--- /dev/null
+/* -*- C++ -*- ------------------------------------------------------------
+
+Copyright (c) 2007 Jesse Anders and Demian Nave http://cmldev.net/
+
+The Configurable Math Library (CML) is distributed under the terms of the
+Boost Software License, v1.0 (see cml/LICENSE for details).
+
+ *-----------------------------------------------------------------------*/
+/** @file
+ * @brief Matrix linear expression classes.
+ *
+ * @todo Dynamic resizing needs to be integrated more naturally into
+ * mul() and matrix transpose():
+ */
+
+#ifndef matrix_expr_h
+#define matrix_expr_h
+
+
+#include <cml/et/size_checking.h>
+#include <cml/matrix/matrix_traits.h>
+#include <cml/matrix/matrix_promotions.h>
+
+/* XXX Don't know which it should be just yet, since RVO seems to obviate the
+ * need for a reference type. However, copy by value copies the *entire
+ * expression tree rooted at the MatrixXpr<>, so this choice is bound to affect
+ * performance for some compiler or another:
+ */
+#define MATXPR_ARG_TYPE const et::MatrixXpr<XprT>&
+#define MATXPR_ARG_TYPE_N(_N_) const et::MatrixXpr<XprT##_N_>&
+
+//#define MATXPR_ARG_TYPE const et::MatrixXpr<XprT>
+//#define MATXPR_ARG_TYPE_N(_N_) const et::MatrixXpr<XprT##_N_>
+
+namespace cml {
+namespace et {
+
+/** A placeholder for a matrix expression in the expression tree. */
+template<class ExprT>
+class MatrixXpr
+{
+ public:
+
+ typedef MatrixXpr<ExprT> expr_type;
+
+ /* Copy the expression by value into higher-up expressions: */
+ typedef expr_type expr_const_reference;
+
+ typedef typename ExprT::value_type value_type;
+ typedef matrix_result_tag result_tag;
+ typedef typename ExprT::size_tag size_tag; // Just inherit size type.
+
+ /* Store the expression traits: */
+ typedef ExprTraits<ExprT> expr_traits;
+
+ /* Get the reference type: */
+ typedef typename expr_traits::const_reference expr_reference;
+
+ /* Get the result type: */
+ typedef typename expr_traits::result_type result_type;
+
+ /* Get the basis type: */
+ typedef typename result_type::basis_orient basis_orient;
+
+ /* Get the temporary type: */
+ typedef typename result_type::temporary_type temporary_type;
+
+ /* For matching by assignability: */
+ typedef cml::et::not_assignable_tag assignable_tag;
+
+
+ public:
+
+ /** Record result size as an enum (if applicable). */
+ enum { array_rows = ExprT::array_rows, array_cols = ExprT::array_cols };
+
+
+ public:
+
+ /** Return the expression size as a pair. */
+ matrix_size size() const {
+ return matrix_size(this->rows(),this->cols());
+ }
+
+ /** Return number of rows in the expression (same as subexpression). */
+ size_t rows() const {
+ return expr_traits().rows(m_expr);
+ }
+
+ /** Return number of columns in the expression (same as subexpression). */
+ size_t cols() const {
+ return expr_traits().cols(m_expr);
+ }
+
+ /** Return reference to contained expression. */
+ expr_reference expression() const { return m_expr; }
+
+ /** Compute value at index i,j of the result matrix. */
+ value_type operator()(size_t i, size_t j) const {
+ return expr_traits().get(m_expr,i,j);
+ }
+
+ /** Return element j of basis vector i. */
+ value_type basis_element(size_t i, size_t j) const {
+ return basis_element(i,j,basis_orient());
+ }
+
+
+ public:
+
+ /** Construct from the subexpression to store. */
+ explicit MatrixXpr(expr_reference expr) : m_expr(expr) {}
+
+ /** Copy constructor. */
+ MatrixXpr(const expr_type& e) : m_expr(e.m_expr) {}
+
+
+ protected:
+
+ value_type basis_element(size_t i, size_t j, row_basis) const {
+ return (*this)(i,j);
+ }
+
+ value_type basis_element(size_t i, size_t j, col_basis) const {
+ return (*this)(j,i);
+ }
+
+
+ protected:
+
+ expr_reference m_expr;
+
+
+ private:
+
+ /* Cannot be assigned to: */
+ expr_type& operator=(const expr_type&);
+};
+
+/** Expression traits for MatrixXpr<>. */
+template<class ExprT>
+struct ExprTraits< MatrixXpr<ExprT> >
+{
+ typedef MatrixXpr<ExprT> expr_type;
+ typedef ExprT arg_type;
+
+ typedef typename expr_type::value_type value_type;
+ typedef typename expr_type::expr_const_reference const_reference;
+ typedef typename expr_type::result_tag result_tag;
+ typedef typename expr_type::size_tag size_tag;
+ typedef typename expr_type::result_type result_type;
+ typedef typename expr_type::assignable_tag assignable_tag;
+ typedef expr_node_tag node_tag;
+
+ value_type get(const expr_type& e, size_t i, size_t j) const {
+ return e(i,j);
+ }
+
+
+ matrix_size size(const expr_type& e) const { return e.size(); }
+ size_t rows(const expr_type& e) const { return e.rows(); }
+ size_t cols(const expr_type& e) const { return e.cols(); }
+};
+
+
+/** A unary matrix expression operating on matrix elements as a list.
+ *
+ * The operator must take exactly one argument.
+ */
+template<class ExprT, class OpT>
+class UnaryMatrixOp
+{
+ public:
+
+ typedef UnaryMatrixOp<ExprT,OpT> expr_type;
+
+ /* Record ary-ness of the expression: */
+ typedef unary_expression expr_ary;
+
+ /* Copy the expression by value into higher-up expressions: */
+ typedef expr_type expr_const_reference;
+
+ typedef typename OpT::value_type value_type;
+ typedef matrix_result_tag result_tag;
+ typedef typename ExprT::size_tag size_tag;
+
+ /* Store the expression traits for the subexpression: */
+ typedef ExprTraits<ExprT> expr_traits;
+
+ /* Reference type for the subexpression: */
+ typedef typename expr_traits::const_reference expr_reference;
+
+ /* Get the result type: */
+ typedef typename expr_traits::result_type result_type;
+
+ /* Get the temporary type: */
+ typedef typename result_type::temporary_type temporary_type;
+
+ /* For matching by assignability: */
+ typedef cml::et::not_assignable_tag assignable_tag;
+
+
+ public:
+
+ /** Record result size as an enum (if applicable). */
+ enum { array_rows = ExprT::array_rows, array_cols = ExprT::array_cols };
+
+
+ public:
+
+ /** Return the expression size as a pair. */
+ matrix_size size() const {
+ return matrix_size(this->rows(),this->cols());
+ }
+
+ /** Return number of rows in the expression (same as argument). */
+ size_t rows() const {
+ return expr_traits().rows(m_expr);
+ }
+
+ /** Return number of columns in the expression (same as argument). */
+ size_t cols() const {
+ return expr_traits().cols(m_expr);
+ }
+
+ /** Compute value at index i,j of the result matrix. */
+ value_type operator()(size_t i, size_t j) const {
+
+ /* This uses the expression traits to figure out how to access the
+ * i,j'th element of the subexpression:
+ */
+ return OpT().apply(expr_traits().get(m_expr,i,j));
+ }
+
+
+ public:
+
+ /** Construct from the subexpression. */
+ explicit UnaryMatrixOp(expr_reference expr) : m_expr(expr) {}
+
+ /** Copy constructor. */
+ UnaryMatrixOp(const expr_type& e) : m_expr(e.m_expr) {}
+
+
+ protected:
+
+ expr_reference m_expr;
+
+
+ private:
+
+ /* Cannot be assigned to: */
+ expr_type& operator=(const expr_type&);
+};
+
+/** Expression traits for UnaryMatrixOp<>. */
+template<class ExprT, class OpT>
+struct ExprTraits< UnaryMatrixOp<ExprT,OpT> >
+{
+ typedef UnaryMatrixOp<ExprT,OpT> expr_type;
+ typedef ExprT arg_type;
+
+ typedef typename expr_type::value_type value_type;
+ typedef typename expr_type::expr_const_reference const_reference;
+ typedef typename expr_type::result_tag result_tag;
+ typedef typename expr_type::size_tag size_tag;
+ typedef typename expr_type::result_type result_type;
+ typedef typename expr_type::assignable_tag assignable_tag;
+ typedef expr_node_tag node_tag;
+
+ value_type get(const expr_type& e, size_t i, size_t j) const {
+ return e(i,j);
+ }
+
+ matrix_size size(const expr_type& e) const { return e.size(); }
+ size_t rows(const expr_type& e) const { return e.rows(); }
+ size_t cols(const expr_type& e) const { return e.cols(); }
+};
+
+
+/** A binary matrix expression. */
+template<class LeftT, class RightT, class OpT>
+class BinaryMatrixOp
+{
+ public:
+
+ typedef BinaryMatrixOp<LeftT,RightT,OpT> expr_type;
+
+ /* Copy the UnaryMatrixOp expression by value into parent
+ * expression tree nodes:
+ */
+ typedef expr_type expr_const_reference;
+
+ typedef typename OpT::value_type value_type;
+ typedef matrix_result_tag result_tag;
+
+ /* For matching by assignability: */
+ typedef cml::et::not_assignable_tag assignable_tag;
+
+ /* Record the expression traits for the two subexpressions: */
+ typedef ExprTraits<LeftT> left_traits;
+ typedef ExprTraits<RightT> right_traits;
+
+ /* Reference types for the two subexpressions: */
+ typedef typename left_traits::const_reference left_reference;
+ typedef typename right_traits::const_reference right_reference;
+
+ /* Figure out the expression's resulting (matrix) type: */
+ typedef typename left_traits::result_type left_result;
+ typedef typename right_traits::result_type right_result;
+ typedef typename MatrixPromote<left_result,right_result>::type result_type;
+ typedef typename result_type::size_tag size_tag;
+
+ /* Get the temporary type: */
+ typedef typename result_type::temporary_type temporary_type;
+
+ /* Define a size checker: */
+ typedef GetCheckedSize<LeftT,RightT,size_tag> checked_size;
+
+
+ public:
+
+ /** Record result size as an enum (if applicable).
+ *
+ * CheckExprSizes<> ensures that this works as expected.
+ */
+ enum {
+ array_rows = result_type::array_rows,
+ array_cols = result_type::array_cols
+ };
+
+
+ public:
+
+ /** Return the expression size as a pair. */
+ matrix_size size() const {
+ return CheckedSize(m_left,m_right,size_tag());
+ }
+
+ /** Return number of rows in the result.
+ *
+ * @note Because this calls size() internally, calling both rows()
+ * and cols() with CML_CHECK_MATRIX_EXPR_SIZES defined will cause the size
+ * checking code to be executed twice.
+ */
+ size_t rows() const {
+#if defined(CML_CHECK_MATRIX_EXPR_SIZES)
+ return this->size().first;
+#else
+ return left_traits().rows(m_left);
+#endif
+ }
+
+ /** Return number of cols in the result.
+ *
+ * @note Because this calls size() internally, calling both rows()
+ * and cols() with CML_CHECK_MATRIX_EXPR_SIZES defined will cause the size
+ * checking code to be executed twice.
+ */
+ size_t cols() const {
+#if defined(CML_CHECK_MATRIX_EXPR_SIZES)
+ return this->size().second;
+#else
+ return right_traits().cols(m_right);
+#endif
+ }
+
+ /** Compute value at index i,j of the result matrix. */
+ value_type operator()(size_t i, size_t j) const {
+
+ /* This uses the expression traits to figure out how to access the
+ * i'th index of the two subexpressions:
+ */
+ return OpT().apply(
+ left_traits().get(m_left,i,j),
+ right_traits().get(m_right,i,j));
+ }
+
+
+ public:
+
+ /** Construct from the two subexpressions.
+ *
+ * @throws std::invalid_argument if the subexpression sizes don't
+ * match.
+ */
+ explicit BinaryMatrixOp(left_reference left, right_reference right)
+ : m_left(left), m_right(right) {}
+
+ /** Copy constructor. */
+ BinaryMatrixOp(const expr_type& e)
+ : m_left(e.m_left), m_right(e.m_right) {}
+
+
+ protected:
+
+ left_reference m_left;
+ right_reference m_right;
+
+
+ private:
+
+ /* This ensures that a compile-time size check is executed: */
+ typename checked_size::check_type _dummy;
+
+
+ private:
+
+ /* Cannot be assigned to: */
+ expr_type& operator=(const expr_type&);
+};
+
+/** Expression traits for BinaryMatrixOp<>. */
+template<class LeftT, class RightT, class OpT>
+struct ExprTraits< BinaryMatrixOp<LeftT,RightT,OpT> >
+{
+ typedef BinaryMatrixOp<LeftT,RightT,OpT> expr_type;
+ typedef LeftT left_type;
+ typedef RightT right_type;
+
+ typedef typename expr_type::value_type value_type;
+ typedef typename expr_type::expr_const_reference const_reference;
+ typedef typename expr_type::result_tag result_tag;
+ typedef typename expr_type::size_tag size_tag;
+ typedef typename expr_type::result_type result_type;
+ typedef typename expr_type::assignable_tag assignable_tag;
+ typedef expr_node_tag node_tag;
+
+ value_type get(const expr_type& e, size_t i, size_t j) const {
+ return e(i,j);
+ }
+
+ matrix_size size(const expr_type& e) const { return e.size(); }
+ size_t rows(const expr_type& e) const { return e.rows(); }
+ size_t cols(const expr_type& e) const { return e.cols(); }
+};
+
+/* Helper struct to verify that both arguments are matrix expressions: */
+template<typename LeftTraits, typename RightTraits>
+struct MatrixExpressions
+{
+ /* Require that both arguments are matrix expressions: */
+ typedef typename LeftTraits::result_tag left_result;
+ typedef typename RightTraits::result_tag right_result;
+ enum { is_true = (same_type<left_result,et::matrix_result_tag>::is_true
+ && same_type<right_result,et::matrix_result_tag>::is_true) };
+};
+
+namespace detail {
+
+/* XXX These are temporary helpers until dynamic resizing is integrated more
+ * naturally into mul() and matrix transpose():
+ */
+template<typename MatT, typename MT> inline
+void Resize(MatT&, size_t, size_t, fixed_size_tag, MT) {}
+
+template<typename MatT> inline
+void Resize(MatT& m,
+ size_t R, size_t C, dynamic_size_tag, dynamic_memory_tag)
+{
+ m.resize(R,C);
+}
+
+template<typename MatT> inline
+void Resize(MatT& m, size_t R, size_t C) {
+ Resize(m, R, C, typename MatT::size_tag(), typename MatT::memory_tag());
+}
+
+template<typename MatT> inline
+void Resize(MatT& m, matrix_size N) {
+ Resize(m, N.first, N.second,
+ typename MatT::size_tag(), typename MatT::memory_tag());
+}
+
+} // namespace detail
+
+} // namespace et
+} // namespace cml
+
+#endif
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp
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