matrix.h

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/*
 *  GiNaC Copyright (C) 1999-2026 Johannes Gutenberg University Mainz, Germany
 *
 *  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 2 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 <https://www.gnu.org/licenses/>.
 */
 
#ifndef GINAC_MATRIX_H
#define GINAC_MATRIX_H
 
#include "basic.h"
#include "ex.h"
#include "archive.h"
#include "compiler.h"
 
#include <string>
#include <vector>
 
namespace GiNaC {
 
class matrix : public basic
{
    GINAC_DECLARE_REGISTERED_CLASS(matrix, basic)
    
    // other constructors
public:
    matrix(unsigned r, unsigned c);
    matrix(unsigned r, unsigned c, const lst & l);
    matrix(std::initializer_list<std::initializer_list<ex>> l);
 
protected:
    matrix(unsigned r, unsigned c, const exvector & m2);
    matrix(unsigned r, unsigned c, exvector && m2);
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
    ex evalm() const override {return *this;}
    ex subs(const exmap & m, unsigned options = 0) const override;
    ex eval_indexed(const basic & i) const override;
    ex add_indexed(const ex & self, const ex & other) const override;
    ex scalar_mul_indexed(const ex & self, const numeric & other) const override;
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
    ex conjugate() const override;
    ex real_part() const override;
    ex imag_part() const override;
 
    void archive(archive_node& n) const override;
    void read_archive(const archive_node& n, lst& syms) override;
protected:
    bool match_same_type(const basic & other) const override;
    unsigned return_type() const override { return return_types::noncommutative; };
    
    // non-virtual functions in this class
public:
    unsigned rows() const        
        { return row; }
    unsigned cols() const        
        { return col; }
    matrix add(const matrix & other) const;
    matrix sub(const matrix & other) const;
    matrix mul(const matrix & other) const;
    matrix mul(const numeric & other) const;
    matrix mul_scalar(const ex & other) const;
    matrix pow(const ex & expn) const;
    const ex & operator() (unsigned ro, unsigned co) const;
    ex & operator() (unsigned ro, unsigned co);
    matrix & set(unsigned ro, unsigned co, const ex & value) { (*this)(ro, co) = value; return *this; }
    matrix transpose() const;
    ex determinant(unsigned algo = determinant_algo::automatic) const;
    ex trace() const;
    ex charpoly(const ex & lambda) const;
    matrix inverse() const;
    matrix inverse(unsigned algo) const;
    matrix solve(const matrix & vars, const matrix & rhs,
                 unsigned algo = solve_algo::automatic) const;
    unsigned rank() const;
    unsigned rank(unsigned solve_algo) const;
    bool is_zero_matrix() const;
protected:
    ex determinant_minor() const;
    std::vector<unsigned> echelon_form(unsigned algo, int n);
    int gauss_elimination(const bool det = false);
    int division_free_elimination(const bool det = false);
    int fraction_free_elimination(const bool det = false);
    std::vector<unsigned> markowitz_elimination(unsigned n);
    int pivot(unsigned ro, unsigned co, bool symbolic = true);
 
    void print_elements(const print_context & c, const char *row_start, const char *row_end, const char *row_sep, const char *col_sep) const;
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
    void do_print_python_repr(const print_python_repr & c, unsigned level) const;
    
// member variables
protected:
    unsigned row;             
    unsigned col;             
    exvector m;               
};
GINAC_DECLARE_UNARCHIVER(matrix); 
 
// wrapper functions around member functions
 
inline size_t nops(const matrix & m)
{ return m.nops(); }
 
inline ex expand(const matrix & m, unsigned options = 0)
{ return m.expand(options); }
 
inline ex evalf(const matrix & m)
{ return m.evalf(); }
 
inline unsigned rows(const matrix & m)
{ return m.rows(); }
 
inline unsigned cols(const matrix & m)
{ return m.cols(); }
 
inline matrix transpose(const matrix & m)
{ return m.transpose(); }
 
inline ex determinant(const matrix & m, unsigned options = determinant_algo::automatic)
{ return m.determinant(options); }
 
inline ex trace(const matrix & m)
{ return m.trace(); }
 
inline ex charpoly(const matrix & m, const ex & lambda)
{ return m.charpoly(lambda); }
 
inline matrix inverse(const matrix & m)
{ return m.inverse(solve_algo::automatic); }
inline matrix inverse(const matrix & m, unsigned algo)
{ return m.inverse(algo); }
 
inline unsigned rank(const matrix & m)
{ return m.rank(); }
inline unsigned rank(const matrix & m, unsigned solve_algo)
{ return m.rank(solve_algo); }
 
// utility functions
 
extern ex lst_to_matrix(const lst & l);
 
extern ex diag_matrix(const lst & l);
extern ex diag_matrix(std::initializer_list<ex> l);
 
extern ex unit_matrix(unsigned r, unsigned c);
 
inline ex unit_matrix(unsigned x)
{ return unit_matrix(x, x); }
 
extern ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name);
 
extern ex reduced_matrix(const matrix& m, unsigned r, unsigned c);
 
extern ex sub_matrix(const matrix&m, unsigned r, unsigned nr, unsigned c, unsigned nc);
 
inline ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name)
{ return symbolic_matrix(r, c, base_name, base_name); }
 
} // namespace GiNaC
 
#endif // ndef GINAC_MATRIX_H