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/*
* Copyright 2008-2009 NVIDIA Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*! \file diffusion.h
* \brief Anisotropic diffusion matrix generators
*/
#pragma once
#include <cusp/detail/config.h>
#include <cusp/gallery/stencil.h>
#ifdef _WIN32
#define _USE_MATH_DEFINES 1 // make sure M_PI is defined
#endif
#include <math.h>
namespace cusp
{
namespace gallery
{
/*! \addtogroup gallery Matrix Gallery
* \ingroup gallery
* \{
*/
struct disc_type {};
struct FD : public disc_type {};
struct FE : public disc_type {};
/*! \p diffusion: Create a matrix representing an anisotropic
* Poisson problem discretized on an \p m by \p n grid with
* the a given direction.
*
* \param matrix output
* \param m number of grid rows
* \param n number of grid columns
* \param eps magnitude of anisotropy
* \param theta angle of anisotropy in radians
*
* \tparam MatrixType matrix container
*
*/
template <typename Method, typename MatrixType>
void diffusion( MatrixType& matrix, size_t m, size_t n,
const double eps = 1e-5,
const double theta = M_PI/4.0)
{
typedef typename MatrixType::index_type IndexType;
typedef typename MatrixType::value_type ValueType;
typedef thrust::tuple<IndexType,IndexType> StencilIndex;
typedef thrust::tuple<StencilIndex,ValueType> StencilPoint;
ValueType C = cos(theta);
ValueType S = sin(theta);
ValueType CC = C*C;
ValueType SS = S*S;
ValueType CS = C*S;
ValueType a;
ValueType b;
ValueType c;
ValueType d;
ValueType e;
if( thrust::detail::is_same<Method, FE>::value )
{
a = (-1.0*eps - 1.0)*CC + (-1.0*eps - 1.0)*SS + ( 3.0*eps - 3.0)*CS;
b = ( 2.0*eps - 4.0)*CC + (-4.0*eps + 2.0)*SS;
c = (-1.0*eps - 1.0)*CC + (-1.0*eps - 1.0)*SS + (-3.0*eps + 3.0)*CS;
d = (-4.0*eps + 2.0)*CC + ( 2.0*eps - 4.0)*SS;
e = ( 8.0*eps + 8.0)*CC + ( 8.0*eps + 8.0)*SS;
a /= 6.0;
b /= 6.0;
c /= 6.0;
d /= 6.0;
e /= 6.0;
}
else if( thrust::detail::is_same<Method, FD>::value )
{
a = 0.5 * (eps-1.0) * CS;
b = -(eps*SS + CC);
c = -a;
d = -(eps*CC + SS);
e = 2.0 * (eps+1.0);
}
else
{
throw cusp::invalid_input_exception("unrecognized discretization method");
}
cusp::array1d<StencilPoint, cusp::host_memory> stencil;
stencil.push_back(StencilPoint(StencilIndex( -1, -1), a));
stencil.push_back(StencilPoint(StencilIndex( 0, -1), b));
stencil.push_back(StencilPoint(StencilIndex( 1, -1), c));
stencil.push_back(StencilPoint(StencilIndex( -1, 0), d));
stencil.push_back(StencilPoint(StencilIndex( 0, 0), e));
stencil.push_back(StencilPoint(StencilIndex( 1, 0), d));
stencil.push_back(StencilPoint(StencilIndex( -1, 1), c));
stencil.push_back(StencilPoint(StencilIndex( 0, 1), b));
stencil.push_back(StencilPoint(StencilIndex( 1, 1), a));
cusp::gallery::generate_matrix_from_stencil(matrix, stencil, StencilIndex(m,n));
}
/*! \}
*/
} // end namespace gallery
} // end namespace cusp
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