...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
The templated class matrix_expression<E>
is required to be a public base of all classes which model the Matrix Expression concept.
Defined in the header expression_types.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None. Not a Matrix Expression!
None.
None.
Member | Description |
---|---|
const expression_type &operator () ()
const |
Returns a const reference of the expression. |
expression_type &operator () () |
Returns a reference of the expression. |
The operator[]
, row
, column
, range
, slice
and project
functions have been removed. Use the free functions defined in matrix proxy instead.
The templated class matrix_container<C>
is required to be a public base of all classes which model the Matrix concept.
This includes the class matrix
itself.
Defined in the header expression_types.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None. Not a Matrix Expression OR Matrix!
None.
matrix_expression<C>
Member | Description |
---|---|
const container_type &operator () ()
const |
Returns a const reference of the container. |
container_type &operator () () |
Returns a reference of the container. |
The templated class matrix_reference<E>
contains a reference to a matrix expression.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_reference<E>
>
Member | Description |
---|---|
matrix_reference (expression_type &e) |
Constructs a constant reference of the expression. |
void resize (size_type size1, size2) |
Resizes the expression to hold at most size1 rows
of size2 elements. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type j)
const |
Returns the value of the j -th element in the
i -th row. |
reference operator () (size_type i, size_type
j) |
Returns a reference of the j -th element in the
i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the expression. |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning of
the expression. |
iterator1 end1 () |
Returns a iterator1 pointing to the end of the
expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the expression. |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning of
the expression. |
iterator2 end2 () |
Returns a iterator2 pointing to the end of the
expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed expression. |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to the
beginning of the reversed expression. |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to the end of
the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed expression. |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to the
beginning of the reversed expression. |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to the end of
the reversed expression. |
The templated classes matrix_unary1<E, F>
and
matrix_unary2<E, F>
describe unary matrix
operations.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E |
The type of the matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_unary1<E, F> >
and matrix_expression<matrix_unary2<E, F>
>
resp.
Member | Description |
---|---|
matrix_unary1 (const expression_type &e) |
Constructs a description of the expression. |
matrix_unary2 (const expression_type &e) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type j)
const |
Returns the value of the j -th element in the
i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed expression. |
template<class E, class F>
struct matrix_unary1_traits {
typedef matrix_unary1<typename E::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (- m) [i] [j] = - m [i] [j]
template<class E>
typename matrix_unary1_traits<E, scalar_negate<typename E::value_type> >::result_type
operator - (const matrix_expression<E> &e);
// (conj m) [i] [j] = conj (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_conj<typename E::value_type> >::result_type
conj (const matrix_expression<E> &e);
// (real m) [i] [j] = real (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_real<typename E::value_type> >::result_type
real (const matrix_expression<E> &e);
// (imag m) [i] [j] = imag (m [i] [j])
template<class E>
typename matrix_unary1_traits<E, scalar_imag<typename E::value_type> >::result_type
imag (const matrix_expression<E> &e);
template<class E, class F>
struct matrix_unary2_traits {
typedef matrix_unary2<typename E::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (trans m) [i] [j] = m [j] [i]
template<class E>
typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type
trans (const matrix_expression<E> &e);
// (herm m) [i] [j] = conj (m [j] [i])
template<class E>
typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type
herm (const matrix_expression<E> &e);
operator -
computes the additive inverse of a
matrix expression. conj
computes the complex conjugate
of a matrix expression. real
and imag
compute the real and imaginary parts of a matrix expression.
trans
computes the transpose of a matrix expression.
herm
computes the hermitian, i.e. the complex
conjugate of the transpose of a matrix expression.
Defined in the header matrix_expression.hpp.
E
is a model of Matrix Expression .None.
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<std::complex<double> > m (3, 3); for (unsigned i = 0; i < m.size1 (); ++ i) for (unsigned j = 0; j < m.size2 (); ++ j) m (i, j) = std::complex<double> (3 * i + j, 3 * i + j); std::cout << - m << std::endl; std::cout << conj (m) << std::endl; std::cout << real (m) << std::endl; std::cout << imag (m) << std::endl; std::cout << trans (m) << std::endl; std::cout << herm (m) << std::endl; }
The templated class matrix_binary<E1, E2, F>
describes a binary matrix operation.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first matrix expression. | |
E2 |
The type of the second matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_binary<E1, E2, F>
>
.
Member | Description |
---|---|
matrix_binary (const expression1_type &e1, const
expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type j)
const |
Returns the value of the j -th element in the
i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed expression. |
template<class E1, class E2, class F>
struct matrix_binary_traits {
typedef matrix_binary<typename E1::const_closure_type,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (m1 + m2) [i] [j] = m1 [i] [j] + m2 [i] [j]
template<class E1, class E2>
typename matrix_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
typename E2::value_type> >::result_type
operator + (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
// (m1 - m2) [i] [j] = m1 [i] [j] - m2 [i] [j]
template<class E1, class E2>
typename matrix_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
typename E2::value_type> >::result_type
operator - (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
operator +
computes the sum of two matrix
expressions. operator -
computes the difference of two
matrix expressions.
Defined in the header matrix_expression.hpp.
E1
is a model of Matrix Expression .E2
is a model of Matrix Expression .e1 ().size1 () == e2 ().size1 ()
e1 ().size2 () == e2 ().size2 ()
Quadratic depending from the size of the matrix expressions.
#include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m1 (3, 3), m2 (3, 3); for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j) m1 (i, j) = m2 (i, j) = 3 * i + j; std::cout << m1 + m2 << std::endl; std::cout << m1 - m2 << std::endl; }
The templated classes matrix_binary_scalar1<E1, E2,
F>
and matrix_binary_scalar2<E1, E2,
F>
describe binary operations between a scalar and a
matrix.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1/E2 |
The type of the scalar expression. | |
E2/E1 |
The type of the matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_binary_scalar1<E1, E2,
F> >
and
matrix_expression<matrix_binary_scalar2<E1, E2, F>
>
resp.
Member | Description |
---|---|
matrix_binary_scalar1 (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
matrix_binary_scalar1 (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type j)
const |
Returns the value of the j -th element in the
i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed expression. |
template<class T1, class E2, class F>
struct matrix_binary_scalar1_traits {
typedef matrix_binary_scalar1<scalar_const_reference<T1>,
typename E2::const_closure_type, F> expression_type;
typedef expression_type result_type;
};
// (t * m) [i] [j] = t * m [i] [j]
template<class T1, class E2>
typename matrix_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
operator * (const T1 &e1,
const matrix_expression<E2> &e2);
template<class E1, class T2, class F>
struct matrix_binary_scalar2_traits {
typedef matrix_binary_scalar2<typename E1::const_closure_type,
scalar_const_reference<T2>, F> expression_type;
typedef expression_type result_type;
};
// (m * t) [i] [j] = m [i] [j] * t
template<class E1, class T2>
typename matrix_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
operator * (const matrix_expression<E1> &e1,
const T2 &e2);
// (m / t) [i] [j] = m [i] [j] / t
template<class E1, class T2>
typename matrix_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
operator / (const matrix_expression<E1> &e1,
const T2 &e2);
operator *
computes the product of a scalar and a
matrix expression. operator /
multiplies the matrix
with the reciprocal of the scalar.
Defined in the header matrix_expression.hpp.
T1/T2
is a model of Scalar Expression .E2/E1
is a model of Matrix Expression .None.
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m (3, 3); for (unsigned i = 0; i < m.size1 (); ++ i) for (unsigned j = 0; j < m.size2 (); ++ j) m (i, j) = 3 * i + j; std::cout << 2.0 * m << std::endl; std::cout << m * 2.0 << std::endl; }
The templated classes matrix_vector_binary1<E1, E2,
F>
and matrix_vector_binary2<E1, E2,
F>
describe binary matrix vector operations.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the matrix or vector expression. | |
E2 |
The type of the vector or matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Vector Expression .
vector_expression<matrix_vector_binary1<E1, E2,
F> >
and
vector_expression<matrix_vector_binary2<E1, E2, F>
>
resp.
Member | Description |
---|---|
matrix_vector_binary1 (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
matrix_vector_binary2 (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
size_type size () const |
Returns the size of the expression. |
const_reference operator () (size_type i)
const |
Returns the value of the i -th element. |
const_iterator begin () const |
Returns a const_iterator pointing to the beginning
of the expression. |
const_iterator end () const |
Returns a const_iterator pointing to the end of
the expression. |
const_reverse_iterator rbegin () const |
Returns a const_reverse_iterator pointing to the
beginning of the reversed expression. |
const_reverse_iterator rend () const |
Returns a const_reverse_iterator pointing to the
end of the reversed expression. |
template<class T1, class E1, class T2, class E2>
struct matrix_vector_binary1_traits {
typedef row_major_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_vector_binary1<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_vector_prod1<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
row_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
row_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class V, class E1, class E2>
V
prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class V, class E1, class E2>
V
prec_prod (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2);
template<class T1, class E1, class T2, class E2>
struct matrix_vector_binary2_traits {
typedef column_major_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_vector_binary2<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_vector_prod2<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
column_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
column_major_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class V, class E1, class E2>
V
prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class V, class E1, class E2>
V
prec_prod (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2);
prod
computes the product of the matrix and the
vector expression. prec_prod
computes the double
precision product of the matrix and the vector expression.
Defined in the header matrix_expression.hpp.
E1
is a model of Matrix Expression or
Vector Expression
.E2
is a model of Vector Expression or
Matrix Expression
.e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m (3, 3); vector<double> v (3); for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) { for (unsigned j = 0; j < m.size2 (); ++ j) m (i, j) = 3 * i + j; v (i) = i; } std::cout << prod (m, v) << std::endl; std::cout << prod (v, m) << std::endl; }
template<class E1, class E2>
struct matrix_vector_solve_traits {
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
typedef vector<promote_type> result_type;
};
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
lower_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
upper_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_lower_tag,
vector_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_upper_tag,
vector_tag);
template<class E1, class E2, class C>
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const matrix_expression<E1> &e1,
const vector_expression<E2> &e2,
C);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
lower_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
upper_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
unit_lower_tag);
template<class E1, class E2>
void inplace_solve (E1 &e1,
const matrix_expression<E2> &e2,
vector_tag,
unit_upper_tag);
template<class E1, class E2, class C>
typename matrix_vector_solve_traits<E1, E2>::result_type
solve (const vector_expression<E1> &e1,
const matrix_expression<E2> &e2,
C);
solve
solves a linear equation for lower or upper
(unit) triangular matrices.
Defined in the header triangular.hpp.
E1
is a model of Matrix Expression or
Vector Expression
.E2
is a model of Vector Expression or
Matrix Expression
.e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()
e2 ().size1 () == e2 ().size2 ()
Quadratic depending from the size of the matrix expression.
#include <boost/numeric/ublas/triangular.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m (3, 3); vector<double> v (3); for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) { for (unsigned j = 0; j <= i; ++ j) m (i, j) = 3 * i + j + 1; v (i) = i; } std::cout << solve (m, v, lower_tag ()) << std::endl; std::cout << solve (v, m, lower_tag ()) << std::endl; }
The templated class matrix_matrix_binary<E1, E2,
F>
describes a binary matrix operation.
Defined in the header matrix_expression.hpp.
Parameter | Description | Default |
---|---|---|
E1 |
The type of the first matrix expression. | |
E2 |
The type of the second matrix expression. | |
F |
The type of the operation. |
None, except for those imposed by the requirements of Matrix Expression .
matrix_expression<matrix_matrix_binary<E1, E2, F>
>
.
Member | Description |
---|---|
matrix_matrix_binary (const expression1_type &e1,
const expression2_type &e2) |
Constructs a description of the expression. |
size_type size1 () const |
Returns the number of rows. |
size_type size2 () const |
Returns the number of columns. |
const_reference operator () (size_type i, size_type j)
const |
Returns the value of the j -th element in the
i -th row. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the expression. |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the expression. |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the expression. |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the expression. |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed expression. |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed expression. |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed expression. |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed expression. |
template<class T1, class E1, class T2, class E2>
struct matrix_matrix_binary_traits {
typedef unknown_orientation_tag dispatch_category;
typedef typename promote_traits<T1, T2>::promote_type promote_type;
typedef matrix_matrix_binary<typename E1::const_closure_type,
typename E2::const_closure_type,
matrix_matrix_prod<T1, T2, promote_type> > expression_type;
typedef expression_type result_type;
};
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
unknown_orientation_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
typename E2::value_type, E2>::result_type
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
unknown_orientation_tag);
// Dispatcher
template<class E1, class E2>
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class M, class E1, class E2>
M
prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
template<class M, class E1, class E2>
M
prec_prod (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2);
prod
computes the product of the matrix
expressions. prec_prod
computes the double precision
product of the matrix expressions.
Defined in the header matrix_expression.hpp.
E1
is a model of Matrix Expression .E2
is a model of Matrix Expression .e1 ().size2 () == e2 ().size1 ()
Cubic depending from the size of the matrix expression.
#include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m1 (3, 3), m2 (3, 3); for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j) m1 (i, j) = m2 (i, j) = 3 * i + j; std::cout << prod (m1, m2) << std::endl; }
template<class E1, class E2>
struct matrix_matrix_solve_traits {
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
typedef matrix<promote_type> result_type;
};
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
lower_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
upper_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_lower_tag,
matrix_tag);
template<class E1, class E2>
void inplace_solve (const matrix_expression<E1> &e1,
E2 &e2,
unit_upper_tag,
matrix_tag);
template<class E1, class E2, class C>
typename matrix_matrix_solve_traits<E1, E2>::result_type
solve (const matrix_expression<E1> &e1,
const matrix_expression<E2> &e2,
C);
solve
solves a linear equation for lower or upper
(unit) triangular matrices.
Defined in the header triangular.hpp.
E1
is a model of Matrix Expression .E2
is a model of Matrix Expression .e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size1 ()
Cubic depending from the size of the matrix expressions.
#include <boost/numeric/ublas/triangular.hpp> #include <boost/numeric/ublas/io.hpp> int main () { using namespace boost::numeric::ublas; matrix<double> m1 (3, 3), m2 (3, 3); for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) for (unsigned j = 0; j <= i; ++ j) m1 (i, j) = m2 (i, j) = 3 * i + j + 1; std::cout << solve (m1, m2, lower_tag ()) << std::endl; }
Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Use, modification and distribution are subject to the
Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt
or copy at
http://www.boost.org/LICENSE_1_0.txt
).