X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=0bedb6bb1a1e506fc0017ea3243d66c64ed3797a;hb=ad7e72a894ece87cd67ee14ba4ed5fc16e59b140;hp=650799e55f6353db6807e1d42a8d7904cc55291b;hpb=08d556dc3ac3fbf2b0ad3acd37016a1f925d7c02;p=ginac.git

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 650799e5..0bedb6bb 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -20,21 +20,22 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <algorithm>
 #include <map>
 #include <stdexcept>
 
 #include "matrix.h"
-#include "archive.h"
 #include "numeric.h"
 #include "lst.h"
 #include "idx.h"
 #include "indexed.h"
-#include "utils.h"
-#include "debugmsg.h"
 #include "power.h"
 #include "symbol.h"
 #include "normal.h"
+#include "print.h"
+#include "archive.h"
+#include "utils.h"
 
 namespace GiNaC {
 
@@ -44,18 +45,12 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 // default ctor, dtor, copy ctor, assignment operator and helpers:
 //////////
 
-// public
-
 /** Default ctor.  Initializes to 1 x 1-dimensional zero-matrix. */
 matrix::matrix() : inherited(TINFO_matrix), row(1), col(1)
 {
-	debugmsg("matrix default ctor",LOGLEVEL_CONSTRUCT);
-	m.push_back(_ex0());
+	m.push_back(_ex0);
 }
 
-// protected
-
-/** For use by copy ctor and assignment operator. */
 void matrix::copy(const matrix & other)
 {
 	inherited::copy(other);
@@ -64,10 +59,7 @@ void matrix::copy(const matrix & other)
 	m = other.m;  // STL's vector copying invoked here
 }
 
-void matrix::destroy(bool call_parent)
-{
-	if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_DESTROY(matrix)
 
 //////////
 // other ctors
@@ -82,18 +74,14 @@ void matrix::destroy(bool call_parent)
 matrix::matrix(unsigned r, unsigned c)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
-	m.resize(r*c, _ex0());
+	m.resize(r*c, _ex0);
 }
 
 // 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)
-{
-	debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
-}
+  : inherited(TINFO_matrix), row(r), col(c), m(m2) {}
 
 /** Construct matrix from (flat) list of elements. If the list has fewer
  *  elements than the matrix, the remaining matrix elements are set to zero.
@@ -102,8 +90,7 @@ matrix::matrix(unsigned r, unsigned c, const exvector & m2)
 matrix::matrix(unsigned r, unsigned c, const lst & l)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix ctor from unsigned,unsigned,lst",LOGLEVEL_CONSTRUCT);
-	m.resize(r*c, _ex0());
+	m.resize(r*c, _ex0);
 
 	for (unsigned i=0; i<l.nops(); i++) {
 		unsigned x = i % c;
@@ -118,10 +105,8 @@ matrix::matrix(unsigned r, unsigned c, const lst & l)
 // archiving
 //////////
 
-/** Construct object from archive_node. */
 matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("matrix ctor from archive_node", LOGLEVEL_CONSTRUCT);
 	if (!(n.find_unsigned("row", row)) || !(n.find_unsigned("col", col)))
 		throw (std::runtime_error("unknown matrix dimensions in archive"));
 	m.reserve(row * col);
@@ -134,13 +119,6 @@ matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst
 	}
 }
 
-/** 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);
@@ -153,42 +131,47 @@ void matrix::archive(archive_node &n) const
 	}
 }
 
+DEFAULT_UNARCHIVE(matrix)
+
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-void matrix::print(std::ostream & os, unsigned upper_precedence) const
+void matrix::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] << "]] ]]";
-}
+	if (is_a<print_tree>(c)) {
+
+		inherited::print(c, level);
+
+	} else {
+
+		if (is_a<print_python_repr>(c))
+			c.s << class_name() << '(';
+
+		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 << "]]";
+
+		if (is_a<print_python_repr>(c))
+			c.s << ')';
 
-void matrix::printraw(std::ostream & os) const
-{
-	debugmsg("matrix printraw",LOGLEVEL_PRINT);
-	os << class_name() << "(" << 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] << "))";
 }
 
 /** nops is defined to be rows x columns. */
@@ -212,37 +195,9 @@ ex & matrix::let_op(int i)
 	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
-{
-	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;
-	
-	return false;
-}
-
 /** 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;
@@ -262,46 +217,22 @@ ex matrix::eval(int level) const
 											   status_flags::evaluated );
 }
 
-/** Evaluate matrix numerically entry by entry. */
-ex matrix::evalf(int level) 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;
-	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);
-}
-
-ex matrix::subs(const lst & ls, const lst & lr) const
+ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) 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);
+			m2[r*col+c] = m[r*col+c].subs(ls, lr, no_pattern);
 
-	return matrix(row, col, m2);
+	return matrix(row, col, m2).basic::subs(ls, lr, no_pattern);
 }
 
 // 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())
@@ -323,11 +254,21 @@ int matrix::compare_same_type(const basic & other) const
 	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_of_type(i, indexed));
-	GINAC_ASSERT(is_ex_of_type(i.op(0), matrix));
+	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);
 
@@ -338,7 +279,7 @@ ex matrix::eval_indexed(const basic & i) const
 		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));
+		const idx & i1 = ex_to<idx>(i.op(1));
 
 		if (col == 1) {
 
@@ -348,7 +289,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 			// Index numeric -> return vector element
 			if (all_indices_unsigned) {
-				unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+				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);
@@ -362,7 +303,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 			// Index numeric -> return vector element
 			if (all_indices_unsigned) {
-				unsigned n1 = ex_to_numeric(i1.get_value()).to_int();
+				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);
@@ -372,8 +313,8 @@ ex matrix::eval_indexed(const basic & i) const
 	} 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));
+		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"));
@@ -386,7 +327,7 @@ ex matrix::eval_indexed(const basic & i) const
 
 		// 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();
+			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)
@@ -403,17 +344,17 @@ ex matrix::eval_indexed(const basic & i) const
 /** Sum of two indexed matrices. */
 ex matrix::add_indexed(const ex & self, const ex & other) const
 {
-	GINAC_ASSERT(is_ex_of_type(self, indexed));
-	GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
-	GINAC_ASSERT(is_ex_of_type(other, indexed));
+	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_ex_of_type(other.op(0), matrix)) {
 		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));
+		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
 
@@ -439,11 +380,11 @@ ex matrix::add_indexed(const ex & self, const ex & other) const
 /** Product of an indexed matrix with a number. */
 ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 {
-	GINAC_ASSERT(is_ex_of_type(self, indexed));
-	GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
+	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));
+	const matrix &self_matrix = ex_to<matrix>(self.op(0));
 
 	if (self.nops() == 2)
 		return indexed(self_matrix.mul(other), self.op(1));
@@ -454,10 +395,10 @@ ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 /** Contraction of an indexed matrix with something else. */
 bool matrix::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
-	GINAC_ASSERT(is_ex_of_type(*self, indexed));
-	GINAC_ASSERT(is_ex_of_type(*other, indexed));
+	GINAC_ASSERT(is_a<indexed>(*self));
+	GINAC_ASSERT(is_a<indexed>(*other));
 	GINAC_ASSERT(self->nops() == 2 || self->nops() == 3);
-	GINAC_ASSERT(is_ex_of_type(self->op(0), matrix));
+	GINAC_ASSERT(is_a<matrix>(self->op(0)));
 
 	// Only contract with other matrices
 	if (!is_ex_of_type(other->op(0), matrix))
@@ -465,14 +406,12 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 
 	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));
+	const matrix &self_matrix = ex_to<matrix>(self->op(0));
+	const matrix &other_matrix = ex_to<matrix>(other->op(0));
 
 	if (self->nops() == 2) {
-		unsigned self_dim = (self_matrix.col == 1) ? self_matrix.row : self_matrix.col;
 
 		if (other->nops() == 2) { // vector * vector (scalar product)
-			unsigned other_dim = (other_matrix.col == 1) ? other_matrix.row : other_matrix.col;
 
 			if (self_matrix.col == 1) {
 				if (other_matrix.col == 1) {
@@ -491,7 +430,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = self_matrix.mul(other_matrix.transpose())(0, 0);
 				}
 			}
-			*other = _ex1();
+			*other = _ex1;
 			return true;
 
 		} else { // vector * matrix
@@ -502,7 +441,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(self_matrix.mul(other_matrix), other->op(2));
 				else
 					*self = indexed(self_matrix.transpose().mul(other_matrix), other->op(2));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 
@@ -512,7 +451,7 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 					*self = indexed(other_matrix.mul(self_matrix), other->op(1));
 				else
 					*self = indexed(other_matrix.mul(self_matrix.transpose()), other->op(1));
-				*other = _ex1();
+				*other = _ex1;
 				return true;
 			}
 		}
@@ -522,28 +461,28 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 		// 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();
+			*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();
+			*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();
+			*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();
+			*other = _ex1;
 			return true;
 		}
 	}
@@ -564,13 +503,13 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 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);
 }
@@ -582,13 +521,13 @@ matrix matrix::add(const matrix & other) const
 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);
 }
@@ -600,7 +539,7 @@ matrix matrix::sub(const matrix & other) const
 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());
 	
@@ -629,7 +568,64 @@ matrix matrix::mul(const numeric & other) const
 }
 
 
-/** operator() to access elements.
+/** 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_ex_exactly_of_type(expn, numeric)) {
+		// 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;
+			// 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) {
+				if (b.is_odd()) {
+					C = C.mul(A);
+					b -= 1;
+				}
+				b *= _num1_2;  // b /= 2, 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
@@ -643,17 +639,18 @@ const ex & matrix::operator() (unsigned ro, unsigned co) const
 }
 
 
-/** 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];
 }
 
 
@@ -670,7 +667,6 @@ matrix matrix::transpose(void) const
 	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
@@ -695,9 +691,10 @@ ex matrix::determinant(unsigned algo) const
 	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) {
+	exvector::const_iterator r = m.begin(), rend = m.end();
+	while (r != rend) {
 		lst 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::numeric))
@@ -705,6 +702,7 @@ ex matrix::determinant(unsigned algo) const
 		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:
@@ -757,7 +755,7 @@ ex matrix::determinant(unsigned algo) const
 			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)
@@ -769,10 +767,13 @@ ex matrix::determinant(unsigned algo) const
 		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) {
@@ -782,14 +783,15 @@ ex matrix::determinant(unsigned algo) const
 						++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)
@@ -845,10 +847,11 @@ ex matrix::charpoly(const symbol & lambda) const
 		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
@@ -889,50 +892,32 @@ matrix matrix::inverse(void) 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 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) {
-				if (!cpy.m[r2*col+r1].is_zero()) {
-					ex a2 = cpy.m[r2*col+r1];
-					// yes, there is something to do in this column
-					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;
 }
 
 
@@ -973,9 +958,11 @@ matrix matrix::solve(const matrix & vars,
 	
 	// 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:
@@ -995,8 +982,10 @@ matrix matrix::solve(const matrix & vars,
 	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();
@@ -1019,19 +1008,18 @@ matrix matrix::solve(const matrix & vars,
 				// 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;
@@ -1075,9 +1063,9 @@ ex matrix::determinant_minor(void) const
 	//     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:
@@ -1121,7 +1109,7 @@ ex matrix::determinant_minor(void) const
 			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())
@@ -1201,12 +1189,12 @@ int matrix::gauss_elimination(const bool det)
 				}
 				// 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;
 		}
@@ -1248,12 +1236,12 @@ int matrix::division_free_elimination(const bool det)
 					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;
 		}
@@ -1321,13 +1309,13 @@ int matrix::fraction_free_elimination(const bool det)
 	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();
+	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;
@@ -1361,7 +1349,7 @@ int matrix::fraction_free_elimination(const bool det)
 				}
 				// 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
@@ -1370,8 +1358,8 @@ int matrix::fraction_free_elimination(const bool det)
 				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;
 					}
 				}
 			}
@@ -1379,11 +1367,11 @@ int matrix::fraction_free_elimination(const bool det)
 		}
 	}
 	// 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);
 	
 	return sign;
 }
@@ -1411,12 +1399,12 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 			++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_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_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;
@@ -1447,15 +1435,16 @@ ex lst_to_matrix(const lst & l)
 	for (i=0; i<rows; i++)
 		if (l.op(i).nops() > cols)
 			cols = l.op(i).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.set(i, j, l.op(i).op(j));
+				m(i, j) = l.op(i).op(j);
 			else
-				m.set(i, j, ex(0));
+				m(i, j) = _ex0;
 	return m;
 }
 
@@ -1464,8 +1453,9 @@ ex diag_matrix(const lst & l)
 	unsigned dim = l.nops();
 
 	matrix &m = *new matrix(dim, dim);
+	m.setflag(status_flags::dynallocated);
 	for (unsigned i=0; i<dim; i++)
-		m.set(i, i, l.op(i));
+		m(i, i) = l.op(i);
 
 	return m;
 }