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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.
*/
#pragma once
#include <cusp/array1d.h>
#include <cusp/array2d.h>
#include <cusp/linear_operator.h>
#include <cmath>
namespace cusp
{
namespace detail
{
template <typename IndexType, typename ValueType, typename MemorySpace, typename Orientation>
int lu_factor(cusp::array2d<ValueType,MemorySpace,Orientation>& A,
cusp::array1d<IndexType,MemorySpace>& pivot)
{
const int n = A.num_rows;
// For each row and column, k = 0, ..., n-1,
for (int k = 0; k < n; k++)
{
// find the pivot row
pivot[k] = k;
ValueType max = std::fabs(A(k,k));
for (int j = k + 1; j < n; j++)
{
if (max < std::fabs(A(j,k)))
{
max = std::fabs(A(j,k));
pivot[k] = j;
}
}
// and if the pivot row differs from the current row, then
// interchange the two rows.
if (pivot[k] != k)
for (int j = 0; j < n; j++)
std::swap(A(k,j), A(pivot[k],j));
// and if the matrix is singular, return error
if (A(k,k) == 0.0)
return -1;
// otherwise find the lower triangular matrix elements for column k.
for (int i = k + 1; i < n; i++)
A(i,k) /= A(k,k);
// update remaining matrix
for (int i = k + 1; i < n; i++)
for (int j = k + 1; j < n; j++)
A(i,j) -= A(i,k) * A(k,j);
}
return 0;
}
template <typename IndexType, typename ValueType, typename MemorySpace, typename Orientation>
int lu_solve(const cusp::array2d<ValueType,MemorySpace,Orientation>& A,
const cusp::array1d<IndexType,MemorySpace>& pivot,
const cusp::array1d<ValueType,MemorySpace>& b,
cusp::array1d<ValueType,MemorySpace>& x)
{
const int n = A.num_rows;
// copy rhs to x
x = b;
// Solve the linear equation Lx = b for x, where L is a lower
// triangular matrix with an implied 1 along the diagonal.
for (int k = 0; k < n; k++)
{
if (pivot[k] != k)
std::swap(x[k],x[pivot[k]]);
for (int i = 0; i < k; i++)
x[k] -= A(k,i) * x[i];
}
// Solve the linear equation Ux = y, where y is the solution
// obtained above of Lx = b and U is an upper triangular matrix.
for (int k = n - 1; k >= 0; k--)
{
for (int i = k + 1; i < n; i++)
x[k] -= A(k,i) * x[i];
if (A(k,k) == 0)
return -1;
x[k] /= A(k,k);
}
return 0;
}
template <typename ValueType, typename MemorySpace>
class lu_solver : public cusp::linear_operator<ValueType,MemorySpace>
{
cusp::array2d<ValueType,cusp::host_memory> lu;
cusp::array1d<int,cusp::host_memory> pivot;
public:
lu_solver()
: linear_operator<ValueType,MemorySpace>()
{ }
lu_solver(const lu_solver<ValueType,MemorySpace>& M)
: lu(M.lu), pivot(M.pivot), linear_operator<ValueType,MemorySpace>(M.num_rows, M.num_cols, M.num_entries)
{ }
template <typename MatrixType>
lu_solver(const MatrixType& A)
: linear_operator<ValueType,MemorySpace>(A.num_rows, A.num_cols, A.num_entries)
{
CUSP_PROFILE_SCOPED();
// TODO assert A is square
lu = A;
pivot.resize(A.num_rows);
lu_factor(lu,pivot);
}
// TODO handle host and device
template <typename VectorType1, typename VectorType2>
void operator()(const VectorType1& x, VectorType2& y) const
{
CUSP_PROFILE_SCOPED();
lu_solve(lu, pivot, x, y);
}
};
} // end namespace detail
} // end namespace cusp
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