/usr/include/dune/grid/yaspgrid/grids.hh is in libdune-grid-dev 2.3.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_YGRIDS_HH
#define DUNE_YGRIDS_HH
// C++ includes
#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <deque>
#include <bitset>
// C includes
#if HAVE_MPI
#include <mpi.h>
#endif
#include <string.h>
// local includes
#include <dune/common/fvector.hh>
#include <dune/common/stdstreams.hh>
#include <dune/common/power.hh>
#include <dune/grid/common/grid.hh>
/** \file
\brief This is the basis for the yaspgrid implementation of the Dune grid interface.
*/
namespace Dune {
// forward declarations
template<int d, typename ct> class YGrid;
template<int d, typename ct> class SubYGrid;
static const double Ytolerance=1E-13;
/**
This is the basis of a parallel implementation of the dune grid interface
supporting codim 0 and dim.
You can also use the structured interface and write really fast code.
The YGrid considered here describes a finite set \f$d\f$-tupels of the form
\f[ G = \{ (k_0,\ldots,k_{d-1}) | o_i \leq k_i < o_i+s_i \} \f]
together with an affine mapping
\f[ t : G \to R^d, \ \ \ t(k)_i = k_i h_i + r_i \f].
Therefore a YGrid is characterized by the following four quantities:
- The origin \f$ o=(o_0,\ldots,o_{d-1}) \in Z^d\f$,
- the size \f$ s=(s_0,\ldots,s_{d-1}) \in Z^d\f$,
- the mesh width \f$ h=(h_0,\ldots,h_{d-1}) \in R^d\f$,
- The shift \f$ r=(r_0,\ldots,r_{d-1}) \in R^d\f$. The shift can be used to interpret the
points of a grid as midpoints of cells, faces, edges, etc.
The YGrid can be parametrized by the dimension d and the type to be used for the coordinates.
Here is a graphical illustration of a grid:
\image html grid.png "A YGrid."
\image latex grid.eps "A YGrid." width=\textwidth
A grid can be manipulated either in the origin/size representation or in the
min index / max index representation.
A YGrid allows to iterate over all its cells with an Iterator class.
*/
template<int d, typename ct>
class YGrid {
public:
//! define types used for arguments
typedef FieldVector<int, d> iTupel;
typedef FieldVector<ct, d> fTupel;
//! Destructor
virtual ~YGrid()
{}
//! Make an empty YGrid with origin 0
YGrid () :
_origin(0), _size(0), _h(0.0), _r(0.0)
{}
//! Make YGrid from origin and size arrays
YGrid (iTupel o, iTupel s, fTupel h, fTupel r) :
_origin(o), _size(s), _h(h), _r(r)
{
#ifndef NDEBUG
for (int i=0; i<d; ++i)
assert (_size[i] >= 0);
#endif
}
//! Return origin in direction i
int origin (int i) const
{
return _origin[i];
}
//! Set origin in direction i
void origin (int i, int oi) const
{
_origin[i] = oi;
}
//! return reference to origin
const iTupel& origin () const
{
return _origin;
}
//! Return size in direction i
int size (int i) const
{
return _size[i];
}
//! Set size in direction i
void size (int i, int si) const
{
_size[i] = si;
if (_size[i]<0) _size[i] = 0;
}
//! Return reference to size tupel
const iTupel& size () const
{
return _size;
}
//! Return total size of index set which is the product of all size per direction.
int totalsize () const
{
int s=1;
for (int i=0; i<d; ++i) s=s*_size[i];
return s;
}
//! Return minimum index in direction i
int min (int i) const
{
return _origin[i];
}
//! Set minimum index in direction i
void min (int i, int mi) const
{
_size[i] = max(i)-mi+1;
_origin[i] = mi;
if (_size[i]<0) _size[i] = 0;
}
//! Return maximum index in direction i
int max (int i) const
{
return _origin[i]+_size[i]-1;
}
//! Set maximum index in direction i
void max (int i, int mi) const
{
_size[i] = mi-min(i)+1;
if (_size[i]<0) _size[i] = 0;
}
//! Return reference to mesh size tupel for read write access
const fTupel& meshsize () const
{
return _h;
}
//! Return mesh size in direction i
ct meshsize (int i) const
{
return _h[i];
}
//! Set mesh size in direction i
void meshsize (int i, int hi) const
{
_h[i] = hi;
}
//! Return shift tupel
const fTupel& shift () const
{
return _r;
}
//! Return shift in direction i
ct shift (int i) const
{
return _r[i];
}
//! Set shift in direction i
void shift (int i, int ri) const
{
_r[i] = ri;
}
//! Return true if YGrid is empty, i.e. has size 0 in all directions.
bool empty () const
{
for (int i=0; i<d; ++i) if (_size[i]<=0) return true;
return false;
}
//! given a tupel compute its index in the lexicographic numbering
int index (const iTupel& coord) const
{
int index = (coord[d-1]-_origin[d-1]);
for (int i=d-2; i>=0; i--)
index = index*_size[i] + (coord[i]-_origin[i]);
return index;
}
//! given a tupel compute its index in the lexicographic numbering
int index (const array<int,d>& coord) const
{
int index = (coord[d-1]-_origin[d-1]);
for (int i=d-2; i>=0; i--)
index = index*_size[i] + (coord[i]-_origin[i]);
return index;
}
//! given a coordinate, return true if it is in the grid
bool inside (const iTupel& coord) const
{
for (int i=0; i<d; i++)
{
if (coord[i]<_origin[i] || coord[i]>=_origin[i]+_size[i]) return false;
}
return true;
}
//! return grid moved by the vector v
YGrid<d,ct> move (iTupel v) const
{
for (int i=0; i<d; i++) v[i] += _origin[i];
return YGrid<d,ct>(v,_size,_h,_r);
}
/*! Iterator class allows one to run over all cells of a grid.
The cells of the grid to iterate over are numbered consecutively starting
with zero. Via the index() method the iterator provides a mapping of the
cells of the grid to a one-dimensional array. The number of entries
in this array must be the size of the grid.
*/
class Iterator {
public:
//! Make iterator pointing to first cell in a grid.
Iterator (const YGrid<d,ct>& r)
{
// copy data coming from grid to iterate over
for (int i=0; i<d; ++i) _origin[i] = r.origin(i);
for (int i=0; i<d; ++i) _end[i] = r.origin(i)+r.size(i)-1;
// initialize to first position in index set
for (int i=0; i<d; ++i) _coord[i] = _origin[i];
_index = 0;
// compute increments;
int inc = 1;
for (int i=0; i<d; ++i)
{
_increment[i] = inc;
inc *= r.size(i);
}
}
//! Make iterator pointing to given cell in a grid.
Iterator (const YGrid<d,ct>& r, const iTupel& coord)
{
// copy data coming from grid to iterate over
for (int i=0; i<d; ++i) _origin[i] = r.origin(i);
for (int i=0; i<d; ++i) _end[i] = r.origin(i)+r.size(i)-1;
// compute increments;
int inc = 1;
for (int i=0; i<d; ++i)
{
_increment[i] = inc;
inc *= r.size(i);
}
// initialize to given position in index set
for (int i=0; i<d; ++i) _coord[i] = coord[i];
_index = r.index(coord);
}
//! reinitialize iterator to given position
void reinit (const YGrid<d,ct>& r, const iTupel& coord)
{
// copy data coming from grid to iterate over
for (int i=0; i<d; ++i) _origin[i] = r.origin(i);
for (int i=0; i<d; ++i) _end[i] = r.origin(i)+r.size(i)-1;
// compute increments;
int inc = 1;
for (int i=0; i<d; ++i)
{
_increment[i] = inc;
inc *= r.size(i);
}
// initialize to given position in index set
for (int i=0; i<d; ++i) _coord[i] = coord[i];
_index = r.index(coord);
}
//! reinitialize iterator to given position
void reinit (const YGrid<d,ct>& r, const array<int,d>& coord)
{
// copy data coming from grid to iterate over
for (int i=0; i<d; ++i) _origin[i] = r.origin(i);
for (int i=0; i<d; ++i) _end[i] = r.origin(i)+r.size(i)-1;
// compute increments;
int inc = 1;
for (int i=0; i<d; ++i)
{
_increment[i] = inc;
inc *= r.size(i);
}
// initialize to given position in index set
for (int i=0; i<d; ++i) _coord[i] = coord[i];
_index = r.index(coord);
}
//! Return true when two iterators over the same grid are equal (!).
bool operator== (const Iterator& i) const
{
return _index == i._index;
}
//! Return true when two iterators over the same grid are not equal (!).
bool operator!= (const Iterator& i) const
{
return _index != i._index;
}
//! Return index of the current cell in the consecutive numbering.
int index () const
{
return _index;
}
//! Return coordinate of the cell in direction i.
int coord (int i) const
{
return _coord[i];
}
//! Return coordinate of the cell as reference (do not modify).
const iTupel& coord () const
{
return _coord;
}
//! Get index of cell which is dist cells away in direction i.
int neighbor (int i, int dist) const
{
return _index+dist*_increment[i];
}
//! Get index of neighboring cell which is -1 away in direction i.
int down (int i) const
{
return _index-_increment[i];
}
//! Get index of neighboring cell which is +1 away in direction i.
int up (int i) const
{
return _index+_increment[i];
}
//! move this iterator dist cells in direction i
void move (int i, int dist)
{
_coord[i] += dist;
_index += dist*_increment[i];
}
//! Increment iterator to next cell.
Iterator& operator++ ()
{
++_index;
for (int i=0; i<d; i++)
if (++(_coord[i])<=_end[i])
return *this;
else
_coord[i]=_origin[i];
return *this;
}
//! Print position of iterator
void print (std::ostream& s) const
{
s << index() << " : [";
for (int i=0; i<d-1; i++) s << coord(i) << ",";
s << coord(d-1) << "]";
}
protected:
int _index; //< current lexicographic position in index set
iTupel _coord; //< current position in index set
iTupel _increment; //< increment for next neighbor in direction i
iTupel _origin; //< origin and
iTupel _end; //< last index in direction i
};
//! return iterator to first element of index set
Iterator begin () const
{
return Iterator(*this);
}
//! return iterator to one past the last element of index set
Iterator end () const {
iTupel last;
for (int i=0; i<d; i++)
last[i] = max(i);
last[0] += 1;
return Iterator(*this,last);
}
/*! TransformingIterator is an Iterator providing in addition a linear transformation
of the coordinates of the grid in the form \f$ y_i = x_i h_i + s_i \f$.
This can be used to interpret the grid cells as vertices, edges, faces, etc.
*/
class TransformingIterator : public Iterator {
public:
//! Make iterator pointing to first cell in a grid.
TransformingIterator (const YGrid<d,ct>& r) : Iterator(r)
{
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = _begin[i];
}
//! Make iterator pointing to given cell in a grid.
TransformingIterator (const YGrid<d,ct>& r, iTupel& coord) : Iterator(r,coord)
{
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = coord[i]*r.meshsize(i)+r.shift(i);
}
//! Make transforming iterator from iterator (used for automatic conversion of end)
TransformingIterator (Iterator i) : Iterator(i)
{}
//! Increment iterator to next cell with position.
TransformingIterator& operator++ ()
{
++(this->_index);
for (int i=0; i<d; i++)
if (++(this->_coord[i])<=this->_end[i])
{
_position[i] += _h[i];
return *this;
}
else
{
this->_coord[i]=this->_origin[i];
_position[i] = _begin[i];
}
return *this;
}
//! Return position of current cell in direction i.
ct position (int i) const
{
return _position[i];
}
//! Return position of current cell as reference.
const fTupel& position () const
{
return _position;
}
//! Return meshsize in direction i
ct meshsize (int i) const
{
return _h[i];
}
//! Return meshsize of current cell as reference.
const fTupel& meshsize () const
{
return _h;
}
//! Move cell position by dist cells in direction i.
void move (int i, int dist)
{
Iterator::move(i,dist);
_position[i] += dist*_h[i];
}
//! Print contents of iterator
void print (std::ostream& s) const
{
Iterator::print(s);
s << " " << _position;
}
private:
fTupel _h; //!< mesh size per direction
fTupel _begin; //!< position of origin of grid
fTupel _position; //!< current position
};
//! return iterator to first element of index set
TransformingIterator tbegin () const
{
return TransformingIterator(*this);
}
//! return iterator to one past the last element of the grid
TransformingIterator tend () const
{
iTupel last;
for (int i=0; i<d; i++) last = max(i);
last[0] += 1;
return TransformingIterator(*this,last);
}
protected:
//! internal representation uses origin/size
iTupel _origin;
iTupel _size;
fTupel _h; //!< mesh size per direction
fTupel _r; //!< shift per direction
};
//! Output operator for grids
template <int d, typename ct>
inline std::ostream& operator<< (std::ostream& s, YGrid<d,ct> e)
{
s << "{";
for (int i=0; i<d-1; i++)
s << "[" << e.min(i) << "," << e.max(i) << "]x";
s << "[" << e.min(d-1) << "," << e.max(d-1) << "]";
s << " = [";
for (int i=0; i<d-1; i++) s << e.origin(i) << ",";
s << e.origin(d-1) << "]x[";
for (int i=0; i<d-1; i++) s << e.size(i) << ",";
s << e.size(d-1) << "]";
s << " h=[";
for (int i=0; i<d-1; i++) s << e.meshsize(i) << ",";
s << e.meshsize(d-1) << "]";
s << " r=[";
for (int i=0; i<d-1; i++) s << e.shift(i) << ",";
s << e.shift(d-1) << "]";
s << "}";
return s;
}
//! Output operator for Iterators
template <int d, typename ct>
inline std::ostream& operator<< (std::ostream& s, typename YGrid<d,ct>::Iterator& e)
{
e.print(s);
return s;
}
/*! A SubYGrid is a grid that is embedded in a larger grid
It is characterized by an offset and an enclosing grid as
shown in the following picture:
\image html subgrid.png "The SubYGrid is shown in red, blue is the enclosing grid."
\image latex subgrid.eps "The SubYGrid is shown in red, blue is the enclosing grid." width=\textwidth
SubYGrid has additional iterators that provide a mapping to
the consecutive index in the enclosing grid.
*/
template<int d, typename ct>
class SubYGrid : public YGrid<d,ct> {
public:
typedef typename YGrid<d,ct>::iTupel iTupel;
typedef typename YGrid<d,ct>::fTupel fTupel;
//! Destructor
virtual ~SubYGrid()
{}
//! make uninitialized subgrid
SubYGrid () {}
//! Make SubYGrid from origin, size, offset and supersize
SubYGrid (iTupel origin, iTupel size, iTupel offset, iTupel supersize, fTupel h, fTupel r)
: YGrid<d,ct>::YGrid(origin,size,h,r), _offset(offset), _supersize(supersize)
{
for (int i=0; i<d; ++i)
{
if (offset[i]<0)
std::cout << "warning: offset["
<< i <<"] negative in SubYGrid"
<< std::endl;
if (-offset[i]+supersize[i]<size[i])
std::cout << "warning: subgrid larger than enclosing grid in direction "
<< i <<" in SubYGrid"
<< std::endl;
}
}
//! Make SubYGrid from YGrid
SubYGrid (YGrid<d,ct> base) : YGrid<d,ct>(base)
{
for (int i=0; i<d; ++i)
{
_offset[i] = 0;
_supersize[i] = this->size(i);
}
}
//! Return offset to origin of enclosing grid
int offset (int i) const
{
return _offset[i];
}
//! Return offset to origin of enclosing grid
const iTupel & offset () const
{
return _offset;
}
//! return size of enclosing grid
int supersize (int i) const
{
return _supersize[i];
}
//! return size of enclosing grid
const iTupel & supersize () const
{
return _supersize;
}
//! Return SubYGrid of supergrid of self which is the intersection of self and another YGrid
virtual SubYGrid<d,ct> intersection (const YGrid<d,ct>& r) const
{
// check if the two grids can be intersected, must have same mesh size and shift
for (int i=0; i<d; i++)
if (fabs(this->meshsize(i)-r.meshsize(i))>Ytolerance) return SubYGrid<d,ct>();
for (int i=0; i<d; i++)
if (fabs(this->shift(i)-r.shift(i))>Ytolerance) return SubYGrid<d,ct>();
iTupel neworigin;
iTupel newsize;
iTupel offset;
for (int i=0; i<d; ++i)
{
// intersect
neworigin[i] = std::max(this->min(i),r.min(i));
newsize[i] = std::min(this->max(i),r.max(i))-neworigin[i]+1;
if (newsize[i]<0) {
newsize[i] = 0;
neworigin[i] = this->min(i);
}
// offset to my supergrid
offset[i] = _offset[i]+neworigin[i]-this->origin(i);
}
return SubYGrid<d,ct>(neworigin,newsize,offset,_supersize,this->meshsize(),this->shift());
}
/*! SubIterator is an Iterator that provides in addition the consecutive
index in the enclosing grid.
*/
class SubIterator : public YGrid<d,ct>::Iterator {
public:
//! Make iterator pointing to first cell in subgrid.
SubIterator (const SubYGrid<d,ct>& r) : YGrid<d,ct>::Iterator::Iterator (r)
{
//! store some grid information
for (int i=0; i<d; ++i) _size[i] = r.size(i);
// compute superincrements
int inc = 1;
for (int i=0; i<d; ++i)
{
_superincrement[i] = inc;
inc *= r.supersize(i);
}
// move superindex to first cell in subgrid
_superindex = 0;
for (int i=0; i<d; ++i)
_superindex += r.offset(i)*_superincrement[i];
}
//! Make iterator pointing to given cell in subgrid.
SubIterator (const SubYGrid<d,ct>& r, const iTupel& coord) : YGrid<d,ct>::Iterator::Iterator (r,coord)
{
//! store some grid information
for (int i=0; i<d; ++i) _size[i] = r.size(i);
// compute superincrements
int inc = 1;
for (int i=0; i<d; ++i)
{
_superincrement[i] = inc;
inc *= r.supersize(i);
}
// move superindex to first cell in subgrid
_superindex = 0;
for (int i=0; i<d; ++i)
_superindex += (r.offset(i)+coord[i]-r.origin(i))*_superincrement[i];
}
//! Make transforming iterator from iterator (used for automatic conversion of end)
SubIterator (const typename YGrid<d,ct>::Iterator& i) : YGrid<d,ct>::Iterator::Iterator(i)
{}
//! Make iterator pointing to given cell in subgrid.
void reinit (const SubYGrid<d,ct>& r, const iTupel& coord)
{
YGrid<d,ct>::Iterator::reinit(r,coord);
//! store some grid information
for (int i=0; i<d; ++i) _size[i] = r.size(i);
// compute superincrements
int inc = 1;
for (int i=0; i<d; ++i)
{
_superincrement[i] = inc;
inc *= r.supersize(i);
}
// move superindex to first cell in subgrid
_superindex = 0;
for (int i=0; i<d; ++i)
_superindex += (r.offset(i)+coord[i]-r.origin(i))*_superincrement[i];
}
//! Make iterator pointing to given cell in subgrid.
void reinit (const SubYGrid<d,ct>& r, const array<int,d>& coord)
{
YGrid<d,ct>::Iterator::reinit(r,coord);
//! store some grid information
for (int i=0; i<d; ++i) _size[i] = r.size(i);
// compute superincrements
int inc = 1;
for (int i=0; i<d; ++i)
{
_superincrement[i] = inc;
inc *= r.supersize(i);
}
// move superindex to first cell in subgrid
_superindex = 0;
for (int i=0; i<d; ++i)
_superindex += (r.offset(i)+coord[i]-r.origin(i))*_superincrement[i];
}
//! Return true when two iterators over the same grid are equal (!).
bool operator== (const SubIterator& i) const
{
return _superindex == i._superindex;
}
//! Return true when two iterators over the same grid are not equal (!).
bool operator!= (const SubIterator& i) const
{
return _superindex != i._superindex;
}
//! Return consecutive index in enclosing grid
int superindex () const
{
return _superindex;
}
//! Get index of cell which is dist cells away in direction i in enclosing grid.
int superneighbor (int i, int dist) const
{
return _superindex+dist*_superincrement[i];
}
//! Get index of neighboring cell which is -1 away in direction i in enclosing grid.
int superdown (int i) const
{
return _superindex-_superincrement[i];
}
//! Get index of neighboring cell which is +1 away in direction i in enclosing grid.
int superup (int i) const
{
return _superindex+_superincrement[i];
}
//! move this iterator dist cells in direction i
void move (int i, int dist)
{
YGrid<d,ct>::Iterator::move(i,dist); // move base iterator
_superindex += dist*_superincrement[i]; // move superindex
}
//! Increment iterator to next cell in subgrid
SubIterator& operator++ ()
{
++(this->_index); // update consecutive index in grid
for (int i=0; i<d; i++) // check for wrap around
{
_superindex += _superincrement[i]; // move on cell in direction i
if (++(this->_coord[i])<=this->_end[i])
return *this;
else
{
this->_coord[i]=this->_origin[i]; // move back to origin in direction i
_superindex -= _size[i]*_superincrement[i];
}
}
// if we wrapped around, back to to begin(), we must put the iterator to end()
if (this->_coord == this->_origin)
{
for (int i=0; i<d; i++)
this->_superindex += (this->_size[i]-1)*this->_superincrement[i];
this->_superindex += this->_superincrement[0];
}
return *this;
}
//! Print position of iterator
void print (std::ostream& s) const
{
YGrid<d,ct>::Iterator::print(s);
s << " super=" << superindex();
}
protected:
int _superindex; //!< consecutive index in enclosing grid
iTupel _superincrement; //!< moves consecutive index by one in this direction in supergrid
iTupel _size; //!< size of subgrid
};
//! return subiterator to first element of index set
SubIterator subbegin () const { return SubIterator(*this); }
//! return subiterator to last element of index set
SubIterator subend () const
{
iTupel last;
for (int i=0; i<d; i++) last[i] = this->max(i);
last[0] += 1;
return SubIterator(*this,last);
}
/*! TransformingSubIterator is a SubIterator providing in addition a linear transformation
of the coordinates of the grid in the form \f$ y_i = x_i h_i + s_i \f$.
This can be used to interpret the grid cells as vertices, edges, faces, etc.
*/
class TransformingSubIterator : public SubIterator {
public:
//! Make iterator pointing to first cell in a grid.
TransformingSubIterator (const SubYGrid<d,ct>& r) : SubIterator(r)
{
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = _begin[i];
}
//! Make iterator pointing to given cell in a grid.
TransformingSubIterator (const SubYGrid<d,ct>& r, const iTupel& coord) : SubIterator(r,coord)
{
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = coord[i]*r.meshsize(i)+r.shift(i);
}
//! Make transforming iterator from iterator (used for automatic conversion of end)
TransformingSubIterator (const SubIterator& i) :
SubIterator(i)
{}
TransformingSubIterator (const TransformingSubIterator & t) :
SubIterator(t), _h(t._h), _begin(t._begin), _position(t._position)
{}
//! Make iterator pointing to given cell in a grid.
void reinit (const SubYGrid<d,ct>& r, const iTupel& coord)
{
SubIterator::reinit(r,coord);
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = coord[i]*r.meshsize(i)+r.shift(i);
}
//! Make iterator pointing to given cell in a grid.
void reinit (const SubYGrid<d,ct>& r, const array<int,d>& coord)
{
SubIterator::reinit(r,coord);
for (int i=0; i<d; ++i) _h[i] = r.meshsize(i);
for (int i=0; i<d; ++i) _begin[i] = r.origin(i)*r.meshsize(i)+r.shift(i);
for (int i=0; i<d; ++i) _position[i] = coord[i]*r.meshsize(i)+r.shift(i);
}
//! Increment iterator to next cell with position.
TransformingSubIterator& operator++ ()
{
++(this->_index); // update consecutive index in subgrid
for (int i=0; i<d; i++) // check for wrap around
{
this->_superindex += this->_superincrement[i]; // move on cell in direction i
if (++(this->_coord[i])<=this->_end[i])
{
_position[i] += _h[i];
return *this;
}
else
{
this->_coord[i]=this->_origin[i]; // move back to origin in direction i
this->_superindex -= this->_size[i]*this->_superincrement[i];
_position[i] = _begin[i];
}
}
// if we wrapped around, back to to begin(), we must put the iterator to end()
if (this->_coord == this->_origin)
{
for (int i=0; i<d; i++)
this->_superindex += (this->_size[i]-1)*this->_superincrement[i];
this->_superindex += this->_superincrement[0];
}
return *this;
}
//! Return position of current cell in direction i.
ct position (int i) const
{
return _position[i];
}
//! Return position of current cell as reference.
const fTupel& position () const
{
return _position;
}
//! Return meshsize in direction i
ct meshsize (int i) const
{
return _h[i];
}
//! Return meshsize of current cell as reference.
const fTupel& meshsize () const
{
return _h;
}
//! Move cell position by dist cells in direction i.
void move (int i, int dist)
{
SubIterator::move(i,dist);
_position[i] += dist*_h[i];
}
//! Print contents of iterator
void print (std::ostream& s) const
{
SubIterator::print(s);
s << " [";
for (int i=0; i<d-1; i++) s << position(i) << ",";
s << position(d-1) << "]";
}
private:
fTupel _h; //!< mesh size per direction
fTupel _begin; //!< position of origin of grid
fTupel _position; //!< current position
};
//! return iterator to first element of index set
TransformingSubIterator tsubbegin () const
{
return TransformingSubIterator(*this);
}
//! return iterator to given element of index set
TransformingSubIterator tsubbegin (iTupel& co) const
{
return TransformingSubIterator(*this,co);
}
//! return subiterator to last element of index set
TransformingSubIterator tsubend () const
{
SubIterator endit = subend();
return TransformingSubIterator(endit);
}
private:
iTupel _offset; //!< offset to origin of the enclosing grid
iTupel _supersize; //!< size of the enclosing grid
};
//! Output operator for subgrids
template <int d, typename ct>
inline std::ostream& operator<< (std::ostream& s, SubYGrid<d,ct> e)
{
YGrid<d,ct> x = e;
s << x << " ofs=" << e.offset() << " ss=" << e.supersize();
return s;
}
//! Output operator for subgrids
template <int d, typename ct>
inline std::ostream& operator<< (std::ostream& s, typename SubYGrid<d,ct>::TransformingSubIterator& e)
{
e.print(s);
return s;
}
/** \brief Implement the default load balance strategy of yaspgrid
*/
template<int d>
class YLoadBalance
{
public:
typedef FieldVector<int, d> iTupel;
virtual ~YLoadBalance() {}
virtual void loadbalance (const iTupel& size, int P, iTupel& dims) const
{
double opt=1E100;
iTupel trydims;
optimize_dims(d-1,size,P,dims,trydims,opt);
}
private:
void optimize_dims (int i, const iTupel& size, int P, iTupel& dims, iTupel& trydims, double &opt ) const
{
if (i>0) // test all subdivisions recursively
{
for (int k=1; k<=P; k++)
if (P%k==0)
{
// P divisible by k
trydims[i] = k;
optimize_dims(i-1,size,P/k,dims,trydims,opt);
}
}
else
{
// found a possible combination
trydims[0] = P;
// check for optimality
double m = -1.0;
for (int k=0; k<d; k++)
{
double mm=((double)size[k])/((double)trydims[k]);
if (fmod((double)size[k],(double)trydims[k])>0.0001) mm*=3;
if ( mm > m ) m = mm;
}
//if (_rank==0) std::cout << "optimize_dims: " << size << " | " << trydims << " norm=" << m << std::endl;
if (m<opt)
{
opt = m;
dims = trydims;
}
}
}
};
/** \brief Implement yaspgrid load balance strategy for P=x^{dim} processors
*/
template<int d>
class YLoadBalancePowerD : public YLoadBalance<d>
{
public:
typedef FieldVector<int, d> iTupel;
virtual void loadbalance (const iTupel& size, int P, iTupel& dims) const
{
bool found=false;
for(int i=1; i<P; ++i)
if(Power<d>::eval(i)==P) {
for(int j=0; j<d; ++j)
dims[j]=i;
found=true;
}
if(!found)
DUNE_THROW(GridError, "Loadbalancing failed\n");
}
};
/*! Torus provides all the functionality to handle a toroidal communication structure:
- Map a set of processes (given by an MPI communicator) to a torus of dimension d. The "optimal"
torus dimensions are determined by a coarse mesh. The maximum side length is minimized.
- Provide lists of neighboring processes and a method for nearest neighbor exchange
using asynchronous communication with MPI. The periodic case is handled where one process
might have to exchange several messages with the same process. (Logically, a process has always
\f$3^d-1\f$ neighbors, but several of these logical neighbors might be identical)
- Provide means to partition a grid to the torus.
*/
template<int d>
class Torus {
public:
//! type used to pass tupels in and out
typedef FieldVector<int, d> iTupel;
private:
struct CommPartner {
int rank;
iTupel delta;
int index;
};
struct CommTask {
int rank; // process to send to / receive from
void *buffer; // buffer to send / receive
int size; // size of buffer
#if HAVE_MPI
MPI_Request request; // used by MPI to handle request
#else
int request;
#endif
int flag; // used by MPI
};
public:
//! constructor making uninitialized object
Torus ()
{}
//! make partitioner from communicator and coarse mesh size
#if HAVE_MPI
Torus (MPI_Comm comm, int tag, iTupel size, const YLoadBalance<d>* lb)
#else
Torus (int tag, iTupel size, const YLoadBalance<d>* lb)
#endif
{
// MPI stuff
#if HAVE_MPI
_comm = comm;
MPI_Comm_size(comm,&_procs);
MPI_Comm_rank(comm,&_rank);
#else
_procs=1; _rank=0;
#endif
_tag = tag;
// determine dimensions
lb->loadbalance(size, _procs, _dims);
// if (_rank==0) std::cout << "Torus<" << d
// << ">: mapping " << _procs << " processes onto "
// << _dims << " torus." << std::endl;
// compute increments for lexicographic ordering
int inc = 1;
for (int i=0; i<d; i++)
{
_increment[i] = inc;
inc *= _dims[i];
}
// make full schedule
proclists();
}
//! make partitioner from communicator and coarse mesh size
#if HAVE_MPI
Torus (MPI_Comm comm, int tag, Dune::array<int,d> size, const YLoadBalance<d>* lb)
#else
Torus (int tag, Dune::array<int,d> size, const YLoadBalance<d>* lb)
#endif
{
// MPI stuff
#if HAVE_MPI
_comm = comm;
MPI_Comm_size(comm,&_procs);
MPI_Comm_rank(comm,&_rank);
#else
_procs=1; _rank=0;
#endif
_tag = tag;
// determine dimensions
iTupel sizeITupel;
std::copy(size.begin(), size.end(), sizeITupel.begin());
lb->loadbalance(sizeITupel, _procs, _dims);
// compute increments for lexicographic ordering
int inc = 1;
for (int i=0; i<d; i++)
{
_increment[i] = inc;
inc *= _dims[i];
}
// make full schedule
proclists();
}
//! return own rank
int rank () const
{
return _rank;
}
//! return own coordinates
iTupel coord () const
{
return rank_to_coord(_rank);
}
//! return number of processes
int procs () const
{
return _procs;
}
//! return dimensions of torus
const iTupel & dims () const
{
return _dims;
}
//! return dimensions of torus in direction i
int dims (int i) const
{
return _dims[i];
}
//! return MPI communicator
#if HAVE_MPI
MPI_Comm comm () const
{
return _comm;
}
#endif
//! return tag used by torus
int tag () const
{
return _tag;
}
//! return true if coordinate is inside torus
bool inside (iTupel c) const
{
for (int i=d-1; i>=0; i--)
if (c[i]<0 || c[i]>=_dims[i]) return false;
return true;
}
//! map rank to coordinate in torus using lexicographic ordering
iTupel rank_to_coord (int rank) const
{
iTupel coord;
rank = rank%_procs;
for (int i=d-1; i>=0; i--)
{
coord[i] = rank/_increment[i];
rank = rank%_increment[i];
}
return coord;
}
//! map coordinate in torus to rank using lexicographic ordering
int coord_to_rank (iTupel coord) const
{
for (int i=0; i<d; i++) coord[i] = coord[i]%_dims[i];
int rank = 0;
for (int i=0; i<d; i++) rank += coord[i]*_increment[i];
return rank;
}
//! return rank of process where its coordinate in direction dir has offset cnt (handles periodic case)
int rank_relative (int rank, int dir, int cnt) const
{
iTupel coord = rank_to_coord(rank);
coord[dir] = (coord[dir]+_dims[dir]+cnt)%_dims[dir];
return coord_to_rank(coord);
}
//! assign color to given coordinate
int color (const iTupel & coord) const
{
int c = 0;
int power = 1;
// interior coloring
for (int i=0; i<d; i++)
{
if (coord[i]%2==1) c += power;
power *= 2;
}
// extra colors for boundary processes
for (int i=0; i<d; i++)
{
if (_dims[i]>1 && coord[i]==_dims[i]-1) c += power;
power *= 2;
}
return c;
}
//! assign color to given rank
int color (int rank) const
{
return color(rank_to_coord(rank));
}
//! return the number of neighbors, which is \f$3^d-1\f$
int neighbors () const
{
int n=1;
for (int i=0; i<d; ++i)
n *= 3;
return n-1;
}
//! return true if neighbor with given delta is a neighbor under the given periodicity
bool is_neighbor (iTupel delta, std::bitset<d> periodic) const
{
iTupel coord = rank_to_coord(_rank); // my own coordinate with 0 <= c_i < dims_i
for (int i=0; i<d; i++)
{
if (delta[i]<0)
{
// if I am on the boundary and domain is not periodic => no neighbor
if (coord[i]==0 && periodic[i]==false) return false;
}
if (delta[i]>0)
{
// if I am on the boundary and domain is not periodic => no neighbor
if (coord[i]==_dims[i]-1 && periodic[i]==false) return false;
}
}
return true;
}
//! partition the given grid onto the torus and return the piece of the process with given rank; returns load imbalance
double partition (int rank, iTupel origin_in, Dune::array<int,d> size_in, iTupel& origin_out, iTupel& size_out) const
{
iTupel coord = rank_to_coord(rank);
double maxsize = 1;
double sz = 1;
// make a tensor product partition
for (int i=0; i<d; i++)
{
// determine
int m = size_in[i]/_dims[i];
int r = size_in[i]%_dims[i];
sz *= size_in[i];
if (coord[i]<_dims[i]-r)
{
origin_out[i] = origin_in[i] + coord[i]*m;
size_out[i] = m;
maxsize *= m;
}
else
{
origin_out[i] = origin_in[i] + (_dims[i]-r)*m + (coord[i]-(_dims[i]-r))*(m+1);
size_out[i] = m+1;
maxsize *= m+1;
}
}
return maxsize/(sz/_procs);
}
/*!
ProcListIterator provides access to a list of neighboring processes. There are always
\f$ 3^d-1 \f$ entries in such a list. Two lists are maintained, one for sending and one for
receiving. The lists are sorted in such a way that in sequence message delivery ensures that
e.g. a message send to the left neighbor is received as a message from the right neighbor.
*/
class ProcListIterator {
public:
//! make an iterator
ProcListIterator (typename std::deque<CommPartner>::const_iterator iter)
{
i = iter;
}
//! return rank of neighboring process
int rank () const
{
return i->rank;
}
//! return distance vector
iTupel delta () const
{
return i->delta;
}
//! return index in proclist
int index () const
{
return i->index;
}
//! return 1-norm of distance vector
int distance () const
{
int dist = 0;
iTupel delta=i->delta;
for (int j=0; j<d; ++j)
dist += std::abs(delta[j]);
return dist;
}
//! Return true when two iterators point to same member
bool operator== (const ProcListIterator& iter)
{
return i == iter.i;
}
//! Return true when two iterators do not point to same member
bool operator!= (const ProcListIterator& iter)
{
return i != iter.i;
}
//! Increment iterator to next cell.
ProcListIterator& operator++ ()
{
++i;
return *this;
}
private:
typename std::deque<CommPartner>::const_iterator i;
};
//! first process in send list
ProcListIterator sendbegin () const
{
return ProcListIterator(_sendlist.begin());
}
//! end of send list
ProcListIterator sendend () const
{
return ProcListIterator(_sendlist.end());
}
//! first process in receive list
ProcListIterator recvbegin () const
{
return ProcListIterator(_recvlist.begin());
}
//! last process in receive list
ProcListIterator recvend () const
{
return ProcListIterator(_recvlist.end());
}
//! store a send request; buffers are sent in order; handles also local requests with memcpy
void send (int rank, void* buffer, int size) const
{
CommTask task;
task.rank = rank;
task.buffer = buffer;
task.size = size;
if (rank!=_rank)
_sendrequests.push_back(task);
else
_localsendrequests.push_back(task);
}
//! store a receive request; buffers are received in order; handles also local requests with memcpy
void recv (int rank, void* buffer, int size) const
{
CommTask task;
task.rank = rank;
task.buffer = buffer;
task.size = size;
if (rank!=_rank)
_recvrequests.push_back(task);
else
_localrecvrequests.push_back(task);
}
//! exchange messages stored in request buffers; clear request buffers afterwards
void exchange () const
{
// handle local requests first
if (_localsendrequests.size()!=_localrecvrequests.size())
{
std::cout << "[" << rank() << "]: ERROR: local sends/receives do not match in exchange!" << std::endl;
return;
}
for (unsigned int i=0; i<_localsendrequests.size(); i++)
{
if (_localsendrequests[i].size!=_localrecvrequests[i].size)
{
std::cout << "[" << rank() << "]: ERROR: size in local sends/receive does not match in exchange!" << std::endl;
return;
}
memcpy(_localrecvrequests[i].buffer,_localsendrequests[i].buffer,_localsendrequests[i].size);
}
_localsendrequests.clear();
_localrecvrequests.clear();
#if HAVE_MPI
// handle foreign requests
int sends=0;
int recvs=0;
// issue sends to foreign processes
for (unsigned int i=0; i<_sendrequests.size(); i++)
if (_sendrequests[i].rank!=rank())
{
// std::cout << "[" << rank() << "]" << " send " << _sendrequests[i].size << " bytes "
// << "to " << _sendrequests[i].rank << " p=" << _sendrequests[i].buffer << std::endl;
MPI_Isend(_sendrequests[i].buffer, _sendrequests[i].size, MPI_BYTE,
_sendrequests[i].rank, _tag, _comm, &(_sendrequests[i].request));
_sendrequests[i].flag = false;
sends++;
}
// issue receives from foreign processes
for (unsigned int i=0; i<_recvrequests.size(); i++)
if (_recvrequests[i].rank!=rank())
{
// std::cout << "[" << rank() << "]" << " recv " << _recvrequests[i].size << " bytes "
// << "fm " << _recvrequests[i].rank << " p=" << _recvrequests[i].buffer << std::endl;
MPI_Irecv(_recvrequests[i].buffer, _recvrequests[i].size, MPI_BYTE,
_recvrequests[i].rank, _tag, _comm, &(_recvrequests[i].request));
_recvrequests[i].flag = false;
recvs++;
}
// poll sends
while (sends>0)
{
for (unsigned int i=0; i<_sendrequests.size(); i++)
if (!_sendrequests[i].flag)
{
MPI_Status status;
MPI_Test( &(_sendrequests[i].request), &(_sendrequests[i].flag), &status);
if (_sendrequests[i].flag)
{
sends--;
// std::cout << "[" << rank() << "]" << " send to " << _sendrequests[i].rank << " OK" << std::endl;
}
}
}
// poll receives
while (recvs>0)
{
for (unsigned int i=0; i<_recvrequests.size(); i++)
if (!_recvrequests[i].flag)
{
MPI_Status status;
MPI_Test( &(_recvrequests[i].request), &(_recvrequests[i].flag), &status);
if (_recvrequests[i].flag)
{
recvs--;
// std::cout << "[" << rank() << "]" << " recv fm " << _recvrequests[i].rank << " OK" << std::endl;
}
}
}
// clear request buffers
_sendrequests.clear();
_recvrequests.clear();
#endif
}
//! global max
double global_max (double x) const
{
double res = 0.0;
if (_procs==1) return x;
#if HAVE_MPI
MPI_Allreduce(&x,&res,1,MPI_DOUBLE,MPI_MAX,_comm);
#endif
return res;
}
//! print contents of torus object
void print (std::ostream& s) const
{
s << "[" << rank() << "]: Torus " << procs() << " processor(s) arranged as " << dims() << std::endl;
for (ProcListIterator i=sendbegin(); i!=sendend(); ++i)
{
s << "[" << rank() << "]: send to "
<< "rank=" << i.rank()
<< " index=" << i.index()
<< " delta=" << i.delta() << " dist=" << i.distance() << std::endl;
}
for (ProcListIterator i=recvbegin(); i!=recvend(); ++i)
{
s << "[" << rank() << "]: recv from "
<< "rank=" << i.rank()
<< " index=" << i.index()
<< " delta=" << i.delta() << " dist=" << i.distance() << std::endl;
}
}
private:
void proclists ()
{
// compile the full neighbor list
CommPartner cp;
iTupel delta;
delta = -1;
bool ready = false;
iTupel me, nb;
me = rank_to_coord(_rank);
int index = 0;
int last = neighbors()-1;
while (!ready)
{
// find neighbors coordinates
for (int i=0; i<d; i++)
nb[i] = ( me[i]+_dims[i]+delta[i] ) % _dims[i];
// find neighbors rank
int nbrank = coord_to_rank(nb);
// check if delta is not zero
for (int i=0; i<d; i++)
if (delta[i]!=0)
{
cp.rank = nbrank;
cp.delta = delta;
cp.index = index;
_recvlist.push_back(cp);
cp.index = last-index;
_sendlist.push_front(cp);
index++;
break;
}
// next neighbor
ready = true;
for (int i=0; i<d; i++)
if (delta[i]<1)
{
(delta[i])++;
ready=false;
break;
}
else
{
delta[i] = -1;
}
}
}
#if HAVE_MPI
MPI_Comm _comm;
#endif
int _rank;
int _procs;
iTupel _dims;
iTupel _increment;
int _tag;
std::deque<CommPartner> _sendlist;
std::deque<CommPartner> _recvlist;
mutable std::vector<CommTask> _sendrequests;
mutable std::vector<CommTask> _recvrequests;
mutable std::vector<CommTask> _localsendrequests;
mutable std::vector<CommTask> _localrecvrequests;
};
//! Output operator for Torus
template <int d>
inline std::ostream& operator<< (std::ostream& s, const Torus<d> & t)
{
t.print(s);
return s;
}
} // namespace Dune
#endif
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