X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=c48fb6b124bc99b090e3e4961c5a795cf71ae8a8;hb=fe86c2b3a16dfcf289adb3923ef0d292f5a740dc;hp=b133b6163beb989ea1a7e0f977d2ba85b0b0ed2e;hpb=d7eee2dd8de4149ff805fd69641316418450275b;p=ginac.git

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index b133b616..c48fb6b1 100644
--- a/ginac/matrix.cpp
+++ b/ginac/matrix.cpp
@@ -141,7 +141,7 @@ 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
@@ -150,7 +150,7 @@ void matrix::print(const print_context & c, unsigned level) const
 {
 	debugmsg("matrix print", LOGLEVEL_PRINT);
 
-	if (is_of_type(c, print_tree)) {
+	if (is_a<print_tree>(c)) {
 
 		inherited::print(c, level);
 
@@ -229,15 +229,15 @@ ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
 		for (unsigned c=0; c<col; ++c)
 			m2[r*col+c] = m[r*col+c].subs(ls, lr, no_pattern);
 
-	return ex(matrix(row, col, m2)).bp->basic::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<const matrix &>(other);
+	GINAC_ASSERT(is_exactly_a<matrix>(other));
+	const matrix &o = static_cast<const matrix &>(other);
 	
 	// compare number of rows
 	if (row != o.rows())
@@ -259,11 +259,21 @@ 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);
 
@@ -339,9 +349,9 @@ 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
@@ -375,8 +385,8 @@ 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));
@@ -390,10 +400,10 @@ 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))
@@ -405,10 +415,8 @@ bool matrix::contract_with(exvector::iterator self, exvector::iterator other, ex
 	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) {
@@ -503,10 +511,10 @@ matrix matrix::add(const matrix & other) const
 		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);
 }
@@ -521,10 +529,10 @@ matrix matrix::sub(const matrix & other) const
 		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);
 }
@@ -591,32 +599,31 @@ matrix matrix::pow(const ex & expn) const
 		// 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 k;
-			matrix prod(row,col);
+			numeric b = ex_to<numeric>(expn);
+			matrix A(row,col);
 			if (expn.info(info_flags::negative)) {
-				k = -ex_to<numeric>(expn);
-				prod = this->inverse();
+				b *= -1;
+				A = this->inverse();
 			} else {
-				k = ex_to<numeric>(expn);
-				prod = *this;
+				A = *this;
 			}
-			matrix result(row,col);
+			matrix C(row,col);
 			for (unsigned r=0; r<row; ++r)
-				result(r,r) = _ex1();
-			numeric b(1);
-			// this loop computes the representation of k in base 2 and
-			// multiplies the factors whenever needed:
-			while (b.compare(k)<=0) {
-				b *= numeric(2);
-				numeric r(mod(k,b));
-				if (!r.is_zero()) {
-					k -= r;
-					result = result.mul(prod);
+				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;
 				}
-				if (b.compare(k)<=0)
-					prod = prod.mul(prod);
+				b *= _num1_2();  // b /= 2, still integer.
+				A = A.mul(A);
 			}
-			return result;
+			return A.mul(C);
 		}
 	}
 	throw (std::runtime_error("matrix::pow(): don't know how to handle exponent"));
@@ -689,9 +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))
@@ -699,6 +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:
@@ -778,13 +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);
 			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)
@@ -840,10 +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
@@ -950,9 +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:
@@ -1299,13 +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;
@@ -1357,11 +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;
 }
@@ -1389,11 +1401,11 @@ 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]));
 		while (kmax<row) {
-			GINAC_ASSERT(is_ex_of_type(this->m[kmax*col+co],numeric));
+			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;