/usr/include/rheolef/interpolate.h is in librheolef-dev 6.7-6.
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#define _RHEOLEF_INTERPOLATE_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//
// interpolation of functions and nonlinear expressions
// also re-interpolation of fields and linear expressions
//
// author: Pierre.Saramito@imag.fr
//
// date: 15 september 2015
//
// Notes; use template expressions and SFINAE techiques
// The interpolation operator is required, as in
// 1/uh and uh*vh that do not belong to Xh when uh, vh in Xh
//
// SUMMARY:
// 1. implementation
// 1.1. scalar-valued result field
// 1.2. vector-valued case
// 1.3. tensor-valued case
// 1.4. undeterminated-valued case: determined at run-time
// 1.5. interface of the internal interpolate() function
// 2. the interpolate() function
// 2.1. nonlinear expression and function/functor
// 2.2. re-interpolation of fields and linear field expressions
#include "rheolef/field.h"
#include "rheolef/field_expr_v2_nonlinear.h"
namespace rheolef {
namespace details {
// --------------------------------------------------------------------------
// 1. implementation: general nonlinear expr
// --------------------------------------------------------------------------
// notes:
// * function template partial specialization is not allowed --> use class-function
// * interpolation on boundary domain spaces (geo_domain) could generate
// some communications (see interpolate_dom[234]_tst.cc for tests)
// * interpolation of functions and functor are be performed in all cases
// without communications, see below for this implementation.
// here we suppose a general nonlinear expression that is interpolated
// by using a loop on mesh elements
//
template<class T, class M, class Expr, class Result, class Status = typename details::is_equal<Result,typename Expr::value_type>::type>
struct interpolate_internal_check {
field_basic<T,M>
operator() (
const space_basic<T,M>& Xh,
const Expr& expr) const
{
trace_macro ("Expr="<<pretty_typename_macro(Expr));
trace_macro ("Result="<<typename_macro(Result));
trace_macro ("Status="<<typename_macro(Status));
trace_macro ("Expr::value_type="<<typename_macro(typename Expr::value_type));
fatal_macro ("invalid type resolution");
return field_basic<T,M>();
}};
// 1.1. scalar-valued result field
template<class T, class M, class Expr>
struct interpolate_internal_check<T,M,Expr,T,std::true_type> {
field_basic<T,M>
operator() (
const space_basic<T,M>& Xh,
const Expr& expr) const
{
check_macro (Xh.valued_tag() == space_constant::scalar,
"interpolate: invalid "<<Xh.valued()<<"-valued space and scalar function");
typedef typename field_basic<T,M>::size_type size_type;
bool is_homogeneous = expr.initialize (Xh);
expr.template valued_check<T>();
const geo_basic<T,M>& omega = Xh.get_geo();
field_basic<T,M> uh (Xh, std::numeric_limits<T>::max());
typename field_basic<T,M>::iterator random_iter_uh = uh.begin_dof();
std::vector<size_type> dis_idof;
distributor ownership = Xh.ownership();
size_type first_dis_idof = ownership.first_index();
std::vector<T> value;
for (typename geo_basic<T,M>::const_iterator
iter_ie = omega.begin(),
last_ie = omega.end(); iter_ie != last_ie; ++iter_ie) {
const geo_element& K = *iter_ie;
Xh.dis_idof (K, dis_idof);
expr.evaluate (K, value);
for (size_type loc_idof = 0, loc_ndof = dis_idof.size(); loc_idof < loc_ndof; ++loc_idof) {
if (ownership.is_owned (dis_idof [loc_idof])) {
size_type idof = dis_idof [loc_idof] - first_dis_idof;
random_iter_uh [idof] = value [loc_idof];
} else {
uh.dis_dof_entry (dis_idof [loc_idof]) = value [loc_idof];
}
}
}
uh.dis_dof_update();
return uh;
}};
// 1.2. vector-valued case
template<class T, class M, class Expr>
struct interpolate_internal_check<T,M,Expr,point_basic<T>,std::true_type> {
field_basic<T,M>
operator() (
const space_basic<T,M>& Xh,
const Expr& expr) const
{
typedef typename field_basic<T,M>::size_type size_type;
bool is_homogeneous = expr.initialize (Xh);
expr.template valued_check<point_basic<T> >();
const geo_basic<T,M>& omega = Xh.get_geo();
field_basic<T,M> uh (Xh, std::numeric_limits<T>::max());
std::vector<size_type> dis_idof;
distributor ownership = Xh.ownership();
size_type first_dis_idof = ownership.first_index();
typename field_basic<T,M>::iterator random_iter_uh = uh.begin_dof();
check_macro (Xh.valued_tag() == space_constant::vector,
"interpolate: incompatible "<<Xh.valued()<<"-valued space and vector function");
std::vector<point_basic<T> > value;
size_type dim = Xh.get_geo().dimension();
size_type n_comp = dim;
for (typename geo_basic<T,M>::const_iterator
iter_ie = omega.begin(),
last_ie = omega.end(); iter_ie != last_ie; ++iter_ie) {
const geo_element& K = *iter_ie;
Xh.dis_idof (K, dis_idof);
expr.evaluate (K, value);
size_type dis_ndof = dis_idof.size();
size_type loc_comp_ndof = dis_ndof/n_comp;
for (size_type loc_comp_idof = 0; loc_comp_idof < loc_comp_ndof; ++loc_comp_idof) {
for (size_type i_comp = 0; i_comp < n_comp; ++i_comp) {
size_type loc_idof = loc_comp_idof + i_comp*loc_comp_ndof;
if (ownership.is_owned (dis_idof [loc_idof])) {
size_type idof = dis_idof [loc_idof] - first_dis_idof;
random_iter_uh [idof] = value [loc_comp_idof][i_comp];
} else {
uh.dis_dof_entry (dis_idof [loc_idof]) = value [loc_comp_idof][i_comp];
}
}
}
}
uh.dis_dof_update();
return uh;
}};
// 1.3. tensor-valued case
template<class T, class M, class Expr>
struct interpolate_internal_check<T,M,Expr,tensor_basic<T>,std::true_type> {
field_basic<T,M>
operator() (
const space_basic<T,M>& Xh,
const Expr& expr) const
{
typedef typename field_basic<T,M>::size_type size_type;
bool is_homogeneous = expr.initialize (Xh);
expr.template valued_check<tensor_basic<T> >();
const geo_basic<T,M>& omega = Xh.get_geo();
field_basic<T,M> uh (Xh, std::numeric_limits<T>::max());
std::vector<size_type> dis_idof;
distributor ownership = Xh.ownership();
size_type first_dis_idof = ownership.first_index();
typename field_basic<T,M>::iterator random_iter_uh = uh.begin_dof();
check_macro (Xh.valued_tag() == space_constant::tensor ||
Xh.valued_tag() == space_constant::unsymmetric_tensor,
"interpolate: invalid "<<Xh.valued()<<"-valued space and vector function");
std::vector<tensor_basic<T> > value;
size_type dim = Xh.get_geo().dimension();
space_constant::coordinate_type sys_coord = uh.get_geo().coordinate_system();
size_type n_comp = space_constant::n_component (space_constant::tensor, dim, sys_coord);
for (typename geo_basic<T,M>::const_iterator
iter_ie = omega.begin(),
last_ie = omega.end(); iter_ie != last_ie; ++iter_ie) {
const geo_element& K = *iter_ie;
expr.evaluate (K, value);
Xh.dis_idof (K, dis_idof);
size_type loc_ndof = dis_idof.size();
size_type loc_comp_ndof = loc_ndof/n_comp;
for (size_type loc_comp_idof = 0; loc_comp_idof < loc_comp_ndof; ++loc_comp_idof) {
for (size_type ij_comp = 0; ij_comp < n_comp; ++ij_comp) {
size_type loc_idof = loc_comp_idof + ij_comp*loc_comp_ndof;
std::pair<size_type,size_type> ij
= space_constant::tensor_subscript (space_constant::tensor, sys_coord, ij_comp);
if (ownership.is_owned (dis_idof [loc_idof])) {
size_type idof = dis_idof [loc_idof] - first_dis_idof;
random_iter_uh [idof] = value [loc_comp_idof](ij.first, ij.second);
} else {
uh.dis_dof_entry (dis_idof [loc_idof]) = value [loc_comp_idof](ij.first, ij.second);
}
}
}
}
uh.dis_dof_update();
return uh;
}};
// 1.4. undeterminated-valued case: determined at run-time
template<class T, class M, class Expr, class Status>
struct interpolate_internal_check<T,M,Expr,undeterminated_basic<T>,Status> {
field_basic<T,M>
operator() (
const space_basic<T,M>& Xh,
const Expr& expr) const
{
switch (expr.valued_tag()) {
case space_constant::scalar: {
interpolate_internal_check<T,M,Expr,T,std::true_type> eval;
return eval (Xh, expr);
}
case space_constant::vector: {
interpolate_internal_check<T,M,Expr,point_basic<T>,std::true_type> eval;
return eval (Xh, expr);
}
case space_constant::tensor:
case space_constant::unsymmetric_tensor: {
interpolate_internal_check<T,M,Expr,tensor_basic<T>,std::true_type> eval;
return eval (Xh, expr);
}
default:
warning_macro ("Expr="<<pretty_typename_macro(Expr));
warning_macro ("Status="<<typename_macro(Status));
error_macro ("unexpected `"
<< space_constant::valued_name (expr.valued_tag())
<< "' valued expression");
return field_basic<T,M>();
}
}};
// 1.5. interface of the internal interpolate() function
template<class T, class M, class Expr, class Result>
field_basic<T,M>
interpolate_internal (
const space_basic<T,M>& Xh,
const Expr& expr)
{
interpolate_internal_check<T,M,Expr,Result> eval;
return eval (Xh,expr);
}
} // namespace details
// --------------------------------------------------------------------------
// 2. implementation: function & functors
// --------------------------------------------------------------------------
// notes:
// * interpolation of functions and functor are be performed in all cases
// without communications: the loop bases on Lagrange nodes directly.
//
namespace details {
// 2.1. scalar valued
template <class T, class M, class Function>
field_basic<T,M>
interpolate_tag (const space_basic<T,M>& Xh, const Function& f, const T&)
{
check_macro (Xh.valued_tag() == space_constant::scalar,
"interpolate: invalid "<<Xh.valued()<<"-valued " <<Xh.stamp()
<< " space and scalar function");
typedef typename space_basic<T,M>::size_type size_type;
field_basic<T,M> u (Xh, std::numeric_limits<T>::max());
for (size_type idof = 0, ndof = Xh.ndof(); idof < ndof; idof++) {
u.dof (idof) = Xh.momentum (f, idof);
}
u.dis_dof_update();
return u;
}
// 2.2. vector valued
template <class T, class M, class Function>
field_basic<T,M>
interpolate_tag (const space_basic<T,M>& Xh, const Function& f, const point_basic<T>&)
{
check_macro (Xh.valued_tag() == space_constant::vector,
"interpolate: invalid "<<Xh.valued()<<"-valued space and vector function");
typedef typename space_basic<T,M>::size_type size_type;
field_basic<T,M> u (Xh, std::numeric_limits<T>::max());
size_type n_comp = Xh.get_geo().dimension();
point_basic<T> value;
for (size_type comp_idof = 0, comp_ndof = Xh.ndof()/n_comp; comp_idof < comp_ndof; comp_idof++) {
value = Xh.vector_momentum (f, comp_idof);
for (size_type i_comp = 0; i_comp < n_comp; i_comp++) {
size_type idof = comp_idof + i_comp*comp_ndof;
u.dof (idof) = value [i_comp];
}
}
u.dis_dof_update();
return u;
}
// 2.2. tensor valued
template <class T, class M, class Function>
field_basic<T,M>
interpolate_tag (const space_basic<T,M>& Xh, const Function& f, const tensor_basic<T>&)
{
check_macro (Xh.valued_tag() == space_constant::tensor,
"interpolate: invalid "<<Xh.valued()<<"-valued space and tensor function");
typedef typename space_basic<T,M>::size_type size_type;
field_basic<T,M> u (Xh, std::numeric_limits<T>::max());
size_type d = Xh.get_geo().dimension();
space_constant::coordinate_type sys_coord = Xh.get_geo().coordinate_system();
size_type n_comp = space_constant::n_component (space_constant::tensor, d, sys_coord);
tensor_basic<T> value;
for (size_type comp_idof = 0, comp_ndof = Xh.ndof()/n_comp; comp_idof < comp_ndof; comp_idof++) {
value = Xh.tensor_momentum (f, comp_idof);
for (size_type ij_comp = 0; ij_comp < n_comp; ij_comp++) {
size_type idof = comp_idof + ij_comp*comp_ndof;
std::pair<size_type,size_type> ij
= space_constant::tensor_subscript (space_constant::tensor, sys_coord, ij_comp);
u.dof (idof) = value (ij.first, ij.second);
}
}
u.dis_dof_update();
return u;
}
} // namespace details
// --------------------------------------------------------------------------
// 2. the interpolate() function
// --------------------------------------------------------------------------
/*Class:interpolate
NAME: @code{interpolate} - Lagrange interpolation of a function
@findex interpolate
@clindex space
@clindex field
DESCRIPTION:
The function @code{interpolation} implements the
Lagrange interpolation of a function or a class-function.
SYNOPSYS:
template <class Function>
field interpolate (const space& Xh, const Function& f);
EXAMPLE:
@noindent
The following code compute the Lagrange interpolation
@code{pi_h_u} of u(x).
@example
Float u(const point& x);
...
geo omega("square");
space Xh (omega, "P1");
field pi_h_u = interpolate (Xh, u);
@end example
ADVANCED EXAMPLE:
It is possible the replace the function @code{u}
by a variable of the @code{field} type that represents
a picewise polynomial function: this invocation allows
the reinterpolation of a field on another mesh or with
another approximation.
@example
geo omega2 ("square2");
space X2h (omega2, "P1");
field uh2 = interpolate (X2h, pi_h_u);
@end example
End: */
//>interpolate:
// ----------------------------------------------------
// 2. public interface
// ----------------------------------------------------
// 2.1. general nonlinear expression
template<class T, class M, class Expr>
typename std::enable_if<
details::is_field_expr_v2_nonlinear_arg<Expr>::value
&& ! details::is_field_expr_v2_linear_arg<Expr>::value
&& ! details::is_field_function<Expr>::value
,field_basic<T,M>
>::type
interpolate (const space_basic<T,M>& Xh, const Expr& expr)
{
typedef typename details::field_expr_v2_nonlinear_terminal_wrapper_traits<Expr>::type wrap_t;
typedef typename wrap_t::value_type result_t;
return details::interpolate_internal<T,M,wrap_t,result_t> (Xh, wrap_t(expr));
}
// 2.2. function & functor
template <class T, class M, class Expr>
inline
typename std::enable_if<
details::is_field_function<Expr>::value
,field_basic<T,M>
>::type
interpolate (const space_basic<T,M>& Xh, const Expr& expr)
{
typedef typename details::function_traits<Expr>::result_type result_t;
return details::interpolate_tag (Xh, expr, result_t());
}
// 2.3. re-interpolation of fields and linear field expressions
// for change of mesh, of approx, ect
template<class T, class M>
field_basic<T,M>
interpolate (const space_basic<T,M>& X2h, const field_basic<T,M>& u1h);
template <class T, class M, class Expr>
inline
typename std::enable_if<
details::is_field_expr_v2_linear_arg<Expr>::value
&& ! details::is_field<Expr>::value
,field_basic<T,M>
>::type
interpolate (const space_basic<T,M>& Xh, const Expr& expr)
{
return interpolate (Xh, field_basic<T,M>(expr));
}
}// namespace rheolef
#endif // _RHEOLEF_INTERPOLATE_H
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