VectorType solve(const MatrixType & matrix, VectorType const & rhs, bicgstab_tag const & tag)
{
typedef typename viennacl::result_of::value_type<VectorType>::type ScalarType;
typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type CPU_ScalarType;
VectorType result = rhs;
viennacl::traits::clear(result);
VectorType residual = rhs;
VectorType p = rhs;
VectorType r0star = rhs;
VectorType tmp0 = rhs;
VectorType tmp1 = rhs;
VectorType s = rhs;
CPU_ScalarType norm_rhs_host = viennacl::linalg::norm_2(residual);
CPU_ScalarType ip_rr0star = norm_rhs_host * norm_rhs_host;
CPU_ScalarType beta;
CPU_ScalarType alpha;
CPU_ScalarType omega;
//ScalarType inner_prod_temp; //temporary variable for inner product computation
CPU_ScalarType new_ip_rr0star = 0;
CPU_ScalarType residual_norm = norm_rhs_host;
if (norm_rhs_host == 0) //solution is zero if RHS norm is zero
return result;
bool restart_flag = true;
vcl_size_t last_restart = 0;
for (vcl_size_t i = 0; i < tag.max_iterations(); ++i)
{
if (restart_flag)
{
residual = rhs;
residual -= viennacl::linalg::prod(matrix, result);
p = residual;
r0star = residual;
ip_rr0star = viennacl::linalg::norm_2(residual);
ip_rr0star *= ip_rr0star;
restart_flag = false;
last_restart = i;
}
tag.iters(i+1);
tmp0 = viennacl::linalg::prod(matrix, p);
alpha = ip_rr0star / viennacl::linalg::inner_prod(tmp0, r0star);
s = residual - alpha*tmp0;
tmp1 = viennacl::linalg::prod(matrix, s);
CPU_ScalarType norm_tmp1 = viennacl::linalg::norm_2(tmp1);
omega = viennacl::linalg::inner_prod(tmp1, s) / (norm_tmp1 * norm_tmp1);
result += alpha * p + omega * s;
residual = s - omega * tmp1;
new_ip_rr0star = viennacl::linalg::inner_prod(residual, r0star);
residual_norm = viennacl::linalg::norm_2(residual);
if (std::fabs(residual_norm / norm_rhs_host) < tag.tolerance())
break;
beta = new_ip_rr0star / ip_rr0star * alpha/omega;
ip_rr0star = new_ip_rr0star;
if (ip_rr0star == 0 || omega == 0 || i - last_restart > tag.max_iterations_before_restart()) //search direction degenerate. A restart might help
restart_flag = true;
// Execution of
// p = residual + beta * (p - omega*tmp0);
// without introducing temporary vectors:
p -= omega * tmp0;
p = residual + beta * p;
}
//store last error estimate:
tag.error(residual_norm / norm_rhs_host);
return result;
}
VectorType solve(const MatrixType & matrix, VectorType const & rhs, bicgstab_tag const & tag, PreconditionerType const & precond)
{
typedef typename viennacl::result_of::value_type<VectorType>::type ScalarType;
typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type CPU_ScalarType;
VectorType result = rhs;
viennacl::traits::clear(result);
VectorType residual = rhs;
VectorType r0star = residual; //can be chosen arbitrarily in fact
VectorType tmp0 = rhs;
VectorType tmp1 = rhs;
VectorType s = rhs;
VectorType p = residual;
CPU_ScalarType ip_rr0star = viennacl::linalg::norm_2(residual);
CPU_ScalarType norm_rhs_host = viennacl::linalg::norm_2(residual);
CPU_ScalarType beta;
CPU_ScalarType alpha;
CPU_ScalarType omega;
CPU_ScalarType new_ip_rr0star = 0;
CPU_ScalarType residual_norm = norm_rhs_host;
if (!norm_rhs_host) //solution is zero if RHS norm is zero
return result;
bool restart_flag = true;
vcl_size_t last_restart = 0;
for (unsigned int i = 0; i < tag.max_iterations(); ++i)
{
if (restart_flag)
{
residual = rhs;
residual -= viennacl::linalg::prod(matrix, result);
precond.apply(residual);
p = residual;
r0star = residual;
ip_rr0star = viennacl::linalg::norm_2(residual);
ip_rr0star *= ip_rr0star;
restart_flag = false;
last_restart = i;
}
tag.iters(i+1);
tmp0 = viennacl::linalg::prod(matrix, p);
precond.apply(tmp0);
alpha = ip_rr0star / viennacl::linalg::inner_prod(tmp0, r0star);
s = residual - alpha*tmp0;
tmp1 = viennacl::linalg::prod(matrix, s);
precond.apply(tmp1);
CPU_ScalarType norm_tmp1 = viennacl::linalg::norm_2(tmp1);
omega = viennacl::linalg::inner_prod(tmp1, s) / (norm_tmp1 * norm_tmp1);
result += alpha * p + omega * s;
residual = s - omega * tmp1;
residual_norm = viennacl::linalg::norm_2(residual);
if (residual_norm / norm_rhs_host < tag.tolerance())
break;
new_ip_rr0star = viennacl::linalg::inner_prod(residual, r0star);
beta = new_ip_rr0star / ip_rr0star * alpha/omega;
ip_rr0star = new_ip_rr0star;
if (!ip_rr0star || !omega || i - last_restart > tag.max_iterations_before_restart()) //search direction degenerate. A restart might help
restart_flag = true;
// Execution of
// p = residual + beta * (p - omega*tmp0);
// without introducing temporary vectors:
p -= omega * tmp0;
p = residual + beta * p;
//std::cout << "Rel. Residual in current step: " << std::sqrt(std::fabs(viennacl::linalg::inner_prod(residual, residual) / norm_rhs_host)) << std::endl;
}
//store last error estimate:
tag.error(residual_norm / norm_rhs_host);
return result;
}
