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// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// 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.
// ------------------------------------------------------------------------
//! \addtogroup fn_spsolve
//! @{
//! Solve a system of linear equations, i.e., A*X = B, where X is unknown,
//! A is sparse, and B is dense. X will be dense too.
template<typename T1, typename T2>
inline
bool
spsolve_helper
(
Mat<typename T1::elem_type>& out,
const SpBase<typename T1::elem_type, T1>& A,
const Base<typename T1::elem_type, T2>& B,
const char* solver,
const spsolve_opts_base& settings,
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
typedef typename T1::elem_type eT;
const char sig = (solver != nullptr) ? solver[0] : char(0);
arma_debug_check( ((sig != 'l') && (sig != 's')), "spsolve(): unknown solver" );
T rcond = T(0);
bool status = false;
superlu_opts superlu_opts_default;
// if(is_float <T>::value) { superlu_opts_default.refine = superlu_opts::REF_SINGLE; }
// if(is_double<T>::value) { superlu_opts_default.refine = superlu_opts::REF_DOUBLE; }
const superlu_opts& opts = (settings.id == 1) ? static_cast<const superlu_opts&>(settings) : superlu_opts_default;
arma_debug_check( ( (opts.pivot_thresh < double(0)) || (opts.pivot_thresh > double(1)) ), "spsolve(): pivot_thresh out of bounds" );
if(sig == 's') // SuperLU solver
{
if( (opts.equilibrate == false) && (opts.refine == superlu_opts::REF_NONE) )
{
status = sp_auxlib::spsolve_simple(out, A.get_ref(), B.get_ref(), opts);
}
else
{
status = sp_auxlib::spsolve_refine(out, rcond, A.get_ref(), B.get_ref(), opts);
}
}
else
if(sig == 'l') // brutal LAPACK solver
{
if( (settings.id != 0) && ((opts.symmetric) || (opts.pivot_thresh != double(1))) )
{
arma_debug_warn("spsolve(): ignoring settings not applicable to LAPACK based solver");
}
Mat<eT> AA;
bool conversion_ok = false;
try
{
Mat<eT> tmp(A.get_ref()); // conversion from sparse to dense can throw std::bad_alloc
AA.steal_mem(tmp);
conversion_ok = true;
}
catch(std::bad_alloc&)
{
arma_debug_warn("spsolve(): not enough memory to use LAPACK based solver");
}
if(conversion_ok)
{
arma_debug_check( (AA.n_rows != AA.n_cols), "spsolve(): matrix A must be square sized" );
uword flags = solve_opts::flag_none;
if(opts.refine != superlu_opts::REF_NONE) { flags |= solve_opts::flag_refine; }
if(opts.equilibrate == true ) { flags |= solve_opts::flag_equilibrate; }
if(opts.allow_ugly == true ) { flags |= solve_opts::flag_allow_ugly; }
status = glue_solve_gen::apply(out, AA, B.get_ref(), flags);
}
}
if(status == false)
{
if(rcond > T(0)) { arma_debug_warn("spsolve(): system seems singular (rcond: ", rcond, ")"); }
else { arma_debug_warn("spsolve(): system seems singular"); }
out.soft_reset();
}
if( (status == true) && (rcond > T(0)) && (rcond < auxlib::epsilon_lapack(out)) )
{
arma_debug_warn("solve(): solution computed, but system seems singular to working precision (rcond: ", rcond, ")");
}
return status;
}
template<typename T1, typename T2>
inline
bool
spsolve
(
Mat<typename T1::elem_type>& out,
const SpBase<typename T1::elem_type, T1>& A,
const Base<typename T1::elem_type, T2>& B,
const char* solver = "superlu",
const spsolve_opts_base& settings = spsolve_opts_none(),
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
const bool status = spsolve_helper(out, A.get_ref(), B.get_ref(), solver, settings);
return status;
}
template<typename T1, typename T2>
arma_warn_unused
inline
Mat<typename T1::elem_type>
spsolve
(
const SpBase<typename T1::elem_type, T1>& A,
const Base<typename T1::elem_type, T2>& B,
const char* solver = "superlu",
const spsolve_opts_base& settings = spsolve_opts_none(),
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
Mat<eT> out;
const bool status = spsolve_helper(out, A.get_ref(), B.get_ref(), solver, settings);
if(status == false)
{
arma_stop_runtime_error("spsolve(): solution not found");
}
return out;
}
//! @}
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