* Interface to symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2014 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#ifndef __GINAC_MATRIX_H__
-#define __GINAC_MATRIX_H__
+#ifndef GINAC_MATRIX_H
+#define GINAC_MATRIX_H
-#include <vector>
-#include <string>
#include "basic.h"
#include "ex.h"
+#include "archive.h"
+
+#include <string>
+#include <vector>
namespace GiNaC {
+/** Helper template to allow initialization of matrices via an overloaded
+ * comma operator (idea stolen from Blitz++). */
+template <typename T, typename It>
+class matrix_init {
+public:
+ matrix_init(It i) : iter(i) {}
+
+ matrix_init<T, It> operator,(const T & x)
+ {
+ *iter = x;
+ return matrix_init<T, It>(++iter);
+ }
+
+ // The following specializations produce much tighter code than the
+ // general case above
+
+ matrix_init<T, It> operator,(int x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+ matrix_init<T, It> operator,(unsigned int x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+ matrix_init<T, It> operator,(long x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+ matrix_init<T, It> operator,(unsigned long x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+ matrix_init<T, It> operator,(double x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+ matrix_init<T, It> operator,(const symbol & x)
+ {
+ *iter = T(x);
+ return matrix_init<T, It>(++iter);
+ }
+
+private:
+ matrix_init();
+ It iter;
+};
+
+
/** Symbolic matrices. */
class matrix : public basic
{
matrix(unsigned r, unsigned c);
matrix(unsigned r, unsigned c, const exvector & m2);
matrix(unsigned r, unsigned c, const lst & l);
+
+ // First step of initialization of matrix with a comma-separated seqeuence
+ // of expressions. Subsequent steps are handled by matrix_init<>::operator,().
+ matrix_init<ex, exvector::iterator> operator=(const ex & x)
+ {
+ m[0] = x;
+ return matrix_init<ex, exvector::iterator>(++m.begin());
+ }
// functions overriding virtual functions from base classes
public:
- void print(const print_context & c, unsigned level = 0) const;
size_t nops() const;
ex op(size_t i) const;
ex & let_op(size_t i);
ex eval(int level=0) const;
ex evalm() const {return *this;}
- ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
+ ex subs(const exmap & m, unsigned options = 0) const;
ex eval_indexed(const basic & i) const;
ex add_indexed(const ex & self, const ex & other) const;
ex scalar_mul_indexed(const ex & self, const numeric & other) const;
bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
-
+ ex conjugate() const;
+ ex real_part() const;
+ ex imag_part() const;
+
+ /** Save (a.k.a. serialize) object into archive. */
+ void archive(archive_node& n) const;
+ /** Read (a.k.a. deserialize) object from archive. */
+ void read_archive(const archive_node& n, lst& syms);
protected:
bool match_same_type(const basic & other) const;
unsigned return_type() const { return return_types::noncommutative; };
matrix transpose() const;
ex determinant(unsigned algo = determinant_algo::automatic) const;
ex trace() const;
- ex charpoly(const symbol & lambda) const;
+ ex charpoly(const ex & lambda) const;
matrix inverse() const;
matrix solve(const matrix & vars, const matrix & rhs,
unsigned algo = solve_algo::automatic) const;
+ unsigned rank() const;
+ bool is_zero_matrix() const;
protected:
ex determinant_minor() const;
int gauss_elimination(const bool det = false);
int division_free_elimination(const bool det = false);
int fraction_free_elimination(const bool det = false);
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 col; ///< number of columns
exvector m; ///< representation (cols indexed first)
};
+GINAC_DECLARE_UNARCHIVER(matrix);
// wrapper functions around member functions
inline ex trace(const matrix & m)
{ return m.trace(); }
-inline ex charpoly(const matrix & m, const symbol & lambda)
+inline ex charpoly(const matrix & m, const ex & lambda)
{ return m.charpoly(lambda); }
inline matrix inverse(const matrix & m)
{ return m.inverse(); }
-// utility functions
+inline unsigned rank(const matrix & m)
+{ return m.rank(); }
-/** Specialization of is_exactly_a<matrix>(obj) for matrix objects. */
-template<> inline bool is_exactly_a<matrix>(const basic & obj)
-{
- return obj.tinfo()==TINFO_matrix;
-}
+// utility functions
/** Convert list of lists to matrix. */
extern ex lst_to_matrix(const lst & l);
* The base name for LaTeX output is specified separately. */
extern ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name);
+/** Return the reduced matrix that is formed by deleting the rth row and cth
+ * column of matrix m. The determinant of the result is the Minor r, c. */
+extern ex reduced_matrix(const matrix& m, unsigned r, unsigned c);
+
+/** Return the nr times nc submatrix starting at position r, c of matrix m. */
+extern ex sub_matrix(const matrix&m, unsigned r, unsigned nr, unsigned c, unsigned nc);
+
/** Create an r times c matrix of newly generated symbols consisting of the
* given base name plus the numeric row/column position of each element. */
inline ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name)
} // namespace GiNaC
-#endif // ndef __GINAC_MATRIX_H__
+#endif // ndef GINAC_MATRIX_H
git://www.ginac.de / ginac.git / blobdiff