* Implementation of symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <string>
-#include <iostream>
-#include <sstream>
-#include <algorithm>
-#include <map>
-#include <stdexcept>
-
#include "matrix.h"
#include "numeric.h"
#include "lst.h"
#include "archive.h"
#include "utils.h"
+#include <algorithm>
+#include <iostream>
+#include <map>
+#include <sstream>
+#include <stdexcept>
+#include <string>
+
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(matrix, basic,
//////////
/** Default ctor. Initializes to 1 x 1-dimensional zero-matrix. */
-matrix::matrix() : inherited(&matrix::tinfo_static), row(1), col(1), m(1, _ex0)
+matrix::matrix() : row(1), col(1), m(1, _ex0)
{
setflag(status_flags::not_shareable);
}
*
* @param r number of rows
* @param c number of cols */
-matrix::matrix(unsigned r, unsigned c)
- : inherited(&matrix::tinfo_static), row(r), col(c), m(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(&matrix::tinfo_static), row(r), col(c), m(m2)
+matrix::matrix(unsigned r, unsigned c) : row(r), col(c), m(r*c, _ex0)
{
setflag(status_flags::not_shareable);
}
* 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(&matrix::tinfo_static), row(r), col(c), m(r*c, _ex0)
+ : 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) {
+ for (auto & it : l) {
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;
+ m[y*c+x] = it;
+ ++i;
}
}
+/** Construct a matrix from an 2 dimensional initializer list.
+ * Throws an exception if some row has a different length than all the others.
+ */
+matrix::matrix(std::initializer_list<std::initializer_list<ex>> l)
+ : row(l.size()), col(l.begin()->size())
+{
+ setflag(status_flags::not_shareable);
+
+ m.reserve(row*col);
+ for (const auto & r : l) {
+ unsigned c = 0;
+ for (const auto & e : r) {
+ m.push_back(e);
+ ++c;
+ }
+ if (c != col)
+ throw std::invalid_argument("matrix::matrix{{}}: wrong dimension");
+ }
+}
+
+// protected
+
+/** Ctor from representation, for internal use only. */
+matrix::matrix(unsigned r, unsigned c, const exvector & m2)
+ : row(r), col(c), m(m2)
+{
+ setflag(status_flags::not_shareable);
+}
+matrix::matrix(unsigned r, unsigned c, exvector && m2)
+ : row(r), col(c), m(std::move(m2))
+{
+ setflag(status_flags::not_shareable);
+}
+
//////////
// archiving
//////////
-matrix::matrix(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+void matrix::read_archive(const archive_node &n, lst &sym_lst)
{
- setflag(status_flags::not_shareable);
+ inherited::read_archive(n, sym_lst);
if (!(n.find_unsigned("row", row)) || !(n.find_unsigned("col", col)))
throw (std::runtime_error("unknown matrix dimensions in archive"));
m.reserve(row * col);
- for (unsigned int i=0; true; i++) {
+ // XXX: default ctor inserts a zero element, we need to erase it here.
+ m.pop_back();
+ auto first = n.find_first("m");
+ auto last = n.find_last("m");
+ ++last;
+ for (auto i=first; i != last; ++i) {
ex e;
- if (n.find_ex("m", e, sym_lst, i))
- m.push_back(e);
- else
- break;
+ n.find_ex_by_loc(i, e, sym_lst);
+ m.push_back(e);
}
}
+GINAC_BIND_UNARCHIVER(matrix);
void matrix::archive(archive_node &n) const
{
inherited::archive(n);
n.add_unsigned("row", row);
n.add_unsigned("col", col);
- exvector::const_iterator i = m.begin(), iend = m.end();
- while (i != iend) {
- n.add_ex("m", *i);
- ++i;
+ for (auto & i : m) {
+ n.add_ex("m", i);
}
}
-DEFAULT_UNARCHIVE(matrix)
-
//////////
// functions overriding virtual functions from base classes
//////////
for (unsigned c=0; c<col; ++c)
m2[r*col+c] = m[r*col+c].eval(level);
- return (new matrix(row, col, m2))->setflag(status_flags::dynallocated |
- status_flags::evaluated);
+ return (new matrix(row, col, std::move(m2)))->setflag(status_flags::dynallocated |
+ status_flags::evaluated);
}
ex matrix::subs(const exmap & mp, unsigned options) const
for (unsigned c=0; c<col; ++c)
m2[r*col+c] = m[r*col+c].subs(mp, options);
- return matrix(row, col, m2).subs_one_level(mp, options);
+ return matrix(row, col, std::move(m2)).subs_one_level(mp, options);
}
/** Complex conjugate every matrix entry. */
ex matrix::conjugate() const
{
- exvector * ev = 0;
- for (exvector::const_iterator i=m.begin(); i!=m.end(); ++i) {
+ std::unique_ptr<exvector> ev(nullptr);
+ for (auto i=m.begin(); i!=m.end(); ++i) {
ex x = i->conjugate();
if (ev) {
ev->push_back(x);
if (are_ex_trivially_equal(x, *i)) {
continue;
}
- ev = new exvector;
+ ev.reset(new exvector);
ev->reserve(m.size());
- for (exvector::const_iterator j=m.begin(); j!=i; ++j) {
+ for (auto j=m.begin(); j!=i; ++j) {
ev->push_back(*j);
}
ev->push_back(x);
}
if (ev) {
- ex result = matrix(row, col, *ev);
- delete ev;
- return result;
+ return matrix(row, col, std::move(*ev));
}
return *this;
}
+ex matrix::real_part() const
+{
+ exvector v;
+ v.reserve(m.size());
+ for (auto & i : m)
+ v.push_back(i.real_part());
+ return matrix(row, col, std::move(v));
+}
+
+ex matrix::imag_part() const
+{
+ exvector v;
+ v.reserve(m.size());
+ for (auto & i : m)
+ v.push_back(i.imag_part());
+ return matrix(row, col, std::move(v));
+}
+
// protected
int matrix::compare_same_type(const basic & other) const
throw std::logic_error("matrix::add(): incompatible matrices");
exvector sum(this->m);
- exvector::iterator i = sum.begin(), end = sum.end();
- exvector::const_iterator ci = other.m.begin();
- while (i != end)
- *i++ += *ci++;
+ auto ci = other.m.begin();
+ for (auto & i : sum)
+ i += *ci++;
- return matrix(row,col,sum);
+ return matrix(row, col, std::move(sum));
}
throw std::logic_error("matrix::sub(): incompatible matrices");
exvector dif(this->m);
- exvector::iterator i = dif.begin(), end = dif.end();
- exvector::const_iterator ci = other.m.begin();
- while (i != end)
- *i++ -= *ci++;
+ auto ci = other.m.begin();
+ for (auto & i : dif)
+ i -= *ci++;
- return matrix(row,col,dif);
+ return matrix(row, col, std::move(dif));
}
for (unsigned r1=0; r1<this->rows(); ++r1) {
for (unsigned c=0; c<this->cols(); ++c) {
+ // Quick test: can we shortcut?
if (m[r1*col+c].is_zero())
continue;
for (unsigned r2=0; r2<other.cols(); ++r2)
- prod[r1*other.col+r2] += (m[r1*col+c] * other.m[c*other.col+r2]).expand();
+ prod[r1*other.col+r2] += (m[r1*col+c] * other.m[c*other.col+r2]);
}
}
- return matrix(row, other.col, prod);
+ return matrix(row, other.col, std::move(prod));
}
for (unsigned c=0; c<col; ++c)
prod[r*col+c] = m[r*col+c] * other;
- return matrix(row, col, prod);
+ return matrix(row, col, std::move(prod));
}
for (unsigned c=0; c<col; ++c)
prod[r*col+c] = m[r*col+c] * other;
- return matrix(row, col, prod);
+ return matrix(row, col, std::move(prod));
}
for (unsigned c=0; c<this->rows(); ++c)
trans[r*this->rows()+c] = m[c*this->cols()+r];
- return matrix(this->cols(),this->rows(),trans);
+ return matrix(this->cols(), this->rows(), std::move(trans));
}
/** Determinant of square matrix. This routine doesn't actually calculate the
bool numeric_flag = true;
bool normal_flag = false;
unsigned sparse_count = 0; // counts non-zero elements
- exvector::const_iterator r = m.begin(), rend = m.end();
- while (r != rend) {
- if (!r->info(info_flags::numeric))
+ for (auto r : m) {
+ if (!r.info(info_flags::numeric))
numeric_flag = false;
exmap srl; // symbol replacement list
- ex rtest = r->to_rational(srl);
+ ex rtest = r.to_rational(srl);
if (!rtest.is_zero())
++sparse_count;
if (!rtest.info(info_flags::crational_polynomial) &&
- rtest.info(info_flags::rational_function))
+ rtest.info(info_flags::rational_function))
normal_flag = true;
- ++r;
}
// Here is the heuristics in case this routine has to decide:
}
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);
+ for (auto & i : c_zeros)
+ pre_sort.push_back(i.second);
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>::const_iterator i=pre_sort.begin();
- i!=pre_sort.end();
- ++i,++c) {
+ for (auto & it : pre_sort) {
for (unsigned r=0; r<row; ++r)
- result[r*col+c] = m[r*col+(*i)];
+ result[r*col+c] = m[r*col+it];
+ ++c;
}
if (normal_flag)
- return (sign*matrix(row,col,result).determinant_minor()).normal();
+ return (sign*matrix(row, col, std::move(result)).determinant_minor()).normal();
else
- return sign*matrix(row,col,result).determinant_minor();
+ return sign*matrix(row, col, std::move(result)).determinant_minor();
}
}
}
/** Characteristic Polynomial. Following mathematica notation the
- * characteristic polynomial of a matrix M is defined as the determiant of
+ * characteristic polynomial of a matrix M is defined as the determinant of
* (M - lambda * 1) where 1 stands for the unit matrix of the same dimension
* as M. Note that some CASs define it with a sign inside the determinant
* which gives rise to an overall sign if the dimension is odd. This method
throw (std::logic_error("matrix::charpoly(): matrix not square"));
bool numeric_flag = true;
- exvector::const_iterator r = m.begin(), rend = m.end();
- while (r!=rend && numeric_flag==true) {
- if (!r->info(info_flags::numeric))
+ for (auto & r : m) {
+ if (!r.info(info_flags::numeric)) {
numeric_flag = false;
- ++r;
+ break;
+ }
}
// The pure numeric case is traditionally rather common. Hence, it is
// Gather some statistical information about the augmented matrix:
bool numeric_flag = true;
- exvector::const_iterator r = aug.m.begin(), rend = aug.m.end();
- while (r!=rend && numeric_flag==true) {
- if (!r->info(info_flags::numeric))
+ for (auto & r : aug.m) {
+ if (!r.info(info_flags::numeric)) {
numeric_flag = false;
- ++r;
+ break;
+ }
}
// Here is the heuristics in case this routine has to decide:
* more than once. According to W.M.Gentleman and S.C.Johnson this algorithm
* is better than elimination schemes for matrices of sparse multivariate
* polynomials and also for matrices of dense univariate polynomials if the
- * matrix' dimesion is larger than 7.
+ * matrix' dimension is larger than 7.
*
* @return the determinant as a new expression (in expanded form)
* @see matrix::determinant() */
for (unsigned j=fc; j<n-c; ++j)
Pkey[j] = Pkey[j-1]+1;
} while(fc);
- // next column, so change the role of A and B:
- A.swap(B);
- B.clear();
+ // next column, clear B and change the role of A and B:
+ A = std::move(B);
}
return det;
matrix tmp_n(*this);
matrix tmp_d(m,n); // for denominators, if needed
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;
+ auto tmp_n_it = tmp_n.m.begin(), tmp_d_it = tmp_d.m.begin();
+ for (auto & it : this->m) {
+ ex nd = it.normal().to_rational(srl).numer_denom();
*tmp_n_it++ = nd.op(0);
*tmp_d_it++ = nd.op(1);
}
unsigned r0 = 0;
for (unsigned c0=0; c0<n && r0<m-1; ++c0) {
- int indx = tmp_n.pivot(r0, c0, true);
- if (indx==-1) {
+ // When trying to find a pivot, we should try a bit harder than expand().
+ // Searching the first non-zero element in-place here instead of calling
+ // pivot() allows us to do no more substitutions and back-substitutions
+ // than are actually necessary.
+ unsigned indx = r0;
+ while ((indx<m) &&
+ (tmp_n[indx*n+c0].subs(srl, subs_options::no_pattern).expand().is_zero()))
+ ++indx;
+ if (indx==m) {
+ // all elements in column c0 below row r0 vanish
sign = 0;
if (det)
return 0;
- }
- if (indx>=0) {
- if (indx>0) {
+ } else {
+ if (indx>r0) {
+ // Matrix needs pivoting, swap rows r0 and indx of tmp_n and tmp_d.
sign = -sign;
- // tmp_n's rows r0 and indx were swapped, do the same in tmp_d:
- for (unsigned c=c0; c<n; ++c)
+ for (unsigned c=c0; c<n; ++c) {
+ tmp_n.m[n*indx+c].swap(tmp_n.m[n*r0+c]);
tmp_d.m[n*indx+c].swap(tmp_d.m[n*r0+c]);
+ }
}
for (unsigned r2=r0+1; r2<m; ++r2) {
for (unsigned c=c0+1; c<n; ++c) {
}
// repopulate *this matrix:
- exvector::iterator it = this->m.begin(), itend = this->m.end();
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, subs_options::no_pattern);
+ for (auto & it : this->m)
+ it = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl, subs_options::no_pattern);
return sign;
}
* @param co is the column to be inspected
* @param symbolic signal if we want the first non-zero element to be pivoted
* (true) or the one with the largest absolute value (false).
- * @return 0 if no interchange occured, -1 if all are zero (usually signaling
+ * @return 0 if no interchange occurred, -1 if all are zero (usually signaling
* a degeneracy) and positive integer k means that rows ro and k were swapped.
*/
int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
return k;
}
-ex lst_to_matrix(const lst & l)
+/** Function to check that all elements of the matrix are zero.
+ */
+bool matrix::is_zero_matrix() const
{
- lst::const_iterator itr, itc;
+ for (auto & i : m)
+ if (!i.is_zero())
+ return false;
+ return true;
+}
+ex lst_to_matrix(const lst & l)
+{
// Find number of rows and columns
size_t rows = l.nops(), cols = 0;
- for (itr = l.begin(); itr != l.end(); ++itr) {
- if (!is_a<lst>(*itr))
+ for (auto & itr : l) {
+ 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();
+ if (itr.nops() > cols)
+ cols = itr.nops();
}
// Allocate and fill matrix
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;
+ unsigned i = 0;
+ for (auto & itr : l) {
+ unsigned j = 0;
+ for (auto & itc : ex_to<lst>(itr)) {
+ M(i, j) = itc;
+ ++j;
+ }
+ ++i;
}
return M;
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;
+ unsigned i = 0;
+ for (auto & it : l) {
+ M(i, i) = it;
+ ++i;
+ }
+
+ return M;
+}
+
+ex diag_matrix(std::initializer_list<ex> l)
+{
+ size_t dim = l.size();
+
+ // Allocate and fill matrix
+ matrix &M = *new matrix(dim, dim);
+ M.setflag(status_flags::dynallocated);
+
+ unsigned i = 0;
+ for (auto & it : l) {
+ M(i, i) = it;
+ ++i;
+ }
return M;
}
ex unit_matrix(unsigned r, unsigned c)
{
matrix &Id = *new matrix(r, c);
- Id.setflag(status_flags::dynallocated);
+ Id.setflag(status_flags::dynallocated | status_flags::evaluated);
for (unsigned i=0; i<r && i<c; i++)
Id(i,i) = _ex1;
git://www.ginac.de / ginac.git / blobdiff