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/*
* Modifications to this file:
* Copyright (c) 2014-2015, The University of Queensland
* Licensed under the Apache License, Version 2.0.
*
*/
#pragma once
#include <thrust/functional.h>
#include <cusp/detail/functional.h>
#ifndef DIA_CHUNKSIZE
#define DIA_CHUNKSIZE 1024
#endif
//MW: add some OpenMP pragmas
namespace cusp
{
namespace detail
{
namespace host
{
//////////////
// COO SpMV //
//////////////
template <typename Matrix,
typename Vector1,
typename Vector2,
typename UnaryFunction,
typename BinaryFunction1,
typename BinaryFunction2>
void spmv_coo(const Matrix& A,
const Vector1& x,
Vector2& y,
UnaryFunction initialize,
BinaryFunction1 combine,
BinaryFunction2 reduce)
{
typedef typename Matrix::index_type IndexType;
typedef typename Vector2::value_type ValueType;
for(size_t i = 0; i < A.num_rows; i++)
y[i] = initialize(y[i]);
for(size_t n = 0; n < A.num_entries; n++)
{
const IndexType& i = A.row_indices[n];
const IndexType& j = A.column_indices[n];
const ValueType& Aij = A.values[n];
const ValueType& xj = x[j];
y[i] = reduce(y[i], combine(Aij, xj));
}
}
template <typename Matrix,
typename Vector1,
typename Vector2>
void spmv_coo(const Matrix& A,
const Vector1& x,
Vector2& y)
{
typedef typename Vector2::value_type ValueType;
spmv_coo(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
}
//////////////
// CSR SpMV //
//////////////
template <typename Matrix,
typename Vector1,
typename Vector2,
typename UnaryFunction,
typename BinaryFunction1,
typename BinaryFunction2>
void spmv_csr(const Matrix& A,
const Vector1& x,
Vector2& y,
UnaryFunction initialize,
BinaryFunction1 combine,
BinaryFunction2 reduce)
{
typedef typename Matrix::index_type IndexType;
typedef typename Vector2::value_type ValueType;
#pragma omp parallel for
for(size_t i = 0; i < A.num_rows; i++)
{
const IndexType& row_start = A.row_offsets[i];
const IndexType& row_end = A.row_offsets[i+1];
ValueType accumulator = initialize(y[i]);
for (IndexType jj = row_start; jj < row_end; jj++)
{
const IndexType& j = A.column_indices[jj];
const ValueType& Aij = A.values[jj];
const ValueType& xj = x[j];
accumulator = reduce(accumulator, combine(Aij, xj));
}
y[i] = accumulator;
}
}
template <typename Matrix,
typename Vector1,
typename Vector2>
void spmv_csr(const Matrix& A,
const Vector1& x,
Vector2& y)
{
typedef typename Vector2::value_type ValueType;
spmv_csr(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
}
//////////////
// DIA SpMV //
//////////////
template <typename Matrix,
typename Vector1,
typename Vector2,
typename UnaryFunction,
typename BinaryFunction1,
typename BinaryFunction2>
void spmv_dia(const Matrix& A,
const Vector1& x,
Vector2& y,
UnaryFunction initialize,
BinaryFunction1 combine,
BinaryFunction2 reduce)
{
typedef typename Matrix::index_type IndexType;
//typedef typename Vector2::value_type ValueType;
const size_t num_diagonals = A.values.num_cols;
if (A.symmetric) {
// if matrix has a main diagonal it is the first in offsets and should
// be skipped in the subdiagonal loop below. The main diagonal is
// processed by the second loop
const size_t d0 = (A.diagonal_offsets[0] == 0 ? 1 : 0);
#pragma omp parallel for
for (size_t ch = 0; ch < A.num_rows; ch += DIA_CHUNKSIZE) {
// initialize chunk
for (size_t row = ch; row < std::min(ch+DIA_CHUNKSIZE,A.num_rows); row++)
{
y[row] = initialize(y[row]);
}
// process subdiagonals
for (size_t d = 0; d < num_diagonals-d0; d++)
{
const size_t diag = num_diagonals-d-1;
for (size_t row = ch; row < std::min(ch+DIA_CHUNKSIZE,A.num_rows); row++)
{
const IndexType col = row - A.diagonal_offsets[diag];
if (col >= 0 && col < A.num_rows)
{
y[row] = reduce(y[row], combine(A.values(col, diag), x[col]));
}
}
}
// process main and upper diagonals
for (size_t d = 0; d < num_diagonals; d++)
{
for (size_t row = ch; row < std::min(ch+DIA_CHUNKSIZE,A.num_rows); row++)
{
const IndexType col = row + A.diagonal_offsets[d];
if (col >= 0 && col < A.num_cols)
{
y[row] = reduce(y[row], combine(A.values(row, d), x[col]));
}
}
}
}
} else { // !A.symmetric
#pragma omp parallel for
for (size_t ch = 0; ch < A.num_rows; ch += DIA_CHUNKSIZE) {
// initialize chunk
for (size_t row = ch; row < std::min(ch+DIA_CHUNKSIZE,A.num_rows); row++)
{
y[row] = initialize(y[row]);
}
// for each diagonal
for (size_t d = 0; d < num_diagonals; d++)
{
for (IndexType row=ch; row<std::min(ch+DIA_CHUNKSIZE,A.num_rows); row++)
{
const IndexType col = row + A.diagonal_offsets[d];
if (col >= 0 && col < A.num_cols)
{
y[row] = reduce(y[row], combine(A.values(row, d), x[col]));
}
}
}
}
}
}
template <typename Matrix,
typename Vector1,
typename Vector2>
void spmv_dia(const Matrix& A,
const Vector1& x,
Vector2& y)
{
typedef typename Vector2::value_type ValueType;
spmv_dia(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
}
//////////////
// CDS SpMV //
//////////////
template <typename Matrix,
typename Vector1,
typename Vector2,
typename UnaryFunction,
typename BinaryFunction1,
typename BinaryFunction2>
void spmv_cds(const Matrix& A,
const Vector1& x,
Vector2& y,
UnaryFunction initialize,
BinaryFunction1 combine,
BinaryFunction2 reduce)
{
typedef typename Matrix::index_type IndexType;
typedef typename Vector2::value_type ValueType;
const IndexType num_diagonals = A.diagonal_offsets.size();
const IndexType block_size = (IndexType)A.block_size;
const IndexType num_rows = (IndexType)A.num_rows;
// make chunksize a multiple of block_size
const IndexType chunksize = block_size*(DIA_CHUNKSIZE/block_size);
// optimization for special case
if (block_size == 2) {
if (A.symmetric) {
// if there is a main diagonal block, it is the first in offsets
// and should be skipped in the first loop below since the main
// diagonal is processed in the second loop
const IndexType d0 = (A.diagonal_offsets[0] == 0 ? 1 : 0);
#pragma omp parallel for
for (IndexType ch = 0; ch < num_rows; ch+=chunksize)
{
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row++)
{
y[row] = initialize(y[row]);
}
// process subdiagonal blocks
for (IndexType d = 0; d < num_diagonals-d0; d++)
{
const IndexType diag = num_diagonals-d-1;
const IndexType k = -2*A.diagonal_offsets[diag];
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row+=2)
{
const IndexType col = row + k;
if (col >= 0 && col <= num_rows-2)
{
y[row] = reduce(y[row], combine(A.values(col, 2*diag), x[col]));
y[row] = reduce(y[row], combine(A.values(col+1,2*diag), x[col+1]));
y[row+1] = reduce(y[row+1],combine(A.values(col, 2*diag+1),x[col]));
y[row+1] = reduce(y[row+1],combine(A.values(col+1,2*diag+1),x[col+1]));
}
}
}
// process main and upper diagonal blocks
for (IndexType d = 0; d < num_diagonals; d++)
{
const IndexType k = 2*A.diagonal_offsets[d];
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row+=2)
{
const IndexType col = row + k;
if (col >= 0 && col <= num_rows-2)
{
y[row] = reduce(y[row], combine(A.values(row, 2*d), x[col]));
y[row+1] = reduce(y[row+1],combine(A.values(row+1,2*d), x[col]));
y[row] = reduce(y[row], combine(A.values(row, 2*d+1),x[col+1]));
y[row+1] = reduce(y[row+1],combine(A.values(row+1,2*d+1),x[col+1]));
}
}
}
}
} else { // !A.symmetric
#pragma omp parallel for
for (IndexType ch = 0; ch < num_rows; ch+=chunksize)
{
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row+=2)
{
ValueType sum1 = initialize(y[row]);
ValueType sum2 = initialize(y[row+1]);
// for each diagonal block
for (IndexType d = 0; d < num_diagonals; d++)
{
const IndexType col = row + A.diagonal_offsets[d]*2;
if (col >= 0 && col <= num_rows-2)
{
sum1 = reduce(sum1,combine(A.values(row, 2*d), x[col]));
sum2 = reduce(sum2,combine(A.values(row+1,2*d), x[col]));
sum1 = reduce(sum1,combine(A.values(row, 2*d+1),x[col+1]));
sum2 = reduce(sum2,combine(A.values(row+1,2*d+1),x[col+1]));
}
}
y[row] = sum1;
y[row+1] = sum2;
}
}
} // A.symmetric
} else { // block size
if (A.symmetric) {
// if there is a main diagonal block, it is the first in offsets
// and should be skipped in the first loop below since the main
// diagonal is processed in the second loop
const IndexType d0 = (A.diagonal_offsets[0] == 0 ? 1 : 0);
const ValueType* values = thrust::raw_pointer_cast(&A.values.values[0]);
const IndexType pitch = A.values.pitch;
#pragma omp parallel for
for (IndexType ch = 0; ch < num_rows; ch+=chunksize)
{
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row++)
{
y[row] = initialize(y[row]);
}
IndexType idx = pitch*block_size*(num_diagonals-1);
// process subdiagonal blocks
for (IndexType d = 0; d < num_diagonals-d0; d++)
{
const IndexType diag = num_diagonals-d-1;
const IndexType k = -block_size*A.diagonal_offsets[diag];
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row+=block_size)
{
const IndexType col = row + k;
if (col >= 0 && col <= num_rows-block_size)
{
// for each row in block
for (IndexType j = 0; j < block_size; j++)
{
// for each column in block
for (IndexType i = 0; i < block_size; i++)
{
const ValueType& Aij = values[idx+col+i+j*pitch];
const ValueType& xj = x[col + i];
y[row+j] = reduce(y[row+j], combine(Aij, xj));
}
}
}
}
idx -= block_size*pitch;
}
// process main and upper diagonal blocks
for (IndexType d = 0; d < num_diagonals; d++)
{
const IndexType k = A.diagonal_offsets[d]*block_size;
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row+=block_size)
{
const IndexType col = row + k;
if (col >= 0 && col <= num_rows-block_size)
{
// for each column in block
for (IndexType i = 0; i < block_size; i++)
{
// for each row in block
for (IndexType j = 0; j < block_size; j++)
{
const ValueType& Aij = values[row+j+(d*block_size+i)*pitch];
const ValueType& xj = x[col + i];
y[row+j] = reduce(y[row+j], combine(Aij, xj));
}
}
}
}
} // diagonals
}
} else { // !A.symmetric
#pragma omp parallel for
for (IndexType ch = 0; ch < num_rows; ch+=chunksize)
{
for (IndexType row = ch; row<std::min(ch+chunksize,num_rows); row++)
{
y[row] = initialize(y[row]);
}
// for each diagonal block
for (IndexType d = 0; d < num_diagonals; d++)
{
const IndexType k = A.diagonal_offsets[d]*block_size;
for (IndexType row=ch; row<std::min(ch+chunksize,num_rows); row+=block_size)
{
const IndexType col = row + k;
if (col >= 0 && col <= num_rows-block_size)
{
// for each column in block
for (IndexType i = 0; i < block_size; i++)
{
// for each row in block
for (IndexType j = 0; j < block_size; j++)
{
const ValueType& Aij = A.values(row+j, d*block_size+i);
const ValueType& xj = x[col + i];
y[row+j] = reduce(y[row+j], combine(Aij, xj));
}
}
}
}
} // diagonals
} // row chunks
} // A.symmetric
} // block size
}
template <typename Matrix,
typename Vector1,
typename Vector2>
void spmv_cds(const Matrix& A,
const Vector1& x,
Vector2& y)
{
typedef typename Vector2::value_type ValueType;
if (A.block_size == 1) {
spmv_dia(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
} else {
spmv_cds(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
}
}
//////////////
// ELL SpMV //
//////////////
template <typename Matrix,
typename Vector1,
typename Vector2,
typename UnaryFunction,
typename BinaryFunction1,
typename BinaryFunction2>
void spmv_ell(const Matrix& A,
const Vector1& x,
Vector2& y,
UnaryFunction initialize,
BinaryFunction1 combine,
BinaryFunction2 reduce)
{
typedef typename Matrix::index_type IndexType;
typedef typename Vector2::value_type ValueType;
const size_t& num_entries_per_row = A.column_indices.num_cols;
const IndexType invalid_index = Matrix::invalid_index;
for(size_t i = 0; i < A.num_rows; i++)
y[i] = initialize(y[i]);
for(size_t n = 0; n < num_entries_per_row; n++)
{
for(size_t i = 0; i < A.num_rows; i++)
{
const IndexType& j = A.column_indices(i, n);
const ValueType& Aij = A.values(i,n);
if (j != invalid_index)
{
const ValueType& xj = x[j];
y[i] = reduce(y[i], combine(Aij, xj));
}
}
}
}
template <typename Matrix,
typename Vector1,
typename Vector2>
void spmv_ell(const Matrix& A,
const Vector1& x,
Vector2& y)
{
typedef typename Vector2::value_type ValueType;
spmv_ell(A, x, y,
cusp::detail::zero_function<ValueType>(),
thrust::multiplies<ValueType>(),
thrust::plus<ValueType>());
}
} // end namespace host
} // end namespace detail
} // end namespace cusp
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