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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.
*/
#include <cusp/array1d.h>
#include <cusp/blas.h>
#include <cusp/multiply.h>
#include <cusp/monitor.h>
#include <cusp/linear_operator.h>
namespace blas = cusp::blas;
namespace cusp
{
namespace krylov
{
template <class LinearOperator,
class Vector>
void bicgstab(LinearOperator& A,
Vector& x,
Vector& b)
{
typedef typename LinearOperator::value_type ValueType;
cusp::default_monitor<ValueType> monitor(b);
cusp::krylov::bicgstab(A, x, b, monitor);
}
template <class LinearOperator,
class Vector,
class Monitor>
void bicgstab(LinearOperator& A,
Vector& x,
Vector& b,
Monitor& monitor)
{
typedef typename LinearOperator::value_type ValueType;
typedef typename LinearOperator::memory_space MemorySpace;
cusp::identity_operator<ValueType,MemorySpace> M(A.num_rows, A.num_cols);
cusp::krylov::bicgstab(A, x, b, monitor, M);
}
template <class LinearOperator,
class Vector,
class Monitor,
class Preconditioner>
void bicgstab(LinearOperator& A,
Vector& x,
Vector& b,
Monitor& monitor,
Preconditioner& M)
{
CUSP_PROFILE_SCOPED();
typedef typename LinearOperator::value_type ValueType;
typedef typename LinearOperator::memory_space MemorySpace;
assert(A.num_rows == A.num_cols); // sanity check
const size_t N = A.num_rows;
// allocate workspace
cusp::array1d<ValueType,MemorySpace> y(N);
cusp::array1d<ValueType,MemorySpace> p(N);
cusp::array1d<ValueType,MemorySpace> r(N);
cusp::array1d<ValueType,MemorySpace> r_star(N);
cusp::array1d<ValueType,MemorySpace> s(N);
cusp::array1d<ValueType,MemorySpace> Mp(N);
cusp::array1d<ValueType,MemorySpace> AMp(N);
cusp::array1d<ValueType,MemorySpace> Ms(N);
cusp::array1d<ValueType,MemorySpace> AMs(N);
// y <- Ax
cusp::multiply(A, x, y);
// r <- b - A*x
blas::axpby(b, y, r, ValueType(1), ValueType(-1));
// p <- r
blas::copy(r, p);
// r_star <- r
blas::copy(r, r_star);
ValueType r_r_star_old = blas::dotc(r_star, r);
while (!monitor.finished(r))
{
// Mp = M*p
cusp::multiply(M, p, Mp);
// AMp = A*Mp
cusp::multiply(A, Mp, AMp);
// alpha = (r_j, r_star) / (A*M*p, r_star)
ValueType alpha = r_r_star_old / blas::dotc(r_star, AMp);
// s_j = r_j - alpha * AMp
blas::axpby(r, AMp, s, ValueType(1), ValueType(-alpha));
if (monitor.finished(s)){
// x += alpha*M*p_j
blas::axpby(x, Mp, x, ValueType(1), ValueType(alpha));
break;
}
// Ms = M*s_j
cusp::multiply(M, s, Ms);
// AMs = A*Ms
cusp::multiply(A, Ms, AMs);
// omega = (AMs, s) / (AMs, AMs)
ValueType omega = blas::dotc(AMs, s) / blas::dotc(AMs, AMs);
// x_{j+1} = x_j + alpha*M*p_j + omega*M*s_j
blas::axpbypcz(x, Mp, Ms, x, ValueType(1), alpha, omega);
// r_{j+1} = s_j - omega*A*M*s
blas::axpby(s, AMs, r, ValueType(1), -omega);
// beta_j = (r_{j+1}, r_star) / (r_j, r_star) * (alpha/omega)
ValueType r_r_star_new = blas::dotc(r_star, r);
ValueType beta = (r_r_star_new / r_r_star_old) * (alpha / omega);
r_r_star_old = r_r_star_new;
// p_{j+1} = r_{j+1} + beta*(p_j - omega*A*M*p)
blas::axpbypcz(r, p, AMp, p, ValueType(1), beta, -beta*omega);
++monitor;
}
}
} // end namespace krylov
} // end namespace cusp
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