/usr/include/libnormaliz/vector_operations.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.
*/
//---------------------------------------------------------------------------
#ifndef VECTOR_OPERATIONS_H
#define VECTOR_OPERATIONS_H
//---------------------------------------------------------------------------
#include <vector>
#include <ostream>
#include <list>
#include <libnormaliz/libnormaliz.h>
#include <libnormaliz/integer.h>
#include <libnormaliz/convert.h>
#include <libnormaliz/matrix.h>
namespace libnormaliz {
using std::vector;
//---------------------------------------------------------------------------
// Output
//---------------------------------------------------------------------------
template <typename T>
std::ostream& operator<< (std::ostream& out, const vector<T>& vec) {
for (size_t i=0; i<vec.size(); ++i) {
out << vec[i] << " ";
}
out << std::endl;
return out;
}
//---------------------------------------------------------------------------
// Prototypes for vector_operations.cpp
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_scalar_product(const vector<Integer>& a,const vector<Integer>& b);
template<typename Integer>
Integer v_make_prime(vector<Integer>& v);
nmz_float l1norm(vector<nmz_float>& v);
template<>
nmz_float v_make_prime<>(vector<nmz_float>& v);
template<typename Integer>
void v_scalar_division(vector<Integer>& v, const Integer scalar);
void order_by_perm_bool(vector<bool>& v, const vector<key_t>& permfix);
//---------------------------------------------------------------------------
// Templated functions
//---------------------------------------------------------------------------
//returns the scalar product of the truncations of vectors a and b to minimum of lengths
// template<typename Integer>
template<typename Integer>
Integer v_scalar_product_vectors_unequal_lungth(const vector<Integer>& a,const vector<Integer>& b){
size_t n=min(a.size(),b.size());
vector<Integer> trunc_a=a;
vector<Integer> trunc_b=b;
trunc_a.resize(n);
trunc_b.resize(n);
return v_scalar_product(trunc_a,trunc_b);
}
//v = v * scalar
template<typename Integer>
void v_scalar_multiplication(vector<Integer>& v, const Integer scalar){
size_t i,size=v.size();
for (i = 0; i <size; i++) {
v[i] *= scalar;
}
}
// make random vector of length n with entries between -m and m
template <typename Integer>
vector<Integer> v_random(size_t n, long m){
vector<Integer> result(n);
for(size_t i=0;i<n;++i)
result[i]=rand()%(2*m+1)-m;
return result;
}
template<typename Integer>
bool compare_last (const vector<Integer>& a, const vector<Integer>& b)
{
return a.back() < b.back();
}
// swaps entry i and j of the vector<bool> v
void v_bool_entry_swap(vector<bool>& v, size_t i, size_t j);
// computes approximating lattice simplex using the A_n dissection of the unit cube
// q is a rational vector with the denominator in the FIRST component q[0]
template<typename Integer>
void approx_simplex(const vector<Integer>& q, std::list<vector<Integer> >& approx, const long approx_level){
//cout << "approximate the point " << q;
long dim=q.size();
long l = approx_level;
//if (approx_level>q[0]) l=q[0]; // approximating on level q[0](=grading) is the best we can do
// TODO in this case, skip the rest and just approximate on q[0]
Matrix<Integer> quot = Matrix<Integer>(l,dim);
Matrix<Integer> remain=Matrix<Integer>(l,dim);
for(long j=0;j<approx_level;j++){
for(long i=0;i<dim;++i){
quot[j][i]=(q[i]*(j+1))/q[0]; // write q[i]=quot*q[0]+remain
//quot[j][0] = 1;
remain[j][i]=(q[i]*(j+1))%q[0]; // with 0 <= remain < q[0]
if(remain[j][i]<0){
remain[j][i]+=q[0];
quot[j][i]--;
}
}
v_make_prime(quot[j]);
remain[j][0]=q[0]; // helps to avoid special treatment of i=0
}
// choose best level
//cout << "this is the qout matrix" << endl;
//quot.pretty_print(cout);
//cout << "this is the remain matrix" << endl;
//remain.pretty_print(cout);
long best_level=l-1;
vector<long> nr_zeros(l);
for(long j=l-1;j>=0;j--){
for(long i=0;i<dim;++i){
if(remain[j][i]==0) nr_zeros[j]++;
}
if (nr_zeros[j]>nr_zeros[best_level]) best_level=j;
}
//cout << "the best level is " << (best_level+1) << endl;
//now we proceed as before
vector<pair<Integer,size_t>> best_remain(dim);
for(long i=0;i<dim;i++){
best_remain[i].first = remain[best_level][i];
best_remain[i].second = i; // after sorting we must lnow where elements come from
}
sort(best_remain.begin(),best_remain.end());
reverse(best_remain.begin(),best_remain.end()); // we sort remain into descending order
/*for(long i=0;i<dim;++i){
cout << remain[i].first << " " << remain[i].second << endl;
} */
for(long i=1;i<dim;++i){
if(best_remain[i].first<best_remain[i-1].first)
{
approx.push_back(quot[best_level]);
//cout << "add the point " << quot[best_level];
// cout << i << " + " << remain[i].first << " + " << quot << endl;
}
quot[best_level][best_remain[i].second]++;
}
if(best_remain[dim-1].first > 0){
// cout << "E " << quot << endl;
approx.push_back(quot[best_level]);
//cout << "add the point " << quot[best_level];
}
}
vector<key_t> identity_key(size_t n);
vector<key_t> reverse_key(size_t n);
template <typename T>
void order_by_perm(vector<T>& v, const vector<key_t>& permfix){
vector<key_t> perm=permfix; // we may want to use permfix a second time
vector<key_t> inv(perm.size());
for(key_t i=0;i<perm.size();++i)
inv[perm[i]]=i;
for(key_t i=0;i<perm.size();++i){
key_t j=perm[i];
swap(v[i],v[perm[i]]);
swap(perm[i],perm[inv[i]]);
swap(inv[i],inv[j]);
}
}
template<typename Integer>
bool v_scalar_mult_mod_inner(vector<Integer>& w, const vector<Integer>& v, const Integer& scalar, const Integer& modulus){
size_t i,size=v.size();
Integer test;
for (i = 0; i <size; i++) {
test=v[i]*scalar;
if(!check_range(test)){
return false;
}
w[i]=test % modulus;
if(w[i]<0)
w[i]+=modulus;
}
return true;
}
template<typename Integer>
vector<Integer> v_scalar_mult_mod(const vector<Integer>& v, const Integer& scalar, const Integer& modulus){
vector<Integer> w(v.size());
if(v_scalar_mult_mod_inner(w,v,scalar,modulus))
return w;
#pragma omp atomic
GMP_scal_prod++;
vector<mpz_class> x,y(v.size());
convert(x,v);
v_scalar_mult_mod_inner(y,x,convertTo<mpz_class>(scalar),convertTo<mpz_class>(modulus));
return convertTo<vector<Integer>>(y);
}
//---------------------------------------------------------------------------
template<typename Integer>
size_t v_nr_negative(const vector<Integer>& v) {
size_t tmp=0;
for (size_t i = 0; i < v.size(); ++i) {
if (v[i] <0) tmp++;
}
return tmp;
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_non_negative(const vector<Integer>& v) {
for (size_t i = 0; i < v.size(); ++i) {
if (v[i] <0) return false;
}
return true;
}
//---------------------------------------------------------------------------
//returns a key vector containing the positions of non-zero entrys of v
template<typename Integer>
vector<key_t> v_non_zero_pos(const vector<Integer>& v){
vector<key_t> key;
size_t size=v.size();
key.reserve(size);
for (key_t i = 0; i <size; i++) {
if (v[i]!=0) {
key.push_back(i);
}
}
return key;
}
//---------------------------------------------------------------------------
// returns the vector of absolute values, does not change the argument
template<typename Integer>
vector<Integer> v_abs_value(vector<Integer>& v){
size_t i, size=v.size();
vector<Integer> w=v;
for (i = 0; i < size; i++) {
if (v[i]<0) w[i] = Iabs(v[i]);
}
return w;
}
//---------------------------------------------------------------------------
//returns gcd of the elements of v
template<typename Integer>
Integer v_gcd(const vector<Integer>& v){
size_t i, size=v.size();
Integer g=0;
for (i = 0; i < size; i++) {
g = libnormaliz::gcd(g,v[i]);
if (g==1) {
return 1;
}
}
return g;
}
//---------------------------------------------------------------------------
//returns lcm of the elements of v
template<typename Integer>
Integer v_lcm(const vector<Integer>& v){
size_t i,size=v.size();
Integer g=1;
for (i = 0; i < size; i++) {
g = libnormaliz::lcm(g,v[i]);
if (g==0) {
return 0;
}
}
return g;
}
//returns lcm of the elements of v from index k up to index j
template<typename Integer>
Integer v_lcm_to(const vector<Integer>& v,const size_t k, const size_t j){
assert(k <= j);
size_t i;
Integer g=1;
for (i = k; i <= j; i++) {
g = libnormaliz::lcm(g,v[i]);
if (g==0) {
return 0;
}
}
return g;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer>& v_abs(vector<Integer>& v){
size_t i, size=v.size();
for (i = 0; i < size; i++) {
if (v[i]<0) v[i] = Iabs(v[i]);
}
return v;
}
//---------------------------------------------------------------------------
//returns a new vector with the content of a extended by b
template<typename T>
vector<T> v_merge(const vector<T>& a, const T& b) {
size_t s=a.size();
vector<T> c(s+1);
for (size_t i = 0; i < s; i++) {
c[i]=a[i];
}
c[s] = b;
return c;
}
//---------------------------------------------------------------------------
template<typename T>
vector<T> v_merge(const vector<T>& a,const vector<T>& b){
size_t s1=a.size(), s2=b.size(), i;
vector<T> c(s1+s2);
for (i = 0; i < s1; i++) {
c[i]=a[i];
}
for (i = 0; i < s2; i++) {
c[s1+i]=b[i];
}
return c;
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_reduction_modulo(vector<Integer>& v, const Integer& modulo){
size_t i,size=v.size();
for (i = 0; i <size; i++) {
v[i]=v[i]%modulo;
if (v[i]<0) {
v[i]=v[i]+modulo;
}
}
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer>& v_add_to_mod(vector<Integer>& a, const vector<Integer>& b, const Integer& m) {
// assert(a.size() == b.size());
size_t i, s=a.size();
for (i = 0; i <s; i++) {
// a[i] = (a[i]+b[i])%m;
if ((a[i] += b[i]) >= m) {
a[i] -= m;
}
}
return a;
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_is_zero(const vector<Integer>& v) {
for (size_t i = 0; i < v.size(); ++i) {
if (v[i] != 0) return false;
}
return true;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer> v_add(const vector<Integer>& a,const vector<Integer>& b){
assert(a.size() == b.size());
size_t i,s=a.size();
vector<Integer> d(s);
for (i = 0; i <s; i++) {
d[i]=a[i]+b[i];
}
return d;
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_add_result(vector<Integer>& result, const size_t s, const vector<Integer>& a,const vector<Integer>& b){
assert(a.size() == b.size() && a.size() == result.size());
size_t i;
// vector<Integer> d(s);
for (i = 0; i <s; i++) {
result[i]=a[i]+b[i];
}
// return d;
}
//---------------------------------------------------------------------------
//returns a new vector with the last size entries of v
template<typename T>
vector<T> v_cut_front(const vector<T>& v, size_t size){
size_t s,k;
vector<T> tmp(size);
s=v.size()-size;
for (k = 0; k < size; k++) {
tmp[k]=v[s+k];
}
return tmp;
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_is_symmetric(const vector<Integer>& v) {
for (size_t i = 0; i < v.size()/2; ++i) {
if (v[i] != v[v.size()-1-i]) return false;
}
return true;
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_el_trans(const vector<Integer>& av,vector<Integer>& bv, const Integer& F, const size_t start){
size_t i,n=av.size();
typename vector<Integer>::const_iterator a=av.begin();
typename vector<Integer>::iterator b=bv.begin();
a += start;
b += start;
n -= start;
if( n >= 8 )
{
for( i = 0; i < ( n >> 3 ); ++i, a += 8, b += 8 ){
b[0] += F*a[0];
b[1] += F*a[1];
b[2] += F*a[2];
b[3] += F*a[3];
b[4] += F*a[4];
b[5] += F*a[5];
b[6] += F*a[6];
b[7] += F*a[7];
}
n -= i << 3;
}
if( n >= 4)
{
b[0] += F*a[0];
b[1] += F*a[1];
b[2] += F*a[2];
b[3] += F*a[3];
n -=4;
a +=4;
b +=4;
}
if( n >= 2)
{
b[0] += F*a[0];
b[1] += F*a[1];
n -=2;
a +=2;
b +=2;
}
if(n>0)
b[0] += F*a[0];
for(size_t i=0;i<bv.size();++i)
if(!check_range(bv[i]))
throw ArithmeticException("Vector entry out of range. Imminent danger of arithmetic overflow.");
}
template<typename Integer>
Integer v_max_abs(const vector<Integer>& v){
Integer tmp = 0;
for (size_t i=0; i<v.size(); i++){
if (Iabs(v[i])>tmp) tmp=Iabs(v[i]);
}
return tmp;
}
} // namespace
//---------------------------------------------------------------------------
#endif
//---------------------------------------------------------------------------
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