* Interface to symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2007 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__
#include <vector>
+#include <string>
#include "basic.h"
#include "ex.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
-/** Symbolic matrices. */
-class matrix : public basic
-{
- GINAC_DECLARE_REGISTERED_CLASS(matrix, basic)
-// friends
-// (none)
-// member functions
-
- // default constructor, destructor, copy constructor, assignment operator
- // and helpers:
+/** 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();
- ~matrix();
- matrix(const matrix & other);
- const matrix & operator=(const matrix & other);
-protected:
- void copy(const matrix & other);
- void destroy(bool call_parent);
+ 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;
+};
- // other constructors
+
+/** Symbolic matrices. */
+class matrix : public basic
+{
+ GINAC_DECLARE_REGISTERED_CLASS(matrix, basic)
+
+ // other constructors
public:
- matrix(unsigned r, unsigned c);
- matrix(unsigned r, unsigned c, const exvector & m2);
-
- // functions overriding virtual functions from bases classes
+ 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:
- basic * duplicate() const;
- void print(std::ostream & os, unsigned upper_precedence=0) const;
- void printraw(std::ostream & os) const;
- unsigned nops() const;
- ex op(int i) const;
- ex & let_op(int i);
- ex expand(unsigned options=0) const;
- bool has(const ex & other) const;
- ex eval(int level=0) const;
- ex evalf(int level=0) const;
- // ex subs(const lst & ls, const lst & lr) 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 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;
+
protected:
- int compare_same_type(const basic & other) const;
- unsigned return_type(void) const { return return_types::noncommutative; };
- // new virtual functions which can be overridden by derived classes
- // (none)
-
- // non-virtual functions in this class
+ bool match_same_type(const basic & other) const;
+ unsigned return_type() const { return return_types::noncommutative; };
+
+ // non-virtual functions in this class
public:
- unsigned rows(void) const //! Get number of rows.
- { return row; }
- unsigned cols(void) const //! Get number of columns.
- { return col; }
- matrix add(const matrix & other) const;
- matrix sub(const matrix & other) const;
- matrix mul(const matrix & other) const;
- const ex & operator() (unsigned ro, unsigned co) const;
- matrix & set(unsigned ro, unsigned co, ex value);
- matrix transpose(void) const;
- ex determinant(unsigned options = determinant_algo::automatic) const;
- ex trace(void) const;
- ex charpoly(const symbol & lambda) const;
- matrix inverse(void) const;
- matrix fraction_free_elim(const matrix & vars, const matrix & v) const;
- matrix solve(const matrix & vars, const matrix & rhs) const;
- matrix old_solve(const matrix & v) const; // FIXME: may be removed
+ unsigned rows() const /// Get number of rows.
+ { return row; }
+ unsigned cols() const /// Get number of columns.
+ { 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 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(void) const;
- int gauss_elimination(void);
- int division_free_elimination(void);
- int fraction_free_elimination(bool det = false);
- int pivot(unsigned ro, bool symbolic=true);
-
+ 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 row; /**< number of rows */
- unsigned col; /**< number of columns */
- exvector m; /**< representation (cols indexed first) */
- static unsigned precedence;
+ unsigned row; ///< number of rows
+ unsigned col; ///< number of columns
+ exvector m; ///< representation (cols indexed first)
};
-// global constants
-extern const matrix some_matrix;
-extern const type_info & typeid_matrix;
-
-
// wrapper functions around member functions
-inline unsigned nops(const matrix & m)
+inline size_t nops(const matrix & m)
{ return m.nops(); }
-inline ex expand(const matrix & m, unsigned options=0)
+inline ex expand(const matrix & m, unsigned options = 0)
{ return m.expand(options); }
-inline bool has(const matrix & m, const ex & other)
-{ return m.has(other); }
-
-inline ex eval(const matrix & m, int level=0)
+inline ex eval(const matrix & m, int level = 0)
{ return m.eval(level); }
-inline ex evalf(const matrix & m, int level=0)
+inline ex evalf(const matrix & m, int level = 0)
{ return m.evalf(level); }
inline unsigned rows(const matrix & m)
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(); }
+inline unsigned rank(const matrix & m)
+{ return m.rank(); }
+
// utility functions
-inline const matrix &ex_to_matrix(const ex &e)
-{
- return static_cast<const matrix &>(*e.bp);
-}
-extern ex lst_to_matrix(const ex &l);
+/** Convert list of lists to matrix. */
+extern ex lst_to_matrix(const lst & l);
+
+/** Convert list of diagonal elements to matrix. */
+extern ex diag_matrix(const lst & l);
+
+/** Create an r times c unit matrix. */
+extern ex unit_matrix(unsigned r, unsigned c);
+
+/** Create a x times x unit matrix. */
+inline ex unit_matrix(unsigned x)
+{ return unit_matrix(x, x); }
+
+/** 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.
+ * 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)
+{ return symbolic_matrix(r, c, base_name, base_name); }
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
#endif // ndef __GINAC_MATRIX_H__
git://www.ginac.de / ginac.git / blobdiff