X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=c48fb6b124bc99b090e3e4961c5a795cf71ae8a8;hp=0b87ed5d3ba843511e144bc3c316bd99dd0a4d50;hb=fe86c2b3a16dfcf289adb3923ef0d292f5a740dc;hpb=e5362a33f72613b324b3714524a8c2e5f7b7f46f

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 0b87ed5d..c48fb6b1 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -25,37 +25,33 @@
 #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 "power.h"
 #include "symbol.h"
 #include "normal.h"
+#include "print.h"
+#include "archive.h"
+#include "utils.h"
+#include "debugmsg.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(matrix, basic)
 
 //////////
-// default constructor, destructor, copy constructor, assignment operator
-// and helpers:
+// 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 constructor",LOGLEVEL_CONSTRUCT);
+	debugmsg("matrix default ctor",LOGLEVEL_CONSTRUCT);
 	m.push_back(_ex0());
 }
 
-// protected
-
 void matrix::copy(const matrix & other)
 {
 	inherited::copy(other);
@@ -64,13 +60,10 @@ 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 constructors
+// other ctors
 //////////
 
 // public
@@ -82,7 +75,7 @@ void matrix::destroy(bool call_parent)
 matrix::matrix(unsigned r, unsigned c)
   : inherited(TINFO_matrix), row(r), col(c)
 {
-	debugmsg("matrix constructor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
+	debugmsg("matrix ctor from unsigned,unsigned",LOGLEVEL_CONSTRUCT);
 	m.resize(r*c, _ex0());
 }
 
@@ -92,17 +85,35 @@ matrix::matrix(unsigned r, unsigned c)
 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);
+	debugmsg("matrix ctor from unsigned,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+}
+
+/** 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)
+{
+	debugmsg("matrix ctor from unsigned,unsigned,lst",LOGLEVEL_CONSTRUCT);
+	m.resize(r*c, _ex0());
+
+	for (unsigned i=0; i<l.nops(); i++) {
+		unsigned x = i % c;
+		unsigned y = i / c;
+		if (y >= r)
+			break; // matrix smaller than list: throw away excessive elements
+		m[y*c+x] = l.op(i);
+	}
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
 matrix::matrix(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("matrix constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	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);
@@ -115,13 +126,6 @@ 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);
@@ -134,48 +138,43 @@ 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
 
-basic * matrix::duplicate() const
+void matrix::print(const print_context & c, unsigned level) const
 {
-	debugmsg("matrix duplicate",LOGLEVEL_DUPLICATE);
-	return new matrix(*this);
-}
+	debugmsg("matrix print", LOGLEVEL_PRINT);
 
-void matrix::print(std::ostream & os, unsigned upper_precedence) 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 {
+
+		c.s << "[";
+		for (unsigned y=0; y<row-1; ++y) {
+			c.s << "[";
+			for (unsigned x=0; x<col-1; ++x) {
+				m[y*col+x].print(c);
+				c.s << ",";
+			}
+			m[col*(y+1)-1].print(c);
+			c.s << "],";
+		}
+		c.s << "[";
+		for (unsigned x=0; x<col-1; ++x) {
+			m[(row-1)*col+x].print(c);
+			c.s << ",";
+		}
+		m[row*col-1].print(c);
+		c.s << "]]";
 
-void matrix::printraw(std::ostream & os) 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] << "))";
 }
 
 /** nops is defined to be rows x columns. */
@@ -199,33 +198,7 @@ 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. */
+/** Evaluate matrix entry by entry. */
 ex matrix::eval(int level) const
 {
 	debugmsg("matrix eval",LOGLEVEL_MEMBER_FUNCTION);
@@ -249,36 +222,22 @@ ex matrix::eval(int level) const
 											   status_flags::evaluated );
 }
 
-/** evaluate matrix numerically entry by entry. */
-ex matrix::evalf(int level) const
+ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) 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(ls, lr, no_pattern);
+
+	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())
@@ -300,6 +259,243 @@ 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_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_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));
+
+		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_ex_of_type(other->op(0), matrix))
+		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
 //////////
@@ -312,13 +508,13 @@ int matrix::compare_same_type(const basic & other) const
 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);
 }
@@ -330,13 +526,13 @@ 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);
 }
@@ -348,7 +544,7 @@ 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());
 	
@@ -364,7 +560,77 @@ matrix matrix::mul(const matrix & other) const
 }
 
 
-/** 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_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
@@ -378,17 +644,18 @@ 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];
 }
 
 
@@ -405,7 +672,6 @@ 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
@@ -430,9 +696,10 @@ 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))
@@ -440,6 +707,7 @@ 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:
@@ -519,12 +787,13 @@ ex matrix::determinant(unsigned algo) const
 			}
 			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)
@@ -580,10 +849,11 @@ 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
@@ -624,50 +894,32 @@ 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;
 }
 
 
@@ -708,9 +960,11 @@ 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:
@@ -730,8 +984,10 @@ 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();
@@ -754,19 +1010,18 @@ 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;
@@ -810,9 +1065,9 @@ 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:
@@ -1056,13 +1311,13 @@ 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;
@@ -1114,11 +1369,11 @@ 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;
 }
@@ -1146,12 +1401,12 @@ 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;
@@ -1175,29 +1430,36 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 	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"));
-	
 	// 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();
-	
+
 	// 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;
+}
+
+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(i, i) = l.op(i);
+
 	return m;
 }
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC