/usr/include/libnormaliz/sublattice_representation.h is in libnormaliz-dev-common 3.5.1+ds-4.
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* Normaliz
* Copyright (C) 2007-2014 Winfried Bruns, Bogdan Ichim, Christof Soeger
* This program 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 3 of the License, or
* (at your option) any later version.
*
* This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
*
* As an exception, when this program is distributed through (i) the App Store
* by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or (iii) Google Play
* by Google Inc., then that store may impose any digital rights management,
* device limits and/or redistribution restrictions that are required by its
* terms of service.
*/
/**
* The class Sublattice_Representation represents a sublattice of Z^n as Z^r.
* To transform vectors of the sublattice use:
* Z^r --> Z^n and Z^n --> Z^r
* v |-> vA u |-> (uB)/c
* A r x n matrix
* B n x r matrix
* c Integer
*
* The composition of the maps from Z^r to Z^r is c times the 9identity.
*/
#ifndef SUBLATTICE_REPRESENTATION_H
#define SUBLATTICE_REPRESENTATION_H
#include <vector>
#include <libnormaliz/libnormaliz.h>
#include <libnormaliz/matrix.h>
//---------------------------------------------------------------------------
namespace libnormaliz {
template<typename Integer> class Matrix;
// template<typename Integer> class Lineare_Transformation;
using std::vector;
template<typename Integer>
class Sublattice_Representation {
template<typename> friend class Sublattice_Representation;
template<typename, typename> friend class ProjectAndLift;
size_t dim, rank;
bool is_identity;
Matrix<Integer> A;
Matrix<Integer> B;
Integer c;
mutable mpz_class external_index;
mutable Matrix<Integer> Equations;
mutable bool Equations_computed;
mutable Matrix<Integer> Congruences;
mutable bool Congruences_computed;
void make_equations() const;
void make_congruences() const;
//---------------------------------------------------------------------------
public:
//---------------------------------------------------------------------------
// Construction and destruction
//---------------------------------------------------------------------------
/**
* creates a dummy object
*/
Sublattice_Representation() {}
/*
creates a representation of Z^n as a sublattice of itself
*/
Sublattice_Representation(size_t n);
// creation from given maps and c
Sublattice_Representation(const Matrix<Integer>& GivenA, const Matrix<Integer>& GivenB, Integer GivenC);
/**
* Main Constructor
* creates a representation of a sublattice of Z^n
* if direct_summand is false the sublattice is generated by the rows of M
* otherwise it is a direct summand of Z^n containing the rows of M
*/
Sublattice_Representation(const Matrix<Integer>& M, bool take_saturation);
template<typename IntegerFC>
Sublattice_Representation(const Sublattice_Representation<IntegerFC>& Original);
//---------------------------------------------------------------------------
// Manipulation operations
//---------------------------------------------------------------------------
/* workhorse for main constructor */
void initialize(const Matrix<Integer>& M, bool take_saturation, bool& success);
//
// applies LLL reduction to the rows of B and composes *this with the resulting transformation
void LLL_improve();
/* first this then SR when going from Z^n to Z^r */
void compose(const Sublattice_Representation<Integer>& SR);
/* compose with the dual of SR */
void compose_dual(const Sublattice_Representation<Integer>& SR);
//---------------------------------------------------------------------------
// Transformations
//---------------------------------------------------------------------------
Matrix<Integer> to_sublattice (const Matrix<Integer>& M) const;
Matrix<Integer> from_sublattice (const Matrix<Integer>& M) const;
Matrix<Integer> to_sublattice_dual (const Matrix<Integer>& M) const;
Matrix<Integer> from_sublattice_dual (const Matrix<Integer>& M) const;
vector<Integer> to_sublattice (const vector<Integer>& V) const;
vector<Integer> from_sublattice (const vector<Integer>& V) const;
vector<Integer> to_sublattice_dual (const vector<Integer>& M) const;
vector<Integer> from_sublattice_dual (const vector<Integer>& V) const;
vector<Integer> to_sublattice_dual_no_div (const vector<Integer>& M) const;
// and with integrated type conversion
// Note: the "to" conversions assume that val has the same integer type as the SLR
// whereas the "from" versions assume that ret has the same integer type as the SLR.
template<typename ToType, typename FromType>
void convert_to_sublattice(ToType& ret, const FromType& val) const {
convert(ret, to_sublattice(val));
}
template<typename ToType>
void convert_to_sublattice(Matrix<ToType>& ret, const Matrix<Integer> & val) const {
ret=Matrix<ToType>(val.nr_of_rows(),rank);
vector<Integer> v;
for(size_t i=0;i<val.nr_of_rows();++i){
v=to_sublattice(val[i]);
convert(ret[i],v);
}
}
template<typename ToType, typename FromType>
void convert_from_sublattice(ToType& ret, const FromType& val) const {
ret = from_sublattice(convertTo<ToType>(val));
}
template<typename FromType>
void convert_from_sublattice(Matrix<Integer>& ret, const Matrix<FromType> & val) const {
ret=Matrix<Integer>(val.nr_of_rows(),dim);
vector<Integer> v;
for(size_t i=0;i<val.nr_of_rows();++i){
INTERRUPT_COMPUTATION_BY_EXCEPTION
convert(v,val[i]);
ret[i]=from_sublattice(v);
}
}
template<typename ToType, typename FromType>
void convert_to_sublattice_dual(ToType& ret, const FromType& val) const {
convert(ret, to_sublattice_dual(val));
}
template<typename ToType>
void convert_to_sublattice_dual(Matrix<ToType>& ret, const Matrix<Integer> & val) const {
ret=Matrix<ToType>(val.nr_of_rows(),rank);
vector<Integer> v;
for(size_t i=0;i<val.nr_of_rows();++i){
v=to_sublattice_dual(val[i]);
convert(ret[i],v);
}
}
template<typename ToType, typename FromType>
void convert_from_sublattice_dual(ToType& ret, const FromType& val) const {
ret = from_sublattice_dual(convertTo<ToType>(val));
}
template<typename FromType>
void convert_from_sublattice_dual(Matrix<Integer>& ret, const Matrix<FromType> & val) const {
ret=Matrix<Integer>(val.nr_of_rows(),dim);
vector<Integer> v;
for(size_t i=0;i<val.nr_of_rows();++i){
INTERRUPT_COMPUTATION_BY_EXCEPTION
convert(v,val[i]);
ret[i]=from_sublattice_dual(v);
}
}
template<typename ToType, typename FromType>
void convert_to_sublattice_dual_no_div(ToType& ret, const FromType& val) const {
convert(ret, to_sublattice_dual_no_div(val));
}
template<typename ToType>
void convert_to_sublattice_dual_no_div(Matrix<ToType>& ret, const Matrix<Integer> & val) const {
ret=Matrix<ToType>(val.nr_of_rows(),rank);
vector<Integer> v;
for(size_t i=0;i<val.nr_of_rows();++i){
v=to_sublattice_dual_no_div(val[i]);
convert(ret[i],v);
}
}
//---------------------------------------------------------------------------
// Data acces
//---------------------------------------------------------------------------
/* returns the dimension of the ambient space */
size_t getDim() const;
/* returns the rank of the sublattice */
size_t getRank() const;
Integer getAnnihilator() const;
bool IsIdentity()const;
const Matrix<Integer>& getEquationsMatrix() const;
const vector<vector<Integer> >& getEquations() const;
const Matrix<Integer>& getCongruencesMatrix() const;
const vector<vector<Integer> >& getCongruences() const;
mpz_class getExternalIndex() const;
const Matrix<Integer>& getEmbeddingMatrix() const;
const vector<vector<Integer> >& getEmbedding() const;
const Matrix<Integer>& getProjectionMatrix() const;
const vector<vector<Integer> >& getProjection() const;
};
//---------------------------------------------------------------------------
// Constructor by conversion
//---------------------------------------------------------------------------
template<typename Integer>
template<typename IntegerFC>
Sublattice_Representation<Integer>::Sublattice_Representation(const
Sublattice_Representation<IntegerFC>& Original) {
convert(A,Original.A);
convert(B,Original.B);
dim=Original.dim;
rank=Original.rank;
convert(c,Original.c);
is_identity=Original.is_identity;
Equations_computed=Original.Equations_computed;
Congruences_computed=Original.Congruences_computed;
convert(Equations,Original.Equations);
convert(Congruences,Original.Congruences);
external_index=Original.external_index;
}
//---------------------------------------------------------------------------
// LLL coordinates
//---------------------------------------------------------------------------
template<typename Integer, typename number>
Sublattice_Representation<Integer> LLL_coordinates(const Matrix<number>& G){
// direction from given coorfinates to LLL_coordinates is "to"
Matrix<number> T,Tinv;
G.LLL_red_transpose(T,Tinv); // Tinv <<--> A, T <--> B
Matrix<Integer> IntT,IntTinv;
convert(IntT,T);
convert(IntTinv,Tinv);
return Sublattice_Representation<Integer>(IntTinv,IntT,1);
}
vector<key_t> reverse_key(size_t n);
vector<key_t> identity_key(size_t n);
template<typename Integer, typename number>
Sublattice_Representation<Integer> LLL_coordinates_dual(const Matrix<number>& G){
// direction from given coorfinates to LLL_coordinates is "to"
Matrix<number> T,Tinv;
G.LLL_red_transpose(T,Tinv); // T <---> A^tr, Tinv <--> B^tr
Matrix<Integer> IntT,IntTinv;
convert(IntT,T);
convert(IntTinv,Tinv); // but we reverse the order of the coordinates
vector<key_t> reverse=reverse_key(T.nr_of_columns());
IntT=IntT.transpose();
IntT=IntT.submatrix(reverse); // rows of A reversed
IntTinv=IntTinv.submatrix(reverse); // adter transposition below, columns are reversed
return Sublattice_Representation<Integer>(IntT,IntTinv.transpose(),1);
}
template<typename Integer,typename number>
void LLL_coordinates_without_1st_col(Sublattice_Representation<Integer>& LLL_Coordinates, const Matrix<number> Supps,
const Matrix<number> Vertices, bool verbose){
// used when the 1st column is the grading or the dehomogenization and should bot be changed
// Important in project_and_lift
// Computed SLR is returned in LLL_Coordinates
Matrix<Integer> HelpA, HelpB;
Integer HelpC;
assert(Supps.nr_of_rows()>0);
size_t EmbDim=Supps.nr_of_columns();
if(Vertices.nr_of_rows()==0 || Vertices.rank()<EmbDim-1){ // use Supps for LLL coordinates
Matrix<nmz_float> SuppHelp=Supps.nmz_float_without_first_column();
if(Supps.rank()<EmbDim)
return;
Sublattice_Representation<Integer> HelpCoord=LLL_coordinates_dual<Integer,nmz_float>(SuppHelp);
convert(HelpA,HelpCoord.getEmbeddingMatrix()); convert(HelpB,HelpCoord.getProjectionMatrix()); convert(HelpC,HelpCoord.getAnnihilator());
if(verbose)
verboseOutput() << "LLL based on support hyperplanes" << endl;
}
else{ // use Vertices for LLL coordinates
Matrix<nmz_float> VertHelp=Vertices.nmz_float_without_first_column();
Sublattice_Representation<Integer> HelpCoord=LLL_coordinates<Integer,nmz_float>(VertHelp);
convert(HelpA,HelpCoord.getEmbeddingMatrix()); convert(HelpB,HelpCoord.getProjectionMatrix()); convert(HelpC,HelpCoord.getAnnihilator());
if(verbose)
verboseOutput() << "LLL based on vertices" << endl;
}
Matrix<Integer> A(EmbDim), B(EmbDim);
//Insert into EmbDim-1 last coordinates of LLL_Coord
for(size_t i=0;i<EmbDim-1;++i)
for(size_t j=0;j<EmbDim-1;++j){
A[i+1][j+1]=HelpA[i][j];
B[i+1][j+1]=HelpB[i][j];
}
LLL_Coordinates=Sublattice_Representation<Integer>(A,B,HelpC);
}
/*
template<typename Integer, typename number>
Sublattice_Representation<Integer> LLL_coordinates_dual(const Matrix<number>& G){
// direction from given coorfinates to LLL_coordinates is "to"
Matrix<number> T,Tinv;
G.LLL_red_transpose(T,Tinv); // T <---> A^tr, Tinv <--> B^tr
Matrix<Integer> IntT,IntTinv;
convert(IntT,T);
convert(IntTinv,Tinv);
return Sublattice_Representation<Integer>(IntT.transpose(),IntTinv.transpose(),1);
}
*/
} // namespace
//---------------------------------------------------------------------------
#endif
//---------------------------------------------------------------------------
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