3 * Interface to symbolic matrices */
6 * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #ifndef __GINAC_MATRIX_H__
24 #define __GINAC_MATRIX_H__
33 /** Symbolic matrices. */
34 class matrix : public basic
36 GINAC_DECLARE_REGISTERED_CLASS(matrix, basic)
40 matrix(unsigned r, unsigned c);
41 matrix(unsigned r, unsigned c, const exvector & m2);
42 matrix(unsigned r, unsigned c, const lst & l);
44 // functions overriding virtual functions from base classes
46 void print(const print_context & c, unsigned level = 0) const;
48 ex op(size_t i) const;
49 ex & let_op(size_t i);
50 ex eval(int level=0) const;
51 ex evalm() const {return *this;}
52 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
53 ex eval_indexed(const basic & i) const;
54 ex add_indexed(const ex & self, const ex & other) const;
55 ex scalar_mul_indexed(const ex & self, const numeric & other) const;
56 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
59 bool match_same_type(const basic & other) const;
60 unsigned return_type() const { return return_types::noncommutative; };
62 // non-virtual functions in this class
64 unsigned rows() const /// Get number of rows.
66 unsigned cols() const /// Get number of columns.
68 matrix add(const matrix & other) const;
69 matrix sub(const matrix & other) const;
70 matrix mul(const matrix & other) const;
71 matrix mul(const numeric & other) const;
72 matrix mul_scalar(const ex & other) const;
73 matrix pow(const ex & expn) const;
74 const ex & operator() (unsigned ro, unsigned co) const;
75 ex & operator() (unsigned ro, unsigned co);
76 matrix & set(unsigned ro, unsigned co, const ex & value) { (*this)(ro, co) = value; return *this; }
77 matrix transpose() const;
78 ex determinant(unsigned algo = determinant_algo::automatic) const;
80 ex charpoly(const symbol & lambda) const;
81 matrix inverse() const;
82 matrix solve(const matrix & vars, const matrix & rhs,
83 unsigned algo = solve_algo::automatic) const;
85 ex determinant_minor() const;
86 int gauss_elimination(const bool det = false);
87 int division_free_elimination(const bool det = false);
88 int fraction_free_elimination(const bool det = false);
89 int pivot(unsigned ro, unsigned co, bool symbolic = true);
93 unsigned row; ///< number of rows
94 unsigned col; ///< number of columns
95 exvector m; ///< representation (cols indexed first)
99 // wrapper functions around member functions
101 inline size_t nops(const matrix & m)
104 inline ex expand(const matrix & m, unsigned options = 0)
105 { return m.expand(options); }
107 inline ex eval(const matrix & m, int level = 0)
108 { return m.eval(level); }
110 inline ex evalf(const matrix & m, int level = 0)
111 { return m.evalf(level); }
113 inline unsigned rows(const matrix & m)
116 inline unsigned cols(const matrix & m)
119 inline matrix transpose(const matrix & m)
120 { return m.transpose(); }
122 inline ex determinant(const matrix & m, unsigned options = determinant_algo::automatic)
123 { return m.determinant(options); }
125 inline ex trace(const matrix & m)
126 { return m.trace(); }
128 inline ex charpoly(const matrix & m, const symbol & lambda)
129 { return m.charpoly(lambda); }
131 inline matrix inverse(const matrix & m)
132 { return m.inverse(); }
136 /** Specialization of is_exactly_a<matrix>(obj) for matrix objects. */
137 template<> inline bool is_exactly_a<matrix>(const basic & obj)
139 return obj.tinfo()==TINFO_matrix;
142 /** Convert list of lists to matrix. */
143 extern ex lst_to_matrix(const lst & l);
145 /** Convert list of diagonal elements to matrix. */
146 extern ex diag_matrix(const lst & l);
148 /** Create an r times c unit matrix. */
149 extern ex unit_matrix(unsigned r, unsigned c);
151 /** Create a x times x unit matrix. */
152 inline ex unit_matrix(unsigned x)
153 { return unit_matrix(x, x); }
155 /** Create an r times c matrix of newly generated symbols consisting of the
156 * given base name plus the numeric row/column position of each element.
157 * The base name for LaTeX output is specified separately. */
158 extern ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name);
160 /** Create an r times c matrix of newly generated symbols consisting of the
161 * given base name plus the numeric row/column position of each element. */
162 inline ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name)
163 { return symbolic_matrix(r, c, base_name, base_name); }
167 #endif // ndef __GINAC_MATRIX_H__