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
47 ex op(size_t i) const;
48 ex & let_op(size_t i);
49 ex eval(int level=0) const;
50 ex evalm() const {return *this;}
51 ex subs(const exmap & m, unsigned options = 0) const;
52 ex eval_indexed(const basic & i) const;
53 ex add_indexed(const ex & self, const ex & other) const;
54 ex scalar_mul_indexed(const ex & self, const numeric & other) const;
55 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
58 bool match_same_type(const basic & other) const;
59 unsigned return_type() const { return return_types::noncommutative; };
61 // non-virtual functions in this class
63 unsigned rows() const /// Get number of rows.
65 unsigned cols() const /// Get number of columns.
67 matrix add(const matrix & other) const;
68 matrix sub(const matrix & other) const;
69 matrix mul(const matrix & other) const;
70 matrix mul(const numeric & other) const;
71 matrix mul_scalar(const ex & other) const;
72 matrix pow(const ex & expn) const;
73 const ex & operator() (unsigned ro, unsigned co) const;
74 ex & operator() (unsigned ro, unsigned co);
75 matrix & set(unsigned ro, unsigned co, const ex & value) { (*this)(ro, co) = value; return *this; }
76 matrix transpose() const;
77 ex determinant(unsigned algo = determinant_algo::automatic) const;
79 ex charpoly(const symbol & lambda) const;
80 matrix inverse() const;
81 matrix solve(const matrix & vars, const matrix & rhs,
82 unsigned algo = solve_algo::automatic) const;
84 ex determinant_minor() const;
85 int gauss_elimination(const bool det = false);
86 int division_free_elimination(const bool det = false);
87 int fraction_free_elimination(const bool det = false);
88 int pivot(unsigned ro, unsigned co, bool symbolic = true);
90 void print_elements(const print_context & c, const char *row_start, const char *row_end, const char *row_sep, const char *col_sep) const;
91 void do_print(const print_context & c, unsigned level) const;
92 void do_print_latex(const print_latex & c, unsigned level) const;
93 void do_print_python_repr(const print_python_repr & c, unsigned level) const;
97 unsigned row; ///< number of rows
98 unsigned col; ///< number of columns
99 exvector m; ///< representation (cols indexed first)
103 // wrapper functions around member functions
105 inline size_t nops(const matrix & m)
108 inline ex expand(const matrix & m, unsigned options = 0)
109 { return m.expand(options); }
111 inline ex eval(const matrix & m, int level = 0)
112 { return m.eval(level); }
114 inline ex evalf(const matrix & m, int level = 0)
115 { return m.evalf(level); }
117 inline unsigned rows(const matrix & m)
120 inline unsigned cols(const matrix & m)
123 inline matrix transpose(const matrix & m)
124 { return m.transpose(); }
126 inline ex determinant(const matrix & m, unsigned options = determinant_algo::automatic)
127 { return m.determinant(options); }
129 inline ex trace(const matrix & m)
130 { return m.trace(); }
132 inline ex charpoly(const matrix & m, const symbol & lambda)
133 { return m.charpoly(lambda); }
135 inline matrix inverse(const matrix & m)
136 { return m.inverse(); }
140 /** Specialization of is_exactly_a<matrix>(obj) for matrix objects. */
141 template<> inline bool is_exactly_a<matrix>(const basic & obj)
143 return obj.tinfo()==TINFO_matrix;
146 /** Convert list of lists to matrix. */
147 extern ex lst_to_matrix(const lst & l);
149 /** Convert list of diagonal elements to matrix. */
150 extern ex diag_matrix(const lst & l);
152 /** Create an r times c unit matrix. */
153 extern ex unit_matrix(unsigned r, unsigned c);
155 /** Create a x times x unit matrix. */
156 inline ex unit_matrix(unsigned x)
157 { return unit_matrix(x, x); }
159 /** Create an r times c matrix of newly generated symbols consisting of the
160 * given base name plus the numeric row/column position of each element.
161 * The base name for LaTeX output is specified separately. */
162 extern ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name);
164 /** Create an r times c matrix of newly generated symbols consisting of the
165 * given base name plus the numeric row/column position of each element. */
166 inline ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name)
167 { return symbolic_matrix(r, c, base_name, base_name); }
171 #endif // ndef __GINAC_MATRIX_H__