X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fmatrix.cpp;h=60869f09fa709bbd17b051206fa4b32c29db0e73;hb=ff7eeaa487dca86b36ddbb19b1dcefb2134327be;hp=65b1254936e0a378eb5ba1760ee9709a3a52c409;hpb=b9cd4b49ffbfbf3e1c36a2b594ec3148a5baca64;p=ginac.git

diff --git a/ginac/matrix.cpp b/ginac/matrix.cpp
index 65b12549..60869f09 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
@@ -156,23 +156,23 @@ void matrix::print(const print_context & c, unsigned level) const
 
 	} else {
 
-		c.s << "[[ ";
+		c.s << "[";
 		for (unsigned y=0; y<row-1; ++y) {
-			c.s << "[[";
+			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 << "],";
 		}
-		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 << "]] ]]";
+		c.s << "]]";
 
 	}
 }
@@ -198,16 +198,6 @@ 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);
-}
-
 /** Evaluate matrix entry by entry. */
 ex matrix::eval(int level) const
 {
@@ -232,30 +222,6 @@ 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, bool no_pattern) const
 {
 	exvector m2(row * col);
@@ -271,7 +237,7 @@ ex matrix::subs(const lst & ls, const lst & lr, bool no_pattern) const
 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));
+	const matrix & o = static_cast<const matrix &>(other);
 	
 	// compare number of rows
 	if (row != o.rows())
@@ -293,6 +259,16 @@ int matrix::compare_same_type(const basic & other) const
 	return 0;
 }
 
+bool matrix::match_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_exactly_of_type(other, matrix));
+	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
 {
@@ -308,7 +284,7 @@ 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) {
 
@@ -318,7 +294,7 @@ 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);
@@ -332,7 +308,7 @@ 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);
@@ -342,8 +318,8 @@ 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"));
@@ -356,7 +332,7 @@ 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)
@@ -382,8 +358,8 @@ ex matrix::add_indexed(const ex & self, const ex & other) const
 	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
 
@@ -413,7 +389,7 @@ ex matrix::scalar_mul_indexed(const ex & self, const numeric & other) const
 	GINAC_ASSERT(is_ex_of_type(self.op(0), matrix));
 	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));
@@ -435,14 +411,12 @@ 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) {
@@ -534,13 +508,13 @@ 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);
 }
@@ -552,13 +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);
 }
@@ -570,7 +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());
 	
@@ -599,7 +573,64 @@ 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
@@ -613,17 +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];
 }
 
 
@@ -640,7 +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
@@ -665,9 +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))
@@ -675,6 +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:
@@ -754,12 +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)
@@ -815,10 +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
@@ -865,7 +900,7 @@ matrix matrix::inverse(void) const
 	// First populate the identity matrix supposed to become the right hand side.
 	matrix identity(row,col);
 	for (unsigned i=0; i<row; ++i)
-		identity.set(i,i,_ex1());
+		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
@@ -873,7 +908,7 @@ matrix matrix::inverse(void) const
 	matrix vars(row,col);
 	for (unsigned r=0; r<row; ++r)
 		for (unsigned c=0; c<col; ++c)
-			vars.set(r,c,symbol());
+			vars(r,c) = symbol();
 	
 	matrix sol(row,col);
 	try {
@@ -925,9 +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:
@@ -973,19 +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;
@@ -1029,9 +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:
@@ -1275,13 +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;
@@ -1333,11 +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;
 }
@@ -1367,10 +1403,10 @@ int matrix::pivot(unsigned ro, unsigned co, bool symbolic)
 		// search largest element in column co beginning at row ro
 		GINAC_ASSERT(is_ex_of_type(this->m[k*col+co],numeric));
 		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]);
+			numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
 			if (abs(tmp) > mmax) {
 				mmax = tmp;
 				k = kmax;
@@ -1408,9 +1444,9 @@ ex lst_to_matrix(const lst & l)
 	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;
 }
 
@@ -1421,7 +1457,7 @@ ex diag_matrix(const lst & l)
 	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;
 }