CoCalc -- vector_operations.h

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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Path: gap4r8 / pkg / NormalizInterface-1.0.2 / Normaliz.git / DST / include / libnormaliz / vector_operations.h
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/*
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 * Normaliz
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 * Copyright (C) 2007-2014  Winfried Bruns, Bogdan Ichim, Christof Soeger
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 * This program is free software: you can redistribute it and/or modify
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 * it under the terms of the GNU General Public License as published by
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 * the Free Software Foundation, either version 3 of the License, or
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 * (at your option) any later version.
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 *
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 * This program is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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 * GNU General Public License for more details.
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 *
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 * You should have received a copy of the GNU General Public License
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 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
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 *
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 * As an exception, when this program is distributed through (i) the App Store
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 * by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or (iii) Google Play
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 * by Google Inc., then that store may impose any digital rights management,
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 * device limits and/or redistribution restrictions that are required by its
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 * terms of service.
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 */
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//---------------------------------------------------------------------------
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#ifndef VECTOR_OPERATIONS_H
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#define VECTOR_OPERATIONS_H
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//---------------------------------------------------------------------------
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#include <vector>
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#include <ostream>
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#include <list>
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#include <libnormaliz/libnormaliz.h>
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#include <libnormaliz/integer.h>
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#include <libnormaliz/convert.h>
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namespace libnormaliz {
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using std::vector;
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//---------------------------------------------------------------------------
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//							Data access
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//---------------------------------------------------------------------------
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template <typename T>
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std::ostream& operator<< (std::ostream& out, const vector<T>& vec) {
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    for (size_t i=0; i<vec.size(); ++i) {
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        out << vec[i] << " ";
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    }
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    out << std::endl;
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    return out;
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}
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//---------------------------------------------------------------------------
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//					    	Vector operations
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//---------------------------------------------------------------------------
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template<typename Integer>
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Integer v_scalar_product(const vector<Integer>& a,const vector<Integer>& b);
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template<typename Integer>
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bool v_scalar_product_nonnegative(const vector<Integer>& a,const vector<Integer>& b);
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template<typename Integer>
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bool v_scalar_product_positive(const vector<Integer>& a,const vector<Integer>& b);
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//returns the scalar product of the truncations of vectors a and b to minimum of lengths
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template<typename Integer>
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Integer v_scalar_product_vectors_unequal_lungth(const vector<Integer>& a,const vector<Integer>& b);
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//returns the addition a + b, vectors must be of equal size
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template<typename Integer>
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vector<Integer> v_add(const vector<Integer>& a,const vector<Integer>& b);
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template<typename Integer>
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vector<Integer> v_add_overflow_check(const vector<Integer>& a,const vector<Integer>& b);
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template<typename Integer>
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void v_add_result(vector<Integer>& result, const size_t length, const vector<Integer>& a,const vector<Integer>& b);
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//adds b to a reduces the result modulo m, a and b must be reduced modulo m!
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template<typename Integer>
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vector<Integer>& v_add_to_mod(vector<Integer>& a, const vector<Integer>& b, const Integer& m);
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//---------------------------------------------------------------------------
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//							abs, gcd and lcm
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//---------------------------------------------------------------------------
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// takes the absolute value of the elements and returns a reference to the changed vector
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template<typename Integer>
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vector<Integer>& v_abs(vector<Integer>& v);
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// returns the vector of absolute values, does not change the argument
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template<typename Integer>
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vector<Integer> v_abs_value(vector<Integer>& v);
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//returns gcd of the elements of v
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template<typename Integer>
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Integer v_gcd(const vector<Integer>& v);
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//returns lcm of the elements of v
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template<typename Integer>
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Integer v_lcm(const vector<Integer>& v);
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//returns lcm of the elements of v from index k up to index j
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template<typename Integer>
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Integer v_lcm_to(const vector<Integer>& v,const size_t k, const size_t j);
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//divides the elements by their gcd and returns the gcd
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template<typename Integer>
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Integer v_make_prime(vector<Integer>& v);
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nmz_float l1norm(vector<nmz_float>& v);
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template<>
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nmz_float v_make_prime<>(vector<nmz_float>& v);
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//---------------------------------------------------------------------------
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//							Scalar operations
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//---------------------------------------------------------------------------
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//v = v * scalar
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template<typename Integer>
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void v_scalar_multiplication(vector<Integer>& v, const Integer scalar){
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    size_t i,size=v.size();
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    for (i = 0; i <size; i++) {
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        v[i] *= scalar;
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    }
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}
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//---------------------------------------------------------------------------
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template<typename Integer>
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void v_scalar_division(vector<Integer>& v, const Integer scalar){
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    size_t i,size=v.size();
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    for (i = 0; i <size; i++) {
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        assert(v[i]%scalar == 0);
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        v[i] /= scalar;
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    }
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}
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//returns v * scalar mod modulus
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template<typename Integer>
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vector<Integer> v_scalar_mult_mod(const vector<Integer>& v, const Integer& scalar, const Integer& modulus, bool& success);
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template<typename Integer>
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void v_reduction_modulo(vector<Integer>& v, const Integer& modulo);
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//v = v mod modulo
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//---------------------------------------------------------------------------
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//								Test
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//---------------------------------------------------------------------------
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template<typename Integer>
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bool v_test_scalar_product(const vector<Integer>& a,const vector<Integer>& b, const Integer& result, const long& m);
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// test the main computation for arithmetic overflow
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// uses multiplication mod m
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//---------------------------------------------------------------------------
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//							   General vector operations
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//---------------------------------------------------------------------------
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//returns a new vector with the content of a extended by b
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template<typename T>
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vector<T> v_merge(const vector<T>& a, const T& b);
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//returns a new vector with the content of a and b
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template<typename T>
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vector<T> v_merge(const vector<T>& a, const vector<T>& b);
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//returns a new vector with the last size entries of v
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template<typename T>
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vector<T> v_cut_front(const vector<T>& v, size_t size);
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//the input vectors must be ordered of equal size
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//if u is different from v by just one element, it returns that element
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//else returns 0 (the elements of u and v are >0)
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//int v_difference_ordered_fast(const vector<size_t>& u,const vector<size_t>& v);
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template<typename Integer>
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bool compare_last (const vector<Integer>& a, const vector<Integer>& b)
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{
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    return a.back() < b.back();
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}
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//returns a key vector containing the positions of non-zero entrys of v
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template<typename Integer>
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vector<key_t> v_non_zero_pos(const vector<Integer>& v);
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// counts the number of positive entries
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template<typename Integer>
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size_t v_nr_positive(const vector<Integer>& v);
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template<typename Integer>
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size_t v_nr_negative(const vector<Integer>& v);
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template<typename Integer>
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bool v_non_negative(const vector<Integer>& v);
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// check whether the vector only contains 0
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template<typename Integer>
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bool v_is_zero(const vector<Integer>& v);
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template<typename Integer>
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bool v_is_symmetric(const vector<Integer>& v);
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template<typename Integer>
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bool v_is_nonnegative(const vector<Integer>& v);
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template<typename Integer>
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Integer v_max_abs(const vector<Integer>& v){
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	Integer tmp = 0;
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	for (size_t i=0; i<v.size(); i++){
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		if (Iabs(v[i])>tmp) tmp=Iabs(v[i]);
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	}
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	return tmp;
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}
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//---------------------------------------------------------------------------
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//							   bool vector operations
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//---------------------------------------------------------------------------
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vector<bool> v_bool_andnot(const vector<bool>& a, const vector<bool>& b);
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// swaps entry i and j of the vector<bool> v
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void v_bool_entry_swap(vector<bool>& v, size_t i, size_t j);
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//---------------------------------------------------------------------------
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//							  Special
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//---------------------------------------------------------------------------
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// computes integral simplex containing a rational vector
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template<typename Integer>
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void approx_simplex(const vector<Integer>& q, std::list<vector<Integer> >& approx,const long k);
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vector<key_t> identity_key(size_t n);
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// compute the degree vector of a hsop
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template<typename Integer>
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vector<Integer> degrees_hsop(const vector<Integer> gen_degrees,const vector<size_t> heights);
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//---------------------------------------------------------------------------
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//                            Sorting
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//---------------------------------------------------------------------------
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template <typename T>
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void order_by_perm(vector<T>& v, const vector<key_t>& permfix);
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// compare sizes of v_scalar_product_unequal_vectors_begin
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} // namespace
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//---------------------------------------------------------------------------
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#endif
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//---------------------------------------------------------------------------
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