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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/blas.h>
#include <cusp/multiply.h>
#include <cusp/krylov/arnoldi.h>
#include <cusp/array1d.h>
#include <cusp/array2d.h>
#include <cusp/detail/random.h>
#include <cusp/detail/format_utils.h>
#include <thrust/extrema.h>
#include <thrust/transform.h>
#include <thrust/iterator/counting_iterator.h>
#include <thrust/reduce.h>
#include <thrust/detail/integer_traits.h>
namespace cusp
{
namespace detail
{
// TODO move this to a shared header
// absolute<T> computes the absolute value of a number f(x) -> |x|
template <typename T>
struct absolute : public thrust::unary_function<T,T>
{
__host__ __device__
T operator()(T x)
{
return x < 0 ? -x : x;
}
};
template <typename Matrix>
double estimate_spectral_radius(const Matrix& A, size_t k = 20)
{
CUSP_PROFILE_SCOPED();
typedef typename Matrix::index_type IndexType;
typedef typename Matrix::value_type ValueType;
typedef typename Matrix::memory_space MemorySpace;
const IndexType N = A.num_rows;
cusp::array1d<ValueType, MemorySpace> x(N);
cusp::array1d<ValueType, MemorySpace> y(N);
// initialize x to random values in [0,1)
cusp::copy(cusp::detail::random_reals<ValueType>(N), x);
for(size_t i = 0; i < k; i++)
{
cusp::blas::scal(x, ValueType(1.0) / cusp::blas::nrmmax(x));
cusp::multiply(A, x, y);
x.swap(y);
}
if (k == 0)
return 0;
else
return cusp::blas::nrm2(x) / cusp::blas::nrm2(y);
}
template <typename Matrix>
double ritz_spectral_radius(const Matrix& A, size_t k = 10)
{
CUSP_PROFILE_SCOPED();
typedef typename Matrix::value_type ValueType;
cusp::array2d<ValueType,cusp::host_memory> H;
cusp::krylov::arnoldi(A, H, k);
return estimate_spectral_radius(H);
}
template <typename Matrix>
double ritz_spectral_radius_symmetric(const Matrix& A, size_t k = 10)
{
CUSP_PROFILE_SCOPED();
typedef typename Matrix::value_type ValueType;
cusp::array2d<ValueType,cusp::host_memory> H;
cusp::krylov::lanczos(A, H, k);
return estimate_spectral_radius(H);
}
template <typename IndexType, typename ValueType, typename MemorySpace>
double disks_spectral_radius(const cusp::coo_matrix<IndexType,ValueType,MemorySpace>& A)
{
CUSP_PROFILE_SCOPED();
const IndexType N = A.num_rows;
// compute sum of absolute values for each row of A
cusp::array1d<IndexType, MemorySpace> row_sums(N);
{
cusp::array1d<IndexType, MemorySpace> temp(N);
thrust::reduce_by_key
(A.row_indices.begin(), A.row_indices.end(),
thrust::make_transform_iterator(A.values.begin(), absolute<ValueType>()),
temp.begin(),
row_sums.begin());
}
return *thrust::max_element(row_sums.begin(), row_sums.end());
}
template <typename Matrix>
double disks_spectral_radius(const Matrix& A)
{
typedef typename Matrix::index_type IndexType;
typedef typename Matrix::value_type ValueType;
typedef typename Matrix::memory_space MemorySpace;
const cusp::coo_matrix<IndexType,ValueType,MemorySpace> C(A);
return disks_spectral_radius(C);
}
} // end namespace detail
} // end namespace cusp
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