* Implementation of symbolic matrices */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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
#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>(&matrix::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);
-
- } else {
-
- if (is_a<print_python_repr>(c))
- c.s << class_name() << '(';
-
- if (is_a<print_latex>(c))
- c.s << "\\left(\\begin{array}{" << std::string(col,'c') << "}";
- else
- c.s << "[";
-
- for (unsigned ro=0; ro<row; ++ro) {
- if (!is_a<print_latex>(c))
- c.s << "[";
- for (unsigned co=0; co<col; ++co) {
- m[ro*col+co].print(c);
- if (co<col-1) {
- if (is_a<print_latex>(c))
- c.s << "&";
- else
- c.s << ",";
- } else {
- if (!is_a<print_latex>(c))
- c.s << "]";
- }
- }
- if (ro<row-1) {
- if (is_a<print_latex>(c))
- c.s << "\\\\";
- else
- c.s << ",";
- }
+ 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;
+ }
+}
- if (is_a<print_latex>(c))
- c.s << "\\end{array}\\right)";
- else
- c.s << "]";
+void matrix::do_print(const print_context & c, unsigned level) const
+{
+ c.s << "[";
+ print_elements(c, "[", "]", ",", ",");
+ c.s << "]";
+}
- if (is_a<print_python_repr>(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];
}
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);
+}
+
+/** Complex conjugate every matrix entry. */
+ex matrix::conjugate() const
+{
+ exvector * ev = 0;
+ for (exvector::const_iterator i=m.begin(); i!=m.end(); ++i) {
+ ex x = i->conjugate();
+ if (ev) {
+ ev->push_back(x);
+ continue;
+ }
+ if (are_ex_trivially_equal(x, *i)) {
+ continue;
+ }
+ ev = new exvector;
+ ev->reserve(m.size());
+ for (exvector::const_iterator 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 *this;
}
// 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)) {
/** 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());
unsigned sparse_count = 0; // counts non-zero elements
exvector::const_iterator r = m.begin(), rend = m.end();
while (r != rend) {
- lst srl; // symbol replacement list
+ exmap srl; // symbol replacement list
ex rtest = r->to_rational(srl);
if (!rtest.is_zero())
++sparse_count;
else
return m[0].expand();
}
-
+
// Compute the determinant
switch(algo) {
case determinant_algo::gauss: {
*
* @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"));
tr += m[r*col+r];
if (tr.info(info_flags::rational_function) &&
- !tr.info(info_flags::crational_polynomial))
+ !tr.info(info_flags::crational_polynomial))
return tr.normal();
else
return tr.expand();
* @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"));
*
* @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)
* @exception runtime_error (inconsistent linear system)
* @see solve_algo */
matrix matrix::solve(const matrix & vars,
- const matrix & rhs,
- unsigned algo) const
+ const matrix & rhs,
+ unsigned algo) const
{
const unsigned m = this->rows();
const unsigned n = this->cols();
}
+/** Compute the rank of this matrix. */
+unsigned matrix::rank() const
+{
+ // Method:
+ // Transform this matrix into upper echelon form and then count the
+ // number of non-zero rows.
+
+ GINAC_ASSERT(row*col==m.capacity());
+
+ // Actually, any elimination scheme will do since we are only
+ // interested in the echelon matrix' zeros.
+ matrix to_eliminate = *this;
+ to_eliminate.fraction_free_elimination();
+
+ unsigned r = row*col; // index of last non-zero element
+ while (r--) {
+ if (!to_eliminate.m[r].is_zero())
+ return 1+r/col;
+ }
+ return 0;
+}
+
+
// protected
/** Recursive determinant for small matrices having at least one symbolic
*
* @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();
Pkey[j] = Pkey[j-1]+1;
} while(fc);
// next column, so change the role of A and B:
- A = B;
+ A.swap(B);
B.clear();
}
int sign = 1;
unsigned r0 = 0;
- for (unsigned r1=0; (r1<n-1)&&(r0<m-1); ++r1) {
- int indx = pivot(r0, r1, true);
+ for (unsigned c0=0; c0<n && r0<m-1; ++c0) {
+ int indx = pivot(r0, c0, true);
if (indx == -1) {
sign = 0;
if (det)
if (indx > 0)
sign = -sign;
for (unsigned r2=r0+1; r2<m; ++r2) {
- if (!this->m[r2*n+r1].is_zero()) {
+ if (!this->m[r2*n+c0].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) {
+ ex piv = this->m[r2*n+c0] / this->m[r0*n+c0];
+ for (unsigned c=c0+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)
+ for (unsigned c=r0; c<=c0; ++c)
this->m[r2*n+c] = _ex0;
}
if (det) {
++r0;
}
}
-
+ // clear remaining rows
+ for (unsigned r=r0+1; r<m; ++r) {
+ for (unsigned c=0; c<n; ++c)
+ this->m[r*n+c] = _ex0;
+ }
+
return sign;
}
int sign = 1;
unsigned r0 = 0;
- for (unsigned r1=0; (r1<n-1)&&(r0<m-1); ++r1) {
- int indx = pivot(r0, r1, true);
+ for (unsigned c0=0; c0<n && r0<m-1; ++c0) {
+ int indx = pivot(r0, c0, true);
if (indx==-1) {
sign = 0;
if (det)
if (indx>0)
sign = -sign;
for (unsigned r2=r0+1; r2<m; ++r2) {
- for (unsigned c=r1+1; c<n; ++c)
- 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();
+ for (unsigned c=c0+1; c<n; ++c)
+ this->m[r2*n+c] = (this->m[r0*n+c0]*this->m[r2*n+c] - this->m[r2*n+c0]*this->m[r0*n+c]).expand();
// fill up left hand side with zeros
- for (unsigned c=0; c<=r1; ++c)
+ for (unsigned c=r0; c<=c0; ++c)
this->m[r2*n+c] = _ex0;
}
if (det) {
++r0;
}
}
-
+ // clear remaining rows
+ for (unsigned r=r0+1; r<m; ++r) {
+ for (unsigned c=0; c<n; ++c)
+ this->m[r*n+c] = _ex0;
+ }
+
return sign;
}
//
// 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
+ 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) {
}
unsigned r0 = 0;
- for (unsigned r1=0; (r1<n-1)&&(r0<m-1); ++r1) {
- int indx = tmp_n.pivot(r0, r1, true);
+ for (unsigned c0=0; c0<n && r0<m-1; ++c0) {
+ int indx = tmp_n.pivot(r0, c0, true);
if (indx==-1) {
sign = 0;
if (det)
if (indx>0) {
sign = -sign;
// tmp_n's rows r0 and indx were swapped, do the same in tmp_d:
- for (unsigned c=r1; c<n; ++c)
+ for (unsigned c=c0; c<n; ++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=r1+1; c<n; ++c) {
- dividend_n = (tmp_n.m[r0*n+r1]*tmp_n.m[r2*n+c]*
- tmp_d.m[r2*n+r1]*tmp_d.m[r0*n+c]
- -tmp_n.m[r2*n+r1]*tmp_n.m[r0*n+c]*
- tmp_d.m[r0*n+r1]*tmp_d.m[r2*n+c]).expand();
- dividend_d = (tmp_d.m[r2*n+r1]*tmp_d.m[r0*n+c]*
- tmp_d.m[r0*n+r1]*tmp_d.m[r2*n+c]).expand();
+ for (unsigned c=c0+1; c<n; ++c) {
+ dividend_n = (tmp_n.m[r0*n+c0]*tmp_n.m[r2*n+c]*
+ tmp_d.m[r2*n+c0]*tmp_d.m[r0*n+c]
+ -tmp_n.m[r2*n+c0]*tmp_n.m[r0*n+c]*
+ tmp_d.m[r0*n+c0]*tmp_d.m[r2*n+c]).expand();
+ dividend_d = (tmp_d.m[r2*n+c0]*tmp_d.m[r0*n+c]*
+ tmp_d.m[r0*n+c0]*tmp_d.m[r2*n+c]).expand();
bool check = divide(dividend_n, divisor_n,
tmp_n.m[r2*n+c], true);
check &= divide(dividend_d, divisor_d,
GINAC_ASSERT(check);
}
// fill up left hand side with zeros
- for (unsigned c=0; c<=r1; ++c)
+ for (unsigned c=r0; c<=c0; ++c)
tmp_n.m[r2*n+c] = _ex0;
}
- if ((r1<n-1)&&(r0<m-1)) {
+ if (c0<n && r0<m-1) {
// compute next iteration's divisor
- divisor_n = tmp_n.m[r0*n+r1].expand();
- divisor_d = tmp_d.m[r0*n+r1].expand();
+ divisor_n = tmp_n.m[r0*n+c0].expand();
+ divisor_d = tmp_d.m[r0*n+c0].expand();
if (det) {
// save space by deleting no longer needed elements
for (unsigned c=0; c<n; ++c) {
++r0;
}
}
+ // clear remaining rows
+ for (unsigned r=r0+1; r<m; ++r) {
+ for (unsigned c=0; c<n; ++c)
+ tmp_n.m[r*n+c] = _ex0;
+ }
+
// 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);
+ *it++ = ((*tmp_n_it++)/(*tmp_d_it++)).subs(srl, subs_options::no_pattern);
return sign;
}
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;
+
+ 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();
- matrix &m = *new matrix(dim, dim);
- m.setflag(status_flags::dynallocated);
- for (unsigned i=0; i<dim; i++)
- m(i, i) = l.op(i);
+ // Allocate and fill matrix
+ matrix &M = *new matrix(dim, dim);
+ M.setflag(status_flags::dynallocated);
- return m;
+ 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)
git://www.ginac.de / ginac.git / blobdiff