* Implementation of symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2000 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 "matrix.h"
-#include "archive.h"
#include "numeric.h"
#include "lst.h"
-#include "utils.h"
-#include "debugmsg.h"
+#include "idx.h"
+#include "indexed.h"
+#include "add.h"
#include "power.h"
#include "symbol.h"
+#include "operators.h"
#include "normal.h"
+#include "archive.h"
+#include "utils.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_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 constructor, destructor, copy constructor, assignment operator
-// and helpers:
+// default constructor
//////////
-// public
-
/** 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)
{
- debugmsg("matrix default constructor",LOGLEVEL_CONSTRUCT);
- m.push_back(_ex0());
-}
-
-matrix::~matrix()
-{
- debugmsg("matrix destructor",LOGLEVEL_DESTRUCT);
- destroy(false);
-}
-
-matrix::matrix(const matrix & other)
-{
- debugmsg("matrix copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const matrix & matrix::operator=(const matrix & other)
-{
- debugmsg("matrix operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(true);
- copy(other);
- }
- return *this;
-}
-
-// protected
-
-void matrix::copy(const matrix & other)
-{
- inherited::copy(other);
- row = other.row;
- col = other.col;
- m = other.m; // STL's vector copying invoked here
-}
-
-void matrix::destroy(bool call_parent)
-{
- if (call_parent) inherited::destroy(call_parent);
+ setflag(status_flags::not_shareable);
}
//////////
* @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)
{
- debugmsg("matrix constructor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
- m.resize(r*c, _ex0());
+ setflag(status_flags::not_shareable);
}
// protected
matrix::matrix(unsigned r, unsigned c, const exvector & m2)
: inherited(TINFO_matrix), row(r), col(c), m(m2)
{
- debugmsg("matrix constructor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+ 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), m(r*c, _ex0)
+{
+ setflag(status_flags::not_shareable);
+
+ 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] = *it;
+ }
}
//////////
// archiving
//////////
-/** Construct object from archive_node. */
-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)
{
- debugmsg("matrix constructor from archive_node", LOGLEVEL_CONSTRUCT);
+ 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);
}
}
-/** Unarchive the object. */
-ex matrix::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new matrix(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
void matrix::archive(archive_node &n) const
{
inherited::archive(n);
}
}
+DEFAULT_UNARCHIVE(matrix)
+
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
// public
-basic * matrix::duplicate() 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
{
- debugmsg("matrix duplicate",LOGLEVEL_DUPLICATE);
- return new matrix(*this);
+ 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;
+ }
}
-void matrix::print(std::ostream & os, unsigned upper_precedence) const
+void matrix::do_print(const print_context & c, unsigned level) const
{
- debugmsg("matrix print",LOGLEVEL_PRINT);
- os << "[[ ";
- for (unsigned r=0; r<row-1; ++r) {
- os << "[[";
- for (unsigned c=0; c<col-1; ++c)
- os << m[r*col+c] << ",";
- os << m[col*(r+1)-1] << "]], ";
- }
- os << "[[";
- for (unsigned c=0; c<col-1; ++c)
- os << m[(row-1)*col+c] << ",";
- os << m[row*col-1] << "]] ]]";
+ c.s << "[";
+ print_elements(c, "[", "]", ",", ",");
+ c.s << "]";
}
-void matrix::printraw(std::ostream & os) const
+void matrix::do_print_latex(const print_latex & c, unsigned level) const
{
- debugmsg("matrix printraw",LOGLEVEL_PRINT);
- os << "matrix(" << row << "," << col <<",";
- for (unsigned r=0; r<row-1; ++r) {
- os << "(";
- for (unsigned c=0; c<col-1; ++c)
- os << m[r*col+c] << ",";
- os << m[col*(r-1)-1] << "),";
- }
- os << "(";
- for (unsigned c=0; c<col-1; ++c)
- os << m[(row-1)*col+c] << ",";
- os << m[row*col-1] << "))";
+ c.s << "\\left(\\begin{array}{" << std::string(col,'c') << "}";
+ print_elements(c, "", "", "\\\\", "&");
+ c.s << "\\end{array}\\right)";
}
-/** nops is defined to be rows x columns. */
-unsigned matrix::nops() const
+void matrix::do_print_python_repr(const print_python_repr & c, unsigned level) const
{
- return row*col;
+ c.s << class_name() << '(';
+ print_elements(c, "[", "]", ",", ",");
+ c.s << ')';
}
-/** returns matrix entry at position (i/col, i%col). */
-ex matrix::op(int i) const
+/** nops is defined to be rows x columns. */
+size_t matrix::nops() const
{
- return m[i];
+ return static_cast<size_t>(row) * static_cast<size_t>(col);
}
/** returns matrix entry at position (i/col, i%col). */
-ex & matrix::let_op(int i)
+ex matrix::op(size_t i) const
{
- GINAC_ASSERT(i>=0);
GINAC_ASSERT(i<nops());
return m[i];
}
-/** expands the elements of a matrix entry by entry. */
-ex matrix::expand(unsigned options) const
-{
- exvector tmp(row*col);
- for (unsigned i=0; i<row*col; ++i)
- tmp[i] = m[i].expand(options);
-
- return matrix(row, col, tmp);
-}
-
-/** Search ocurrences. A matrix 'has' an expression if it is the expression
- * itself or one of the elements 'has' it. */
-bool matrix::has(const ex & other) const
+/** returns writable matrix entry at position (i/col, i%col). */
+ex & matrix::let_op(size_t i)
{
- GINAC_ASSERT(other.bp!=0);
-
- // tautology: it is the expression itself
- if (is_equal(*other.bp)) return true;
-
- // search all the elements
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r)
- if ((*r).has(other)) return true;
+ GINAC_ASSERT(i<nops());
- return false;
+ ensure_if_modifiable();
+ return m[i];
}
-/** evaluate matrix entry by entry. */
+/** Evaluate matrix entry by entry. */
ex matrix::eval(int level) const
{
- debugmsg("matrix eval",LOGLEVEL_MEMBER_FUNCTION);
-
// check if we have to do anything at all
if ((level==1)&&(flags & status_flags::evaluated))
return *this;
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);
}
-/** evaluate matrix numerically entry by entry. */
-ex matrix::evalf(int level) const
+ex matrix::subs(const exmap & mp, unsigned options) const
{
- debugmsg("matrix evalf",LOGLEVEL_MEMBER_FUNCTION);
-
- // check if we have to do anything at all
- if (level==1)
- return *this;
-
- // emergency break
- if (level == -max_recursion_level) {
- throw (std::runtime_error("matrix::evalf(): recursion limit exceeded"));
- }
-
- // evalf() entry by entry
- exvector m2(row*col);
- --level;
+ 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].evalf(level);
-
- return matrix(row, col, m2);
+ m2[r*col+c] = m[r*col+c].subs(mp, options);
+
+ return matrix(row, col, m2).subs_one_level(mp, options);
}
// protected
int matrix::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_exactly_of_type(other, matrix));
- const matrix & o = static_cast<matrix &>(const_cast<basic &>(other));
+ GINAC_ASSERT(is_exactly_a<matrix>(other));
+ const matrix &o = static_cast<const matrix &>(other);
// compare number of rows
if (row != o.rows())
return 0;
}
+bool matrix::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_exactly_a<matrix>(other));
+ const matrix & o = static_cast<const matrix &>(other);
+
+ // The number of rows and columns must be the same. This is necessary to
+ // prevent a 2x3 matrix from matching a 3x2 one.
+ return row == o.rows() && col == o.cols();
+}
+
+/** Automatic symbolic evaluation of an indexed matrix. */
+ex matrix::eval_indexed(const basic & i) const
+{
+ GINAC_ASSERT(is_a<indexed>(i));
+ GINAC_ASSERT(is_a<matrix>(i.op(0)));
+
+ bool all_indices_unsigned = static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint);
+
+ // Check indices
+ if (i.nops() == 2) {
+
+ // One index, must be one-dimensional vector
+ if (row != 1 && col != 1)
+ throw (std::runtime_error("matrix::eval_indexed(): vector must have exactly 1 index"));
+
+ const idx & i1 = ex_to<idx>(i.op(1));
+
+ if (col == 1) {
+
+ // Column vector
+ if (!i1.get_dim().is_equal(row))
+ throw (std::runtime_error("matrix::eval_indexed(): dimension of index must match number of vector elements"));
+
+ // Index numeric -> return vector element
+ if (all_indices_unsigned) {
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
+ if (n1 >= row)
+ throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
+ return (*this)(n1, 0);
+ }
+
+ } else {
+
+ // Row vector
+ if (!i1.get_dim().is_equal(col))
+ throw (std::runtime_error("matrix::eval_indexed(): dimension of index must match number of vector elements"));
+
+ // Index numeric -> return vector element
+ if (all_indices_unsigned) {
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int();
+ if (n1 >= col)
+ throw (std::runtime_error("matrix::eval_indexed(): value of index exceeds number of vector elements"));
+ return (*this)(0, n1);
+ }
+ }
+
+ } else if (i.nops() == 3) {
+
+ // Two indices
+ const idx & i1 = ex_to<idx>(i.op(1));
+ const idx & i2 = ex_to<idx>(i.op(2));
+
+ if (!i1.get_dim().is_equal(row))
+ throw (std::runtime_error("matrix::eval_indexed(): dimension of first index must match number of rows"));
+ if (!i2.get_dim().is_equal(col))
+ throw (std::runtime_error("matrix::eval_indexed(): dimension of second index must match number of columns"));
+
+ // Pair of dummy indices -> compute trace
+ if (is_dummy_pair(i1, i2))
+ return trace();
+
+ // Both indices numeric -> return matrix element
+ if (all_indices_unsigned) {
+ unsigned n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
+ if (n1 >= row)
+ throw (std::runtime_error("matrix::eval_indexed(): value of first index exceeds number of rows"));
+ if (n2 >= col)
+ throw (std::runtime_error("matrix::eval_indexed(): value of second index exceeds number of columns"));
+ return (*this)(n1, n2);
+ }
+
+ } else
+ throw (std::runtime_error("matrix::eval_indexed(): matrix must have exactly 2 indices"));
+
+ return i.hold();
+}
+
+/** Sum of two indexed matrices. */
+ex matrix::add_indexed(const ex & self, const ex & other) const
+{
+ GINAC_ASSERT(is_a<indexed>(self));
+ GINAC_ASSERT(is_a<matrix>(self.op(0)));
+ GINAC_ASSERT(is_a<indexed>(other));
+ GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
+
+ // Only add two matrices
+ 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));
+ const matrix &other_matrix = ex_to<matrix>(other.op(0));
+
+ if (self.nops() == 2 && other.nops() == 2) { // vector + vector
+
+ if (self_matrix.row == other_matrix.row)
+ return indexed(self_matrix.add(other_matrix), self.op(1));
+ else if (self_matrix.row == other_matrix.col)
+ return indexed(self_matrix.add(other_matrix.transpose()), self.op(1));
+
+ } else if (self.nops() == 3 && other.nops() == 3) { // matrix + matrix
+
+ if (self.op(1).is_equal(other.op(1)) && self.op(2).is_equal(other.op(2)))
+ return indexed(self_matrix.add(other_matrix), self.op(1), self.op(2));
+ else if (self.op(1).is_equal(other.op(2)) && self.op(2).is_equal(other.op(1)))
+ return indexed(self_matrix.add(other_matrix.transpose()), self.op(1), self.op(2));
+
+ }
+ }
+
+ // Don't know what to do, return unevaluated sum
+ return self + other;
+}
+
+/** Product of an indexed matrix with a number. */
+ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
+{
+ GINAC_ASSERT(is_a<indexed>(self));
+ GINAC_ASSERT(is_a<matrix>(self.op(0)));
+ GINAC_ASSERT(self.nops() == 2 || self.nops() == 3);
+
+ const matrix &self_matrix = ex_to<matrix>(self.op(0));
+
+ if (self.nops() == 2)
+ return indexed(self_matrix.mul(other), self.op(1));
+ else // self.nops() == 3
+ return indexed(self_matrix.mul(other), self.op(1), self.op(2));
+}
+
+/** Contraction of an indexed matrix with something else. */
+bool matrix::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 2 || self->nops() == 3);
+ GINAC_ASSERT(is_a<matrix>(self->op(0)));
+
+ // Only contract with other matrices
+ if (!is_a<matrix>(other->op(0)))
+ return false;
+
+ GINAC_ASSERT(other->nops() == 2 || other->nops() == 3);
+
+ const matrix &self_matrix = ex_to<matrix>(self->op(0));
+ const matrix &other_matrix = ex_to<matrix>(other->op(0));
+
+ if (self->nops() == 2) {
+
+ if (other->nops() == 2) { // vector * vector (scalar product)
+
+ if (self_matrix.col == 1) {
+ if (other_matrix.col == 1) {
+ // Column vector * column vector, transpose first vector
+ *self = self_matrix.transpose().mul(other_matrix)(0, 0);
+ } else {
+ // Column vector * row vector, swap factors
+ *self = other_matrix.mul(self_matrix)(0, 0);
+ }
+ } else {
+ if (other_matrix.col == 1) {
+ // Row vector * column vector, perfect
+ *self = self_matrix.mul(other_matrix)(0, 0);
+ } else {
+ // Row vector * row vector, transpose second vector
+ *self = self_matrix.mul(other_matrix.transpose())(0, 0);
+ }
+ }
+ *other = _ex1;
+ return true;
+
+ } else { // vector * matrix
+
+ // B_i * A_ij = (B*A)_j (B is row vector)
+ if (is_dummy_pair(self->op(1), other->op(1))) {
+ if (self_matrix.row == 1)
+ *self = indexed(self_matrix.mul(other_matrix), other->op(2));
+ else
+ *self = indexed(self_matrix.transpose().mul(other_matrix), other->op(2));
+ *other = _ex1;
+ return true;
+ }
+
+ // B_j * A_ij = (A*B)_i (B is column vector)
+ if (is_dummy_pair(self->op(1), other->op(2))) {
+ if (self_matrix.col == 1)
+ *self = indexed(other_matrix.mul(self_matrix), other->op(1));
+ else
+ *self = indexed(other_matrix.mul(self_matrix.transpose()), other->op(1));
+ *other = _ex1;
+ return true;
+ }
+ }
+
+ } else if (other->nops() == 3) { // matrix * matrix
+
+ // A_ij * B_jk = (A*B)_ik
+ if (is_dummy_pair(self->op(2), other->op(1))) {
+ *self = indexed(self_matrix.mul(other_matrix), self->op(1), other->op(2));
+ *other = _ex1;
+ return true;
+ }
+
+ // A_ij * B_kj = (A*Btrans)_ik
+ if (is_dummy_pair(self->op(2), other->op(2))) {
+ *self = indexed(self_matrix.mul(other_matrix.transpose()), self->op(1), other->op(1));
+ *other = _ex1;
+ return true;
+ }
+
+ // A_ji * B_jk = (Atrans*B)_ik
+ if (is_dummy_pair(self->op(1), other->op(1))) {
+ *self = indexed(self_matrix.transpose().mul(other_matrix), self->op(2), other->op(2));
+ *other = _ex1;
+ return true;
+ }
+
+ // A_ji * B_kj = (B*A)_ki
+ if (is_dummy_pair(self->op(1), other->op(2))) {
+ *self = indexed(other_matrix.mul(self_matrix), other->op(1), self->op(2));
+ *other = _ex1;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+
//////////
// non-virtual functions in this class
//////////
matrix matrix::add(const matrix & other) const
{
if (col != other.col || row != other.row)
- throw (std::logic_error("matrix::add(): incompatible matrices"));
+ throw std::logic_error("matrix::add(): incompatible matrices");
exvector sum(this->m);
- exvector::iterator i;
- exvector::const_iterator ci;
- for (i=sum.begin(), ci=other.m.begin(); i!=sum.end(); ++i, ++ci)
- (*i) += (*ci);
+ exvector::iterator i = sum.begin(), end = sum.end();
+ exvector::const_iterator ci = other.m.begin();
+ while (i != end)
+ *i++ += *ci++;
return matrix(row,col,sum);
}
matrix matrix::sub(const matrix & other) const
{
if (col != other.col || row != other.row)
- throw (std::logic_error("matrix::sub(): incompatible matrices"));
+ throw std::logic_error("matrix::sub(): incompatible matrices");
exvector dif(this->m);
- exvector::iterator i;
- exvector::const_iterator ci;
- for (i=dif.begin(), ci=other.m.begin(); i!=dif.end(); ++i, ++ci)
- (*i) -= (*ci);
+ exvector::iterator i = dif.begin(), end = dif.end();
+ exvector::const_iterator ci = other.m.begin();
+ while (i != end)
+ *i++ -= *ci++;
return matrix(row,col,dif);
}
matrix matrix::mul(const matrix & other) const
{
if (this->cols() != other.rows())
- throw (std::logic_error("matrix::mul(): incompatible matrices"));
+ throw std::logic_error("matrix::mul(): incompatible matrices");
exvector prod(this->rows()*other.cols());
}
-/** operator() to access elements.
+/** Product of matrix and scalar. */
+matrix matrix::mul(const numeric & other) const
+{
+ exvector prod(row * col);
+
+ for (unsigned r=0; r<row; ++r)
+ for (unsigned c=0; c<col; ++c)
+ prod[r*col+c] = m[r*col+c] * other;
+
+ return matrix(row, col, prod);
+}
+
+
+/** Product of matrix and scalar expression. */
+matrix matrix::mul_scalar(const ex & other) const
+{
+ if (other.return_type() != return_types::commutative)
+ throw std::runtime_error("matrix::mul_scalar(): non-commutative scalar");
+
+ exvector prod(row * col);
+
+ for (unsigned r=0; r<row; ++r)
+ for (unsigned c=0; c<col; ++c)
+ prod[r*col+c] = m[r*col+c] * other;
+
+ return matrix(row, col, prod);
+}
+
+
+/** Power of a matrix. Currently handles integer exponents only. */
+matrix matrix::pow(const ex & expn) const
+{
+ if (col!=row)
+ throw (std::logic_error("matrix::pow(): matrix not square"));
+
+ 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)) {
+ numeric b = ex_to<numeric>(expn);
+ matrix A(row,col);
+ if (expn.info(info_flags::negative)) {
+ b *= -1;
+ A = this->inverse();
+ } else {
+ A = *this;
+ }
+ 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!=_num1) {
+ if (b.is_odd()) {
+ C = C.mul(A);
+ --b;
+ }
+ b /= _num2; // still integer.
+ A = A.mul(A);
+ }
+ return A.mul(C);
+ }
+ }
+ throw (std::runtime_error("matrix::pow(): don't know how to handle exponent"));
+}
+
+
+/** operator() to access elements for reading.
*
* @param ro row of element
* @param co column of element
}
-/** Set individual elements manually.
+/** operator() to access elements for writing.
*
+ * @param ro row of element
+ * @param co column of element
* @exception range_error (index out of range) */
-matrix & matrix::set(unsigned ro, unsigned co, ex value)
+ex & matrix::operator() (unsigned ro, unsigned co)
{
if (ro>=row || co>=col)
- throw (std::range_error("matrix::set(): index out of range"));
-
+ throw (std::range_error("matrix::operator(): index out of range"));
+
ensure_if_modifiable();
- m[ro*col+co] = value;
- return *this;
+ return m[ro*col+co];
}
/** 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());
return matrix(this->cols(),this->rows(),trans);
}
-
/** Determinant of square matrix. This routine doesn't actually calculate the
* determinant, it only implements some heuristics about which algorithm to
* run. If all the elements of the matrix are elements of an integral domain
bool numeric_flag = true;
bool normal_flag = false;
unsigned sparse_count = 0; // counts non-zero elements
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
- lst srl; // symbol replacement list
- ex rtest = (*r).to_rational(srl);
+ exvector::const_iterator r = m.begin(), rend = m.end();
+ while (r != rend) {
+ exmap srl; // symbol replacement list
+ ex rtest = r->to_rational(srl);
if (!rtest.is_zero())
++sparse_count;
if (!rtest.info(info_flags::numeric))
if (!rtest.info(info_flags::crational_polynomial) &&
rtest.info(info_flags::rational_function))
normal_flag = true;
+ ++r;
}
// Here is the heuristics in case this routine has to decide:
int sign;
sign = tmp.division_free_elimination(true);
if (sign==0)
- return _ex0();
+ return _ex0;
ex det = tmp.m[row*col-1];
// factor out accumulated bogus slag
for (unsigned d=0; d<row-2; ++d)
default: {
// This is the minor expansion scheme. We always develop such
// that the smallest minors (i.e, the trivial 1x1 ones) are on the
- // rightmost column. For this to be efficient it turns out that
- // the emptiest columns (i.e. the ones with most zeros) should be
- // the ones on the right hand side. Therefore we presort the
- // columns of the matrix:
+ // rightmost column. For this to be efficient, empirical tests
+ // have shown that the emptiest columns (i.e. the ones with most
+ // zeros) should be the ones on the right hand side -- although
+ // this might seem counter-intuitive (and in contradiction to some
+ // literature like the FORM manual). Please go ahead and test it
+ // if you don't believe me! Therefore we presort the columns of
+ // the matrix:
typedef std::pair<unsigned,unsigned> uintpair;
std::vector<uintpair> c_zeros; // number of zeros in column
for (unsigned c=0; c<col; ++c) {
++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>::iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
+ for (std::vector<uintpair>::const_iterator i=c_zeros.begin(); i!=c_zeros.end(); ++i)
pre_sort.push_back(i->second);
- int sign = permutation_sign(pre_sort);
+ std::vector<unsigned> pre_sort_test(pre_sort); // permutation_sign() modifies the vector so we make a copy here
+ int sign = permutation_sign(pre_sort_test.begin(), pre_sort_test.end());
exvector result(row*col); // represents sorted matrix
unsigned c = 0;
- for (std::vector<unsigned>::iterator i=pre_sort.begin();
+ for (std::vector<unsigned>::const_iterator i=pre_sort.begin();
i!=pre_sort.end();
++i,++c) {
for (unsigned r=0; r<row; ++r)
*
* @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"));
bool numeric_flag = true;
- for (exvector::const_iterator r=m.begin(); r!=m.end(); ++r) {
- if (!(*r).info(info_flags::numeric)) {
+ exvector::const_iterator r = m.begin(), rend = m.end();
+ while (r!=rend && numeric_flag==true) {
+ if (!r->info(info_flags::numeric))
numeric_flag = false;
- }
+ ++r;
}
// The pure numeric case is traditionally rather common. Hence, it is
// 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"));
- // NOTE: the Gauss-Jordan elimination used here can in principle be
- // replaced this by two clever calls to gauss_elimination() and some to
- // transpose(). Wouldn't be more efficient (maybe less?), just more
- // orthogonal.
- matrix tmp(row,col);
- // set tmp to the unit matrix
- for (unsigned i=0; i<col; ++i)
- tmp.m[i*col+i] = _ex1();
+ // This routine actually doesn't do anything fancy at all. We compute the
+ // inverse of the matrix A by solving the system A * A^{-1} == Id.
- // create a copy of this matrix
- matrix cpy(*this);
- for (unsigned r1=0; r1<row; ++r1) {
- int indx = cpy.pivot(r1, r1);
- if (indx == -1) {
+ // First populate the identity matrix supposed to become the right hand side.
+ matrix identity(row,col);
+ for (unsigned i=0; i<row; ++i)
+ identity(i,i) = _ex1;
+
+ // Populate a dummy matrix of variables, just because of compatibility with
+ // matrix::solve() which wants this (for compatibility with under-determined
+ // systems of equations).
+ matrix vars(row,col);
+ for (unsigned r=0; r<row; ++r)
+ for (unsigned c=0; c<col; ++c)
+ vars(r,c) = symbol();
+
+ matrix sol(row,col);
+ try {
+ sol = this->solve(vars,identity);
+ } catch (const std::runtime_error & e) {
+ if (e.what()==std::string("matrix::solve(): inconsistent linear system"))
throw (std::runtime_error("matrix::inverse(): singular matrix"));
- }
- if (indx != 0) { // swap rows r and indx of matrix tmp
- for (unsigned i=0; i<col; ++i)
- tmp.m[r1*col+i].swap(tmp.m[indx*col+i]);
- }
- ex a1 = cpy.m[r1*col+r1];
- for (unsigned c=0; c<col; ++c) {
- cpy.m[r1*col+c] /= a1;
- tmp.m[r1*col+c] /= a1;
- }
- for (unsigned r2=0; r2<row; ++r2) {
- if (r2 != r1) {
- ex a2 = cpy.m[r2*col+r1];
- for (unsigned c=0; c<col; ++c) {
- cpy.m[r2*col+c] -= a2 * cpy.m[r1*col+c];
- if (!cpy.m[r2*col+c].info(info_flags::numeric))
- cpy.m[r2*col+c] = cpy.m[r2*col+c].normal();
- tmp.m[r2*col+c] -= a2 * tmp.m[r1*col+c];
- if (!tmp.m[r2*col+c].info(info_flags::numeric))
- tmp.m[r2*col+c] = tmp.m[r2*col+c].normal();
- }
- }
- }
+ else
+ throw;
}
-
- return tmp;
+ return sol;
}
*
* @param vars n x p matrix, all elements must be symbols
* @param rhs m x p matrix
+ * @param algo selects the solving algorithm
* @return n x p solution matrix
* @exception logic_error (incompatible matrices)
* @exception invalid_argument (1st argument must be matrix of symbols)
// Gather some statistical information about the augmented matrix:
bool numeric_flag = true;
- for (exvector::const_iterator r=aug.m.begin(); r!=aug.m.end(); ++r) {
- if (!(*r).info(info_flags::numeric))
+ exvector::const_iterator r = aug.m.begin(), rend = aug.m.end();
+ while (r!=rend && numeric_flag==true) {
+ if (!r->info(info_flags::numeric))
numeric_flag = false;
+ ++r;
}
// Here is the heuristics in case this routine has to decide:
switch(algo) {
case solve_algo::gauss:
aug.gauss_elimination();
+ break;
case solve_algo::divfree:
aug.division_free_elimination();
+ break;
case solve_algo::bareiss:
default:
aug.fraction_free_elimination();
// assign solutions for vars between fnz+1 and
// last_assigned_sol-1: free parameters
for (unsigned c=fnz; c<last_assigned_sol-1; ++c)
- sol.set(c,co,vars.m[c*p+co]);
+ sol(c,co) = vars.m[c*p+co];
ex e = aug.m[r*(n+p)+n+co];
for (unsigned c=fnz; c<n; ++c)
e -= aug.m[r*(n+p)+c]*sol.m[c*p+co];
- sol.set(fnz-1,co,
- (e/(aug.m[r*(n+p)+(fnz-1)])).normal());
+ sol(fnz-1,co) = (e/(aug.m[r*(n+p)+(fnz-1)])).normal();
last_assigned_sol = fnz;
}
}
// assign solutions for vars between 1 and
// last_assigned_sol-1: free parameters
for (unsigned ro=0; ro<last_assigned_sol-1; ++ro)
- sol.set(ro,co,vars(ro,co));
+ sol(ro,co) = vars(ro,co);
}
return sol;
*
* @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();
// for (unsigned r=0; r<minorM.rows(); ++r) {
// for (unsigned c=0; c<minorM.cols(); ++c) {
// if (r<r1)
- // minorM.set(r,c,m[r*col+c+1]);
+ // minorM(r,c) = m[r*col+c+1];
// else
- // minorM.set(r,c,m[(r+1)*col+c+1]);
+ // minorM(r,c) = m[(r+1)*col+c+1];
// }
// }
// // recurse down and care for sign:
Pkey.push_back(i);
unsigned fc = 0; // controls logic for our strange flipper counter
do {
- det = _ex0();
+ det = _ex0;
for (unsigned r=0; r<n-c; ++r) {
// maybe there is nothing to do?
if (m[Pkey[r]*n+c].is_zero())
if (Pkey[fc-1]<fc+c)
break;
}
- if (fc<n-c)
+ if (fc<n-c && fc>0)
for (unsigned j=fc; j<n-c; ++j)
Pkey[j] = Pkey[j-1]+1;
} while(fc);
if (indx > 0)
sign = -sign;
for (unsigned r2=r0+1; r2<m; ++r2) {
- ex piv = this->m[r2*n+r1] / this->m[r0*n+r1];
- for (unsigned c=r1+1; c<n; ++c) {
- this->m[r2*n+c] -= piv * this->m[r0*n+c];
- if (!this->m[r2*n+c].info(info_flags::numeric))
- this->m[r2*n+c] = this->m[r2*n+c].normal();
+ if (!this->m[r2*n+r1].is_zero()) {
+ // yes, there is something to do in this row
+ ex piv = this->m[r2*n+r1] / this->m[r0*n+r1];
+ for (unsigned c=r1+1; c<n; ++c) {
+ this->m[r2*n+c] -= piv * this->m[r0*n+c];
+ if (!this->m[r2*n+c].info(info_flags::numeric))
+ this->m[r2*n+c] = this->m[r2*n+c].normal();
+ }
}
// fill up left hand side with zeros
for (unsigned c=0; c<=r1; ++c)
- this->m[r2*n+c] = _ex0();
+ this->m[r2*n+c] = _ex0;
}
if (det) {
// save space by deleting no longer needed elements
for (unsigned c=r0+1; c<n; ++c)
- this->m[r0*n+c] = _ex0();
+ this->m[r0*n+c] = _ex0;
}
++r0;
}
this->m[r2*n+c] = (this->m[r0*n+r1]*this->m[r2*n+c] - this->m[r2*n+r1]*this->m[r0*n+c]).expand();
// fill up left hand side with zeros
for (unsigned c=0; c<=r1; ++c)
- this->m[r2*n+c] = _ex0();
+ this->m[r2*n+c] = _ex0;
}
if (det) {
// save space by deleting no longer needed elements
for (unsigned c=r0+1; c<n; ++c)
- this->m[r0*n+c] = _ex0();
+ this->m[r0*n+c] = _ex0;
}
++r0;
}
//
// 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
// makes things more complicated than they need to be.
matrix tmp_n(*this);
matrix tmp_d(m,n); // for denominators, if needed
- lst srl; // symbol replacement list
- exvector::iterator it = this->m.begin();
- exvector::iterator tmp_n_it = tmp_n.m.begin();
- exvector::iterator tmp_d_it = tmp_d.m.begin();
- for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it) {
- (*tmp_n_it) = (*it).normal().to_rational(srl);
- (*tmp_d_it) = (*tmp_n_it).denom();
- (*tmp_n_it) = (*tmp_n_it).numer();
+ exmap srl; // symbol replacement list
+ exvector::const_iterator cit = this->m.begin(), citend = this->m.end();
+ exvector::iterator tmp_n_it = tmp_n.m.begin(), tmp_d_it = tmp_d.m.begin();
+ while (cit != citend) {
+ ex nd = cit->normal().to_rational(srl).numer_denom();
+ ++cit;
+ *tmp_n_it++ = nd.op(0);
+ *tmp_d_it++ = nd.op(1);
}
unsigned r0 = 0;
}
// fill up left hand side with zeros
for (unsigned c=0; c<=r1; ++c)
- tmp_n.m[r2*n+c] = _ex0();
+ tmp_n.m[r2*n+c] = _ex0;
}
if ((r1<n-1)&&(r0<m-1)) {
// compute next iteration's divisor
if (det) {
// save space by deleting no longer needed elements
for (unsigned c=0; c<n; ++c) {
- tmp_n.m[r0*n+c] = _ex0();
- tmp_d.m[r0*n+c] = _ex1();
+ tmp_n.m[r0*n+c] = _ex0;
+ tmp_d.m[r0*n+c] = _ex1;
}
}
}
}
}
// repopulate *this matrix:
- it = this->m.begin();
+ exvector::iterator it = this->m.begin(), itend = this->m.end();
tmp_n_it = tmp_n.m.begin();
tmp_d_it = tmp_d.m.begin();
- for (; it!= this->m.end(); ++it, ++tmp_n_it, ++tmp_d_it)
- (*it) = ((*tmp_n_it)/(*tmp_d_it)).subs(srl);
+ while (it != itend)
+ *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_ex_of_type(this->m[k*col+co],numeric));
+ 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]));
+ numeric mmax = abs(ex_to<numeric>(m[kmax*col+co]));
while (kmax<row) {
- GINAC_ASSERT(is_ex_of_type(this->m[kmax*col+co],numeric));
- numeric tmp = ex_to_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;
k = kmax;
// matrix needs pivoting, so swap rows k and ro
ensure_if_modifiable();
for (unsigned c=0; c<col; ++c)
- m[k*col+c].swap(m[ro*col+c]);
+ this->m[k*col+c].swap(this->m[ro*col+c]);
return k;
}
-/** Convert list of lists to matrix. */
-ex lst_to_matrix(const ex &l)
+ex lst_to_matrix(const lst & l)
{
- if (!is_ex_of_type(l, lst))
- throw(std::invalid_argument("argument to lst_to_matrix() must be a lst"));
-
+ 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);
- for (i=0; i<rows; i++)
- for (j=0; j<cols; j++)
- if (l.op(i).nops() > j)
- m.set(i, j, l.op(i).op(j));
- else
- m.set(i, j, ex(0));
- 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;
}
-//////////
-// global constants
-//////////
+ex diag_matrix(const lst & l)
+{
+ 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;
+}
+
+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());
+ }
+ }
-const matrix some_matrix;
-const std::type_info & typeid_matrix = typeid(some_matrix);
+ return M;
+}
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff