matrix.h File Reference

Contains definitions of matrix and vector template classes and other useful stuff. More...

Go to the source code of this file.

Classes
struct	access_error
	Access error. More...
struct	add< type1, type2 >
	Binary addition operator. More...
struct	base_column_iterator< iterator_type >
	Base type for column iterators. More...
struct	base_matrix_expression< value_t, expr_t, tag, shape >
	Base matrix expression template class. More...
struct	base_matrix_expression< value_t, expr_t, tag, rectangular >
	Base matrix expression template class partial specialization. More...
struct	base_row_iterator< iterator_type >
	Base type for row iterators. More...
struct	base_vector_iterator< iterator_type >
	Base type for vector iterators. More...
class	binary< expression1, expression2, op >
	Binary expression template class. More...
class	binary< vector_expression< value_t, expr1, tag1 >, vector_expression< value_t, expr2, tag2 >, op >
	Binary expression template class specialization. More...
struct	column
	Column vector orientation. More...
struct	column_const_iterator< t >
	Iterator type for iterating over a column of a matrix. More...
struct	column_iterator< t >
	Iterator type for iterating over a column of a matrix. More...
class	column_wrapper< value_t, expr_t, tag_t >
	Column vector wrapper template class. More...
struct	conj< type >
	Unary conjugate operation. More...
struct	const_iterator< t >
	Iterator type for iterating over a vector. More...
struct	const_iterator< vector_ref< expression_type, tag, orientation::column > >
	Iterator type for iterating over a row of a matrix. More...
struct	const_iterator< vector_ref< expression_type, tag, orientation::row > >
	Iterator type for iterating over a row of a matrix. More...
struct	constrained_index
	Constrained index. More...
struct	div< type1, type2 >
	Binary division operator. More...
struct	expr_traits< matrix_expression< value_t, expr_t, tag_t > >
	Expression traits template class partial specialization. More...
struct	expr_traits< shaped_expression< value_t, expr_t, tag_t, shape_t > >
	Expression traits template class partial specialization. More...
struct	expr_traits< vector_expression< value_t, expr_t, tag_t, orientation_t > >
	Expression traits template class partial specialization. More...
struct	expression< complexity >
	Expression tag. More...
struct	iterator< t >
	Iterator type for iterating over a vector. More...
struct	iterator< vector_ref< expression_type, tag, orientation::column > >
	Iterator type for iterating over a row of a matrix. More...
struct	iterator< vector_ref< expression_type, tag, orientation::row > >
	Iterator type for iterating over a row of a matrix. More...
struct	lower_triangular
	Lower triangle shape of matrix. More...
class	matrix< value_t, shape >
	Square matrix template class. More...
class	matrix< value_t, rectangular >
	General matrix template class. More...
struct	matrix_expression< value_t, expr_t, tag >
	Matrix expression template class. More...
struct	minus< type >
	Unary minus operator. More...
struct	mul< type1, type2 >
	Binary multiplication operator. More...
struct	operation< type >
	Unary "no op" operator. More...
struct	pair_const_ref< expr1, expr2 >
	Pair of references. More...
struct	plus< type >
	Unary plus operator. More...
class	product< expression1, expression2 >
	Matrix product template class. More...
class	product< expression1, vector_expression< value_t, expr2, tag2 > >
	Matrix product template class partial specialization. More...
struct	rectangular
	General shape of matrix. More...
struct	reference
	Reference tag. More...
struct	reshape_constraint< target_shape >
	Constraints for reshape operation template class. More...
struct	reshape_constraint< rectangular >
	Constraints for reshape operation template class specialization. More...
struct	reshape_error
	Reshape exception class. More...
struct	reshape_return< matrix_expression< value_t, expr_t, tag >, rectangular, side >
	Defines reshape() return type. More...
struct	reshape_return< matrix_expression< value_t, expr_t, tag >, target_shape, side >
	Defines reshape() return type. More...
class	reshaped< matrix_expression< value_t, expr_t, tag_t >, target_shape, lower_triangular >
	Partial specialization of reshaped. More...
class	reshaped< matrix_expression< value_t, expr_t, tag_t >, target_shape, upper_triangular >
	Partial specialization of reshaped. More...
struct	row
	Row vector orientation. More...
struct	row_const_iterator< t >
	Iterator type for iterating over a row of a matrix. More...
struct	row_iterator< t >
	Iterator type for iterating over a row of a matrix. More...
class	row_wrapper< value_t, expr_t, tag_t >
	Row vector wrapper template class. More...
struct	rvalue< type >
	Represents an "rvalue". More...
class	scaled< expression_type >
	Scaled expression template class. More...
class	scaled< vector_expression< value_t, expr_t, tag_t > >
	Scaled expression template class partial specialization. More...
struct	shaped_expression< value_t, expr_t, tag_t, shape >
	Shaped matrix expression template class. More...
struct	size_error
	Argument size error. More...
struct	storage
	Storage tag. More...
struct	sub< type1, type2 >
	Binary subtraction operator. More...
struct	symmetric
	Symmetric shape of matrix. More...
class	temporary< type >
	Temporary object template class. More...
class	traits< type >
	Type traits class. More...
class	transposed< expression_type, op >
	Transposition expression template class. More...
struct	column_const_iterator< matrix< value_t > >::type
	Iterator type. More...
struct	column_iterator< matrix< value_t > >::type
	Iterator type. More...
struct	row_const_iterator< matrix< value_t > >::type
	Iterator type. More...
struct	row_iterator< matrix< value_t > >::type
	Iterator type. More...
struct	column_const_iterator< matrix< value_t, symmetric > >::type
	Iterator type. More...
struct	column_iterator< matrix< value_t, symmetric > >::type
	Iterator type. More...
struct	row_const_iterator< matrix< value_t, symmetric > >::type
	Iterator type. More...
struct	row_iterator< matrix< value_t, symmetric > >::type
	Iterator type. More...
struct	const_iterator< t >::type
	Iterator type. More...
struct	iterator< t >::type
	Iterator type. More...
struct	column_const_iterator< t >::type
	Iterator type. More...
struct	column_iterator< t >::type
	Iterator type. More...
struct	row_const_iterator< t >::type
	Iterator type. More...
struct	row_iterator< t >::type
	Iterator type. More...
class	unary< expression_type, op >
	Unary expression template class. More...
class	unary< vector_expression< value_t, expr_t, tag_t >, op >
	Unary expression template class specialization. More...
struct	undefined
	Undefined orientation of vector. More...
struct	upper_triangular
	Upper triangle shape of matrix. More...
class	vector< value_t >
	Vector template class. More...
struct	vector_expression< value_t, expr_t, tag, orientation >
	Vector expression template class. More...
class	vector_expression< value_t, expr_t, tag, orientation::column >
	Vector expression template class specialization. More...
class	vector_expression< value_t, expr_t, tag, orientation::row >
	Vector expression template class specialization. More...
class	vector_ref< expression_type, tag::expression< complexity >, orientation::column >
	Constant column reference template class partial specialization. More...
class	vector_ref< expression_type, tag::expression< complexity >, orientation::row >
	Constant row reference template class partial specialization. More...
class	vector_ref< expression_type, tag::reference, orientation::column >
	Column reference template class partial specialization. More...
class	vector_ref< expression_type, tag::reference, orientation::row >
	Row reference template class partial specialization. More...

Namespaces
namespace	nabla
	Contains matrix and vector template classes and related stuff.
namespace	nabla::dummy
	Contains dummy entities.
namespace	nabla::op
	Contains scalar operations.
namespace	nabla::orientation
	Contains definitions for vector orientation types.
namespace	nabla::tag
	Contains expression tags.

Typedefs
typedef lower_triangular	lower_tr
	Convenient alias for lower_triangular matrix shape.
typedef upper_triangular	upper_tr
	Convenient alias for upper_triangular matrix shape.

Functions
template<typename value_t , typename expr_t , typename tag >
iterator< expr_t >::type	begin (vector_expression< value_t, expr_t, tag > &v, size_t i=0)
	Returns iterator.
template<typename value_t , typename expr_t , typename tag >
const_iterator< expr_t >::type	begin (const vector_expression< value_t, expr_t, tag > &v, size_t i=0)
	Returns iterator.
template<typename value_t >
const value_t &	conj (const value_t &a)
	This function returns its argument. It does nothing.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
op::mul< value_t, value_t > ::result_type	sum_of_products (const vector_expression< value_t, expr1, tag1 > &a, const vector_expression< value_t, expr2, tag2 > &b)
	Returns sum of products of corresponding elements.
Implementation details
template<typename expr_t >
util::non_zero_in_row < rectangular >::first_type	first_non_zero_in_row (const expr_t &m, size_t row)
	Returns index of the first non zero element in row row.
template<typename expr_t >
util::non_zero_in_row < rectangular >::last_type	last_non_zero_in_row (const expr_t &m, size_t row)
	Returns index of the last non zero element in row row.
template<typename expr_t >
util::non_zero_in_column < rectangular >::first_type	first_non_zero_in_column (const expr_t &m, size_t column)
	Returns index of the first non zero element in column column.
template<typename expr_t >
util::non_zero_in_column < rectangular >::last_type	last_non_zero_in_column (const expr_t &m, size_t column)
	Returns index of the last non zero element in column column.
template<typename expr_t >
orientation::undefined	orientation_type (expr_t *)
	Defines orientation type for arbitrary vector.
template<typename type >
rvalue< type > &	to_rvalue_ref (type &a)
	Turns a reference into a "reference to rvalue".
template<typename expression_type , typename tag >
util::non_zero_in_row < typename expr_traits < expression_type >::shape > ::first_type	first_non_zero (const vector_ref< expression_type, tag, orientation::row > &v)
	Returns index of the first non zero element in row reference.
template<typename expression_type , typename tag >
util::non_zero_in_row < typename expr_traits < expression_type >::shape > ::last_type	last_non_zero (const vector_ref< expression_type, tag, orientation::row > &v)
	Returns index of the last non zero element in row reference.
template<typename expression_type , typename tag >
util::non_zero_in_column < typename expr_traits < expression_type >::shape > ::first_type	first_non_zero (const vector_ref< expression_type, tag, orientation::column > &v)
	Returns index of the first non zero element in row reference.
template<typename expression_type , typename tag >
util::non_zero_in_column < typename expr_traits < expression_type >::shape > ::last_type	last_non_zero (const vector_ref< expression_type, tag, orientation::column > &v)
	Returns index of the last non zero element in row reference.
template<typename expr_t >
size_t	first_non_zero (const expr_t &)
	Returns index of the first non zero element in vector v.
template<typename expr_t >
size_t	last_non_zero (const expr_t &v)
	Returns index of the first non zero element in row row.
template<typename expr1 , typename expr2 >
size_t	first_non_zero (const expr1 &a, const expr2 &b)
	Returns index of the first non zero element in both vectors.
template<typename expr1 , typename expr2 >
size_t	last_non_zero (const expr1 &a, const expr2 &b)
	Returns index of the last non zero element in both vectors.
Miscellaneous
template<typename value_t , typename expr_t , typename tag >
expr_t &	get_matrix (matrix_expression< value_t, expr_t, tag > &a)
	Returns underlying matrix expression.
template<typename value_t , typename expr_t , typename tag >
const expr_t &	get_matrix (const matrix_expression< value_t, expr_t, tag > &a)
	Returns underlying matrix expression.
template<typename value_t , typename expr_t , typename tag >
expr_t &	get_vector (vector_expression< value_t, expr_t, tag > &a)
	Returns underlying vector expression.
template<typename value_t , typename expr_t , typename tag >
const expr_t &	get_vector (const vector_expression< value_t, expr_t, tag > &a)
	Returns underlying vector expression.
template<typename value_t , typename expr_t >
void	swap (matrix_expression< value_t, expr_t, tag::storage > &a, matrix_expression< value_t, expr_t, tag::storage > &b)
	Swaps contents of two matrices.
template<typename value_t , typename expr_t , typename shape >
void	swap (shaped_expression< value_t, expr_t, tag::storage, shape > &a, shaped_expression< value_t, expr_t, tag::storage, shape > &b)
	Swaps contents of two matrices.
template<typename target_shape , typename value_t , typename expr_t , typename tag >
util::reshape_return < matrix_expression< value_t, expr_t, tag >, target_shape > ::type	reshape (const matrix_expression< value_t, expr_t, tag > &a)
	Reshapes a matrix expression.
template<typename target_shape , typename side , typename value_t , typename expr_t , typename tag >
util::reshape_return < matrix_expression< value_t, expr_t, tag >, target_shape, side >::type	reshape (const matrix_expression< value_t, expr_t, tag > &a)
	Returns underlying matrix expression.
template<typename value_t , typename expr_t , typename tag >
util::row_ref < matrix_expression< value_t, expr_t, tag > >::type	row (matrix_expression< value_t, expr_t, tag > &a, size_t r)
	Returns reference to a matrix row.
template<typename value_t , typename expr_t , typename tag_t >
util::const_row_ref < matrix_expression< value_t, expr_t, tag_t > >::type	row (const matrix_expression< value_t, expr_t, tag_t > &a, size_t r)
	Returns reference to a matrix row.
template<typename value_t , typename expr_t , typename tag , typename shape >
util::row_ref < shaped_expression< value_t, expr_t, tag, shape > >::type	row (shaped_expression< value_t, expr_t, tag, shape > &a, size_t r)
	Returns reference to a matrix row.
template<typename value_t , typename expr_t , typename tag_t , typename shape >
util::const_row_ref < shaped_expression< value_t, expr_t, tag_t, shape > >::type	row (const shaped_expression< value_t, expr_t, tag_t, shape > &a, size_t r)
	Returns reference to a matrix row.
template<typename value_t , typename expr_t , typename tag >
util::column_ref < matrix_expression< value_t, expr_t, tag > >::type	column (matrix_expression< value_t, expr_t, tag > &a, size_t c)
	Returns reference to a matrix column.
template<typename value_t , typename expr_t , typename tag_t >
util::const_column_ref < matrix_expression< value_t, expr_t, tag_t > >::type	column (const matrix_expression< value_t, expr_t, tag_t > &a, size_t c)
	Returns reference to a matrix column.
template<typename value_t , typename expr_t , typename tag , typename shape >
util::column_ref < shaped_expression< value_t, expr_t, tag, shape > >::type	column (shaped_expression< value_t, expr_t, tag, shape > &a, size_t c)
	Returns reference to a matrix column.
template<typename value_t , typename expr_t , typename tag_t , typename shape >
util::const_column_ref < shaped_expression< value_t, expr_t, tag_t, shape > >::type	column (const shaped_expression< value_t, expr_t, tag_t, shape > &a, size_t c)
	Returns reference to a matrix column.
template<typename value_t , typename expr_t >
void	swap (vector_expression< value_t, expr_t, tag::storage > &a, vector_expression< value_t, expr_t, tag::storage > &b)
	Swaps contents of two vectors.
template<typename value_t , typename expr1 , typename expr2 >
void	swap (vector_expression< value_t, expr1, tag::storage > &a, vector_expression< value_t, expr2, tag::storage > &b)
	Swaps contents of two vector expressions.
template<typename value_t , typename expr1 , typename expr2 , typename orientation >
void	swap (vector_expression< value_t, expr1, tag::storage > &a, vector_ref< expr2, tag::reference, orientation > b)
	Swaps contents of two vector expressions.
template<typename expr1 , typename orientation , typename value_t , typename expr2 >
void	swap (vector_ref< expr1, tag::reference, orientation > a, vector_expression< value_t, expr2, tag::storage > &b)
	Swaps contents of two vector expressions.
template<typename expr1 , typename orientation1 , typename expr2 , typename orientation2 >
void	swap (vector_ref< expr1, tag::reference, orientation1 > a, vector_ref< expr2, tag::reference, orientation2 > b)
	Swaps contents of two vector expressions.
Matrix operations
template<typename value_t , typename expr_t , typename tag >
const unary< matrix_expression < value_t, expr_t, tag > , op::plus >	operator+ (const matrix_expression< value_t, expr_t, tag > &a)
	Unary plus operator.
template<typename value_t , typename expr_t , typename tag , typename shape >
const unary< shaped_expression < value_t, expr_t, tag, shape > , op::plus >	operator+ (const shaped_expression< value_t, expr_t, tag, shape > &a)
	Unary plus operator.
template<typename value_t , typename expr_t , typename tag >
const unary< matrix_expression < value_t, expr_t, tag > , op::minus >	operator- (const matrix_expression< value_t, expr_t, tag > &a)
	Unary minus operator.
template<typename value_t , typename expr_t , typename tag , typename shape >
const unary< shaped_expression < value_t, expr_t, tag, shape > , op::minus >	operator- (const shaped_expression< value_t, expr_t, tag, shape > &a)
	Unary minus operator.
template<typename value_t , typename expr_t , typename tag >
const unary< matrix_expression < value_t, expr_t, tag > , op::conj >	conj (const matrix_expression< value_t, expr_t, tag > &a)
	Returns conjugated matrix.
template<typename value_t , typename expr_t , typename tag , typename shape >
const unary< shaped_expression < value_t, expr_t, tag, shape > , op::conj >	conj (const shaped_expression< value_t, expr_t, tag, shape > &a)
	Returns conjugated matrix.
template<typename value_t , typename expr_t , typename tag >
const transposed < matrix_expression< value_t, expr_t, tag > >	transpose (const matrix_expression< value_t, expr_t, tag > &a)
	Returns transposed matrix.
template<typename value_t , typename expr_t , typename tag , typename shape >
const transposed < shaped_expression< value_t, expr_t, tag, shape > >	transpose (const shaped_expression< value_t, expr_t, tag, shape > &a)
	Returns transposed matrix.
template<typename value_t , typename expr_t , typename tag >
const expr_t &	transpose (const shaped_expression< value_t, expr_t, tag, symmetric > &a)
	Returns transposed matrix.
template<typename value_t , typename expr_t , typename tag >
const reshaped < shaped_expression< value_t, expr_t, tag, lower_triangular > , upper_triangular, lower_triangular >	transpose (const shaped_expression< value_t, expr_t, tag, lower_triangular > &a)
	Returns transposed matrix.
template<typename value_t , typename expr_t , typename tag >
const reshaped < shaped_expression< value_t, expr_t, tag, upper_triangular > , lower_triangular, upper_triangular >	transpose (const shaped_expression< value_t, expr_t, tag, upper_triangular > &a)
	Returns transposed matrix.
template<typename value_t , typename expr_t , typename tag >
const scaled < matrix_expression< value_t, expr_t, tag > >	operator* (const matrix_expression< value_t, expr_t, tag > &a, const typename expr_t::value_type &s)
	Binary multiplication operator.
template<typename value_t , typename expr_t , typename tag , typename shape >
const scaled < shaped_expression< value_t, expr_t, tag, shape > >	operator* (const shaped_expression< value_t, expr_t, tag, shape > &a, const typename expr_t::value_type &s)
	Binary multiplication operator.
template<typename value_t , typename expr_t , typename tag >
const scaled < matrix_expression< value_t, expr_t, tag > >	operator* (const typename expr_t::value_type &s, const matrix_expression< value_t, expr_t, tag > &a)
	Binary multiplication operator.
template<typename value_t , typename expr_t , typename tag , typename shape >
const scaled < shaped_expression< value_t, expr_t, tag, shape > >	operator* (const typename expr_t::value_type &s, const shaped_expression< value_t, expr_t, tag, shape > &a)
	Binary multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < matrix_expression< value_t, expr1, tag1 > , matrix_expression< value_t, expr2, tag2 >, op::add >	operator+ (const matrix_expression< value_t, expr1, tag1 > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Binary addition operator.
template<typename value_t , typename expr1 , typename tag1 , typename shape1 , typename expr2 , typename tag2 , typename shape2 >
const binary < shaped_expression< value_t, expr1, tag1, shape1 > , shaped_expression< value_t, expr2, tag2, shape1 >, op::add >	operator+ (const shaped_expression< value_t, expr1, tag1, shape1 > &left, const shaped_expression< value_t, expr2, tag2, shape2 > &right)
	Binary addition operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < matrix_expression< value_t, expr1, tag1 > , matrix_expression< value_t, expr2, tag2 >, op::sub >	operator- (const matrix_expression< value_t, expr1, tag1 > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Binary subtraction operator.
template<typename value_t , typename expr1 , typename tag1 , typename shape1 , typename expr2 , typename tag2 , typename shape2 >
const binary < shaped_expression< value_t, expr1, tag1, shape1 > , shaped_expression< value_t, expr2, tag2, shape2 >, op::sub >	operator- (const shaped_expression< value_t, expr1, tag1, shape1 > &left, const shaped_expression< value_t, expr2, tag2, shape2 > &right)
	Binary subtraction operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < matrix_expression< value_t, expr1, tag1 > , matrix_expression< value_t, expr2, tag2 >, op::mul >	mul (const matrix_expression< value_t, expr1, tag1 > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Binary element-wise multiplication operation.
template<typename value_t , typename expr1 , typename tag1 , typename shape1 , typename expr2 , typename tag2 , typename shape2 >
const binary < shaped_expression< value_t, expr1, tag1, shape1 > , shaped_expression< value_t, expr2, tag2, shape2 >, op::mul >	mul (const shaped_expression< value_t, expr1, tag1, shape1 > &left, const shaped_expression< value_t, expr2, tag2, shape2 > &right)
	Binary element-wise multiplication operation.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < matrix_expression< value_t, expr1, tag1 > , matrix_expression< value_t, expr2, tag2 >, op::div >	div (const matrix_expression< value_t, expr1, tag1 > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Binary element-wise multiplication operation.
template<typename value_t , typename expr1 , typename tag1 , typename shape1 , typename expr2 , typename tag2 , typename shape2 >
const binary < shaped_expression< value_t, expr1, tag1, shape1 > , shaped_expression< value_t, expr2, tag2, shape2 >, op::div >	div (const shaped_expression< value_t, expr1, tag1, shape1 > &left, const shaped_expression< value_t, expr2, tag2, shape2 > &right)
	Binary element-wise multiplication operation.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
product< matrix_expression < value_t, expr1, tag1 > , matrix_expression< value_t, expr2, tag2 > >	operator* (const matrix_expression< value_t, expr1, tag1 > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Binary matrix multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename shape1 , typename expr2 , typename tag2 , typename shape2 >
product< shaped_expression < value_t, expr1, tag1, shape1 > , shaped_expression< value_t, expr2, tag2, shape2 > >	operator* (const shaped_expression< value_t, expr1, tag1, shape1 > &left, const shaped_expression< value_t, expr2, tag2, shape2 > &right)
	Binary matrix multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
product< matrix_expression < value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 > >	operator* (const matrix_expression< value_t, expr1, tag1 > &left, const vector_expression< value_t, expr2, tag2, orientation::column > &right)
	Binary matrix-vector multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename shape , typename expr2 , typename tag2 >
product< shaped_expression < value_t, expr1, tag1, shape > , vector_expression< value_t, expr2, tag2 > >	operator* (const shaped_expression< value_t, expr1, tag1, shape > &left, const vector_expression< value_t, expr2, tag2, orientation::column > &right)
	Binary matrix-vector multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
product< matrix_expression < value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 > >	map (const matrix_expression< value_t, expr1, tag1 > &linear_map, const vector_expression< value_t, expr2, tag2 > &v)
	Transforms a vector using provided transformation map.
template<typename value_t , typename expr1 , typename tag1 , typename shape , typename expr2 , typename tag2 >
product< shaped_expression < value_t, expr1, tag1, shape > , vector_expression< value_t, expr2, tag2 > >	map (const shaped_expression< value_t, expr1, tag1, shape > &linear_map, const vector_expression< value_t, expr2, tag2 > &v)
	Transforms a vector using provided transformation map.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator+= (matrix_expression< value_t, expr1, tag::storage > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Matrix addition assignment operator.
template<typename value_t , typename expr1 , typename shape , typename expr2 , typename tag2 >
expr1 &	operator+= (shaped_expression< value_t, expr1, tag::storage, shape > &left, const shaped_expression< value_t, expr2, tag2, shape > &right)
	Matrix addition assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator-= (matrix_expression< value_t, expr1, tag::storage > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Matrix subtraction assignment operator.
template<typename value_t , typename expr1 , typename shape , typename expr2 , typename tag2 >
expr1 &	operator-= (shaped_expression< value_t, expr1, tag::storage, shape > &left, const shaped_expression< value_t, expr2, tag2, shape > &right)
	Matrix subtraction assignment operator.
template<typename value_t , typename expr_t >
expr_t &	operator*= (matrix_expression< value_t, expr_t, tag::storage > &left, const value_t &right)
	Matrix multiplication assignment operator.
template<typename value_t , typename expr_t , typename shape >
expr_t &	operator*= (shaped_expression< value_t, expr_t, tag::storage, shape > &left, const value_t &right)
	Matrix multiplication assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator*= (matrix_expression< value_t, expr1, tag::storage > &left, const matrix_expression< value_t, expr2, tag2 > &right)
	Matrix multiplication assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator*= (shaped_expression< value_t, expr1, tag::storage, lower_triangular > &left, const shaped_expression< value_t, expr2, tag2, lower_triangular > &right)
	Matrix multiplication assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator*= (shaped_expression< value_t, expr1, tag::storage, upper_triangular > &left, const shaped_expression< value_t, expr2, tag2, upper_triangular > &right)
	Matrix multiplication assignment operator.
Vector operations
template<template< typename, typename > class op, typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
op< value_t, value_t >::result_type	accumulate (const vector_expression< value_t, expr1, tag1 > &a, const vector_expression< value_t, expr2, tag2 > &b)
	Accumulates combined values of two vectors.
template<template< typename, typename > class op_t, typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
op_t< value_t, value_t > ::result_type	accumulate_skip_zeros (const vector_expression< value_t, expr1, tag1 > &a, const vector_expression< value_t, expr2, tag2 > &b)
	Accumulates combined values of two vectors.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
util::mul_conj< value_t, value_t >::result_type	dot_product (const vector_expression< value_t, expr1, tag1 > &v1, const vector_expression< value_t, expr2, tag2 > &v2)
	Dot product is a sum of products of corresponding elements of first vector and conjugated elements of the second one:
template<template< typename > class op, typename value_t , typename expr_t , typename tag >
op< value_t >::result_type	accumulate (const vector_expression< value_t, expr_t, tag > &a)
	Accumulates modified values of a vector.
template<template< typename > class op_t, typename value_t , typename expr_t , typename tag >
op_t< value_t >::result_type	accumulate_skip_zeros (const vector_expression< value_t, expr_t, tag > &a)
	Accumulates combined values of two vectors.
template<typename value_t , typename expr_t , typename tag >
value_t	sqrnorm (const vector_expression< value_t, expr_t, tag > &v)
	Returns squared Euclidean norm of a vector.
template<typename value_t , typename expr_t , typename tag >
value_t	norm (const vector_expression< value_t, expr_t, tag > &v)
	Returns Euclidean norm of a vector.
template<typename value_t , typename expr_t , typename tag >
const unary< vector_expression < value_t, expr_t, tag > , op::plus >	operator+ (const vector_expression< value_t, expr_t, tag > &a)
	Unary plus operator.
template<typename value_t , typename expr_t , typename tag >
const unary< vector_expression < value_t, expr_t, tag > , op::minus >	operator- (const vector_expression< value_t, expr_t, tag > &a)
	Unary minus operator.
template<typename value_t , typename expr_t , typename tag >
const unary< vector_expression < value_t, expr_t, tag > , op::conj >	conj (const vector_expression< value_t, expr_t, tag > &a)
	Returns conjugated vector.
template<typename value_t , typename expr_t , typename tag >
const scaled < vector_expression< value_t, expr_t, tag > >	operator* (const vector_expression< value_t, expr_t, tag > &a, const typename expr_t::value_type &s)
	Binary multiplication operator.
template<typename value_t , typename expr_t , typename tag >
const scaled < vector_expression< value_t, expr_t, tag > >	operator* (const typename expr_t::value_type &s, const vector_expression< value_t, expr_t, tag > &a)
	Binary multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < vector_expression< value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 >, op::add >	operator+ (const vector_expression< value_t, expr1, tag1 > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Binary addition operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < vector_expression< value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 >, op::sub >	operator- (const vector_expression< value_t, expr1, tag1 > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Binary subtraction operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < vector_expression< value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 >, op::mul >	mul (const vector_expression< value_t, expr1, tag1 > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Binary element-wise multiplication operator.
template<typename value_t , typename expr1 , typename tag1 , typename expr2 , typename tag2 >
const binary < vector_expression< value_t, expr1, tag1 > , vector_expression< value_t, expr2, tag2 >, op::div >	div (const vector_expression< value_t, expr1, tag1 > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Binary element-wise division operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator+= (vector_expression< value_t, expr1, tag::storage > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Vector addition assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator+= (vector_expression< value_t, expr1, tag::reference > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Vector addition assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator-= (vector_expression< value_t, expr1, tag::storage > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Vector subtraction assignment operator.
template<typename value_t , typename expr1 , typename expr2 , typename tag2 >
expr1 &	operator-= (vector_expression< value_t, expr1, tag::reference > &left, const vector_expression< value_t, expr2, tag2 > &right)
	Vector subtraction assignment operator.
template<typename value_t , typename expr_t >
expr_t &	operator*= (vector_expression< value_t, expr_t, tag::storage > &left, const value_t &right)
	Vector multiplication assignment operator.
template<typename value_t , typename expr_t >
expr_t &	operator*= (vector_expression< value_t, expr_t, tag::reference > &left, const value_t &right)
	Vector multiplication assignment operator.

Detailed Description

Contains definitions of matrix and vector template classes and other useful stuff.

Definition in file matrix.h.