
double scaleFactor = 1.0;
for (int j=1; j<=derivativeOrder; j++)
{
scaleFactor *= 0.5 * (j+alpha+beta+i);
}
// wrap invocation in parallel_for just to ensure execution on device (for CUDA)
auto policy = Kokkos::RangePolicy<>(ExecutionSpace(),0,1);
Kokkos::parallel_for(policy, KOKKOS_LAMBDA(const int dummy_index)
{
Intrepid2::Polylib::Serial::JacobiPolynomial(numPoints, inputPoints, jacobiValue, null, i-derivativeOrder, alpha+derivativeOrder, beta+derivativeOrder);
});
auto jacobiValueHost = getHostCopy(jacobiValue);
expectedValue = scaleFactor * jacobiValueHost(0);
bool valuesAreBothSmall = valuesAreSmall(expectedValue, legendreDerivativesHost(i), tol);
if (! valuesAreBothSmall)
{
if (! approximatelyEqual(expectedValue, legendreDerivativesHost(i), tol) )
{
double diff = abs(expectedValue - legendreDerivativesHost(i));
success = false;
out << "FAILURE: testLegendreDerivative -- expectedValue was " << expectedValue;
out << "; actual was " << legendreDerivativesHost(i) << " (diff: " << diff << ") for derivative " << derivativeOrder << " of i = " << i;
out << " at x = " << x << std::endl;
}
}
}
}
}
TEUCHOS_UNIT_TEST( Legendre, DerivativesMatchJacobi )
{
// test confirms that legendreDerivativeValues() and JacobiPolynomial() values agree
const double tol = TEST_TOLERANCE_TIGHT;
std::vector<double> x_values = {{-1.0,-0.5,-1.0/3.0,0.0,1.0/3.0,0.50,1.0}};
int polyOrderMax = 10;
for (int derivativeOrder=1; derivativeOrder<=10; derivativeOrder++)
{
for (auto x : x_values)
{
testLegendreDerivatives(x, polyOrderMax, derivativeOrder, tol, out, success);
}
}
}
} // namespace
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