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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/detail/config.h>
#include <cusp/multiply.h>
#include <cusp/array1d.h>
#include <cusp/detail/random.h>
namespace cusp
{
namespace krylov
{
template <typename Matrix, typename Array2d>
void lanczos(const Matrix& A, Array2d& H, size_t k = 10)
{
typedef typename Matrix::value_type ValueType;
typedef typename Matrix::memory_space MemorySpace;
size_t N = A.num_cols;
size_t maxiter = std::min(N, k);
// allocate workspace
cusp::array1d<ValueType,MemorySpace> v0(N);
cusp::array1d<ValueType,MemorySpace> v1(N);
cusp::array1d<ValueType,MemorySpace> w(N);
// initialize starting vector to random values in [0,1)
cusp::copy(cusp::detail::random_reals<ValueType>(N), v1);
cusp::blas::scal(v1, ValueType(1) / cusp::blas::nrm2(v1));
Array2d H_(maxiter + 1, maxiter, 0);
ValueType alpha = 0.0, beta = 0.0;
size_t j;
for(j = 0; j < maxiter; j++)
{
cusp::multiply(A, v1, w);
if(j >= 1)
{
H_(j - 1, j) = beta;
cusp::blas::axpy(v0, w, -beta);
}
alpha = cusp::blas::dot(w, v1);
H_(j,j) = alpha;
cusp::blas::axpy(v1, w, -alpha);
beta = cusp::blas::nrm2(w);
H_(j + 1, j) = beta;
if(beta < 1e-10) break;
cusp::blas::scal(w, ValueType(1) / beta);
// [v0 v1 w] - > [v1 w v0]
v0.swap(v1);
v1.swap(w);
}
H.resize(j,j);
for(size_t row = 0; row < j; row++)
for(size_t col = 0; col < j; col++)
H(row,col) = H_(row,col);
}
template <typename Matrix, typename Array2d>
void arnoldi(const Matrix& A, Array2d& H, size_t k = 10)
{
typedef typename Matrix::value_type ValueType;
typedef typename Matrix::memory_space MemorySpace;
size_t N = A.num_rows;
size_t maxiter = std::min(N, k);
Array2d H_(maxiter + 1, maxiter, 0);
// allocate workspace of k + 1 vectors
std::vector< cusp::array1d<ValueType,MemorySpace> > V(maxiter + 1);
for (size_t i = 0; i < maxiter + 1; i++)
V[i].resize(N);
// initialize starting vector to random values in [0,1)
cusp::copy(cusp::detail::random_reals<ValueType>(N), V[0]);
// normalize v0
cusp::blas::scal(V[0], ValueType(1) / cusp::blas::nrm2(V[0]));
size_t j;
for(j = 0; j < maxiter; j++)
{
cusp::multiply(A, V[j], V[j + 1]);
for(size_t i = 0; i <= j; i++)
{
H_(i,j) = cusp::blas::dot(V[i], V[j + 1]);
cusp::blas::axpy(V[i], V[j + 1], -H_(i,j));
}
H_(j+1,j) = cusp::blas::nrm2(V[j + 1]);
if(H_(j+1,j) < 1e-10) break;
cusp::blas::scal(V[j + 1], ValueType(1) / H_(j+1,j));
}
H.resize(j,j);
for( size_t row = 0; row < j; row++ )
for( size_t col = 0; col < j; col++ )
H(row,col) = H_(row,col);
}
} // end namespace krylov
} // end namespace cusp
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