* Implementation of symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <string>
+#include <iostream>
+#include <sstream>
#include <algorithm>
#include <map>
#include <stdexcept>
#include "lst.h"
#include "idx.h"
#include "indexed.h"
+#include "add.h"
#include "power.h"
#include "symbol.h"
+#include "operators.h"
#include "normal.h"
-#include "print.h"
#include "archive.h"
#include "utils.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(matrix, basic,
+ print_func<print_context>(&matrix::do_print).
+ print_func<print_latex>(&matrix::do_print_latex).
+ print_func<print_tree>(&basic::do_print_tree).
+ print_func<print_python_repr>(&matrix::do_print_python_repr))
//////////
-// default ctor, dtor, copy ctor, assignment operator and helpers:
+// default constructor
//////////
/** Default ctor. Initializes to 1 x 1-dimensional zero-matrix. */
-matrix::matrix() : inherited(TINFO_matrix), row(1), col(1)
+matrix::matrix() : inherited(TINFO_matrix), row(1), col(1), m(1, _ex0)
{
- m.push_back(_ex0);
+ setflag(status_flags::not_shareable);
}
-void matrix::copy(const matrix & other)
-{
- inherited::copy(other);
- row = other.row;
- col = other.col;
- m = other.m; // STL's vector copying invoked here
-}
-
-DEFAULT_DESTROY(matrix)
-
//////////
-// other ctors
+// other constructors
//////////
// public
* @param r number of rows
* @param c number of cols */
matrix::matrix(unsigned r, unsigned c)
- : inherited(TINFO_matrix), row(r), col(c)
+ : inherited(TINFO_matrix), row(r), col(c), m(r*c, _ex0)
{
- m.resize(r*c, _ex0);
+ setflag(status_flags::not_shareable);
}
// protected
/** Ctor from representation, for internal use only. */
matrix::matrix(unsigned r, unsigned c, const exvector & m2)
- : inherited(TINFO_matrix), row(r), col(c), m(m2) {}
+ : inherited(TINFO_matrix), row(r), col(c), m(m2)
+{
+ setflag(status_flags::not_shareable);
+}
/** Construct matrix from (flat) list of elements. If the list has fewer
* elements than the matrix, the remaining matrix elements are set to zero.
* If the list has more elements than the matrix, the excessive elements are
* thrown away. */
matrix::matrix(unsigned r, unsigned c, const lst & l)
- : inherited(TINFO_matrix), row(r), col(c)
+ : inherited(TINFO_matrix), row(r), col(c), m(r*c, _ex0)
{
- m.resize(r*c, _ex0);
+ setflag(status_flags::not_shareable);
- for (unsigned i=0; i<l.nops(); i++) {
- unsigned x = i % c;
- unsigned y = i / c;
+ size_t i = 0;
+ for (lst::const_iterator it = l.begin(); it != l.end(); ++it, ++i) {
+ size_t x = i % c;
+ size_t y = i / c;
if (y >= r)
break; // matrix smaller than list: throw away excessive elements
- m[y*c+x] = l.op(i);
+ m[y*c+x] = *it;
}
}
// archiving
//////////
-matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+matrix::matrix(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
+ setflag(status_flags::not_shareable);
+
if (!(n.find_unsigned("row", row)) || !(n.find_unsigned("col", col)))
throw (std::runtime_error("unknown matrix dimensions in archive"));
m.reserve(row * col);
// public
-void matrix::print(const print_context & c, unsigned level) const
+void matrix::print_elements(const print_context & c, const char *row_start, const char *row_end, const char *row_sep, const char *col_sep) const
{
- if (is_a<print_tree>(c)) {
-
- inherited::print(c, level);
+ for (unsigned ro=0; ro<row; ++ro) {
+ c.s << row_start;
+ for (unsigned co=0; co<col; ++co) {
+ m[ro*col+co].print(c);
+ if (co < col-1)
+ c.s << col_sep;
+ else
+ c.s << row_end;
+ }
+ if (ro < row-1)
+ c.s << row_sep;
+ }
+}
- } else {
+void matrix::do_print(const print_context & c, unsigned level) const
+{
+ c.s << "[";
+ print_elements(c, "[", "]", ",", ",");
+ c.s << "]";
+}
- c.s << "[";
- for (unsigned y=0; y<row-1; ++y) {
- c.s << "[";
- for (unsigned x=0; x<col-1; ++x) {
- m[y*col+x].print(c);
- c.s << ",";
- }
- m[col*(y+1)-1].print(c);
- c.s << "],";
- }
- c.s << "[";
- for (unsigned x=0; x<col-1; ++x) {
- m[(row-1)*col+x].print(c);
- c.s << ",";
- }
- m[row*col-1].print(c);
- c.s << "]]";
+void matrix::do_print_latex(const print_latex & c, unsigned level) const
+{
+ c.s << "\\left(\\begin{array}{" << std::string(col,'c') << "}";
+ print_elements(c, "", "", "\\\\", "&");
+ c.s << "\\end{array}\\right)";
+}
- }
+void matrix::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << '(';
+ print_elements(c, "[", "]", ",", ",");
+ c.s << ')';
}
/** nops is defined to be rows x columns. */
-unsigned matrix::nops() const
+size_t matrix::nops() const
{
- return row*col;
+ return static_cast<size_t>(row) * static_cast<size_t>(col);
}
/** returns matrix entry at position (i/col, i%col). */
-ex matrix::op(int i) const
+ex matrix::op(size_t i) const
{
+ GINAC_ASSERT(i<nops());
+
return m[i];
}
-/** returns matrix entry at position (i/col, i%col). */
-ex & matrix::let_op(int i)
+/** returns writable matrix entry at position (i/col, i%col). */
+ex & matrix::let_op(size_t i)
{
- GINAC_ASSERT(i>=0);
GINAC_ASSERT(i<nops());
+ ensure_if_modifiable();
return m[i];
}
m2[r*col+c] = m[r*col+c].eval(level);
return (new matrix(row, col, m2))->setflag(status_flags::dynallocated |
- status_flags::evaluated );
+ status_flags::evaluated);
}
-ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
+ex matrix::subs(const exmap & mp, unsigned options) const
{
exvector m2(row * col);
for (unsigned r=0; r<row; ++r)
for (unsigned c=0; c<col; ++c)
- m2[r*col+c] = m[r*col+c].subs(ls, lr, no_pattern);
+ m2[r*col+c] = m[r*col+c].subs(mp, options);
- return matrix(row, col, m2).basic::subs(ls, lr, no_pattern);
+ return matrix(row, col, m2).subs_one_level(mp, options);
}
// protected
GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
// Only add two matrices
- if (is_ex_of_type(other.op(0), matrix)) {
+ if (is_a<matrix>(other.op(0))) {
GINAC_ASSERT(other.nops() == 2 || other.nops() == 3);
const matrix &self_matrix = ex_to<matrix>(self.op(0));
GINAC_ASSERT(is_a<matrix>(self->op(0)));
// Only contract with other matrices
- if (!is_ex_of_type(other->op(0), matrix))
+ if (!is_a<matrix>(other->op(0)))
return false;
GINAC_ASSERT(other->nops() == 2 || other->nops() == 3);
if (col!=row)
throw (std::logic_error("matrix::pow(): matrix not square"));
- if (is_ex_exactly_of_type(expn, numeric)) {
+ if (is_exactly_a<numeric>(expn)) {
// Integer cases are computed by successive multiplication, using the
// obvious shortcut of storing temporaries, like A^4 == (A*A)*(A*A).
if (expn.info(info_flags::integer)) {
matrix C(row,col);
for (unsigned r=0; r<row; ++r)
C(r,r) = _ex1;
+ if (b.is_zero())
+ return C;
// This loop computes the representation of b in base 2 from right
// to left and multiplies the factors whenever needed. Note
// that this is not entirely optimal but close to optimal and
// "better" algorithms are much harder to implement. (See Knuth,
// TAoCP2, section "Evaluation of Powers" for a good discussion.)
- while (b!=1) {
+ while (b!=_num1) {
if (b.is_odd()) {
C = C.mul(A);
- b -= 1;
+ --b;
}
- b *= _num1_2; // b /= 2, still integer.
+ b /= _num2; // still integer.
A = A.mul(A);
}
return A.mul(C);
/** Transposed of an m x n matrix, producing a new n x m matrix object that
* represents the transposed. */
-matrix matrix::transpose(void) const
+matrix matrix::transpose() const
{
exvector trans(this->cols()*this->rows());
++acc;
c_zeros.push_back(uintpair(acc,c));
}
- sort(c_zeros.begin(),c_zeros.end());
+ std::sort(c_zeros.begin(),c_zeros.end());
std::vector<unsigned> pre_sort;
for (std::vector<uintpair>::const_iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
pre_sort.push_back(i->second);
*
* @return the sum of diagonal elements
* @exception logic_error (matrix not square) */
-ex matrix::trace(void) const
+ex matrix::trace() const
{
if (row != col)
throw (std::logic_error("matrix::trace(): matrix not square"));
* @return characteristic polynomial as new expression
* @exception logic_error (matrix not square)
* @see matrix::determinant() */
-ex matrix::charpoly(const symbol & lambda) const
+ex matrix::charpoly(const ex & lambda) const
{
if (row != col)
throw (std::logic_error("matrix::charpoly(): matrix not square"));
// trapped and we use Leverrier's algorithm which goes as row^3 for
// every coefficient. The expensive part is the matrix multiplication.
if (numeric_flag) {
+
matrix B(*this);
ex c = B.trace();
- ex poly = power(lambda,row)-c*power(lambda,row-1);
+ ex poly = power(lambda, row) - c*power(lambda, row-1);
for (unsigned i=1; i<row; ++i) {
for (unsigned j=0; j<row; ++j)
B.m[j*col+j] -= c;
B = this->mul(B);
- c = B.trace()/ex(i+1);
- poly -= c*power(lambda,row-i-1);
+ c = B.trace() / ex(i+1);
+ poly -= c*power(lambda, row-i-1);
}
if (row%2)
return -poly;
else
return poly;
- }
+
+ } else {
- matrix M(*this);
- for (unsigned r=0; r<col; ++r)
- M.m[r*col+r] -= lambda;
+ matrix M(*this);
+ for (unsigned r=0; r<col; ++r)
+ M.m[r*col+r] -= lambda;
- return M.determinant().collect(lambda);
+ return M.determinant().collect(lambda);
+ }
}
* @return the inverted matrix
* @exception logic_error (matrix not square)
* @exception runtime_error (singular matrix) */
-matrix matrix::inverse(void) const
+matrix matrix::inverse() const
{
if (row != col)
throw (std::logic_error("matrix::inverse(): matrix not square"));
*
* @return the determinant as a new expression (in expanded form)
* @see matrix::determinant() */
-ex matrix::determinant_minor(void) const
+ex matrix::determinant_minor() const
{
// for small matrices the algorithm does not make any sense:
const unsigned n = this->cols();
//
// Bareiss (fraction-free) elimination in addition divides that element
// by m[k-1](k-1,k-1) for k>1, where it can be shown by means of the
- // Sylvester determinant that this really divides m[k+1](r,c).
+ // Sylvester identity that this really divides m[k+1](r,c).
//
// We also allow rational functions where the original prove still holds.
// However, we must care for numerator and denominator separately and
tmp_n_it = tmp_n.m.begin();
tmp_d_it = tmp_d.m.begin();
while (it != itend)
- *it++ = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl);
+ *it++ = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl, subs_options::no_pattern);
return sign;
}
++k;
} else {
// search largest element in column co beginning at row ro
- GINAC_ASSERT(is_a<numeric>(this->m[k*col+co]));
+ GINAC_ASSERT(is_exactly_a<numeric>(this->m[k*col+co]));
unsigned kmax = k+1;
numeric mmax = abs(ex_to<numeric>(m[kmax*col+co]));
while (kmax<row) {
- GINAC_ASSERT(is_a<numeric>(this->m[kmax*col+co]));
+ GINAC_ASSERT(is_exactly_a<numeric>(this->m[kmax*col+co]));
numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
if (abs(tmp) > mmax) {
mmax = tmp;
ex lst_to_matrix(const lst & l)
{
+ lst::const_iterator itr, itc;
+
// Find number of rows and columns
- unsigned rows = l.nops(), cols = 0, i, j;
- for (i=0; i<rows; i++)
- if (l.op(i).nops() > cols)
- cols = l.op(i).nops();
+ size_t rows = l.nops(), cols = 0;
+ for (itr = l.begin(); itr != l.end(); ++itr) {
+ if (!is_a<lst>(*itr))
+ throw (std::invalid_argument("lst_to_matrix: argument must be a list of lists"));
+ if (itr->nops() > cols)
+ cols = itr->nops();
+ }
// Allocate and fill matrix
- matrix &m = *new matrix(rows, cols);
- m.setflag(status_flags::dynallocated);
- for (i=0; i<rows; i++)
- for (j=0; j<cols; j++)
- if (l.op(i).nops() > j)
- m(i, j) = l.op(i).op(j);
- else
- m(i, j) = _ex0;
- return m;
+ matrix &M = *new matrix(rows, cols);
+ M.setflag(status_flags::dynallocated);
+
+ unsigned i;
+ for (itr = l.begin(), i = 0; itr != l.end(); ++itr, ++i) {
+ unsigned j;
+ for (itc = ex_to<lst>(*itr).begin(), j = 0; itc != ex_to<lst>(*itr).end(); ++itc, ++j)
+ M(i, j) = *itc;
+ }
+
+ return M;
}
ex diag_matrix(const lst & l)
{
- unsigned dim = l.nops();
+ lst::const_iterator it;
+ size_t dim = l.nops();
+
+ // Allocate and fill matrix
+ matrix &M = *new matrix(dim, dim);
+ M.setflag(status_flags::dynallocated);
+
+ unsigned i;
+ for (it = l.begin(), i = 0; it != l.end(); ++it, ++i)
+ M(i, i) = *it;
+
+ return M;
+}
- matrix &m = *new matrix(dim, dim);
- m.setflag(status_flags::dynallocated);
- for (unsigned i=0; i<dim; i++)
- m(i, i) = l.op(i);
+ex unit_matrix(unsigned r, unsigned c)
+{
+ matrix &Id = *new matrix(r, c);
+ Id.setflag(status_flags::dynallocated);
+ for (unsigned i=0; i<r && i<c; i++)
+ Id(i,i) = _ex1;
+
+ return Id;
+}
+
+ex symbolic_matrix(unsigned r, unsigned c, const std::string & base_name, const std::string & tex_base_name)
+{
+ matrix &M = *new matrix(r, c);
+ M.setflag(status_flags::dynallocated | status_flags::evaluated);
+
+ bool long_format = (r > 10 || c > 10);
+ bool single_row = (r == 1 || c == 1);
+
+ for (unsigned i=0; i<r; i++) {
+ for (unsigned j=0; j<c; j++) {
+ std::ostringstream s1, s2;
+ s1 << base_name;
+ s2 << tex_base_name << "_{";
+ if (single_row) {
+ if (c == 1) {
+ s1 << i;
+ s2 << i << '}';
+ } else {
+ s1 << j;
+ s2 << j << '}';
+ }
+ } else {
+ if (long_format) {
+ s1 << '_' << i << '_' << j;
+ s2 << i << ';' << j << "}";
+ } else {
+ s1 << i << j;
+ s2 << i << j << '}';
+ }
+ }
+ M(i, j) = symbol(s1.str(), s2.str());
+ }
+ }
- return m;
+ return M;
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff