Matrix Expressions

Matrix Expression

Description

The templated class matrix_expression<E> is required to be a public base of all classes which model the Matrix Expression concept.

Definition

Defined in the header expression_types.hpp.

Template parameters

Parameter	Description	Default
`E`	The type of the matrix expression.

Model of

None. Not a Matrix Expression!

Type requirements

None.

Public base classes

None.

Members

Member	Description
`const expression_type &operator () () const`	Returns a `const` reference of the expression.
`expression_type &operator () ()`	Returns a reference of the expression.

Notes

The operator[], row, column, range, slice and project functions have been removed. Use the free functions defined in matrix proxy instead.

Matrix Container

Description

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.

Definition

Defined in the header expression_types.hpp.

Template parameters

Parameter	Description	Default
`E`	The type of the matrix expression.

Model of

None. Not a Matrix Expression OR Matrix!

Type requirements

None.

Public base classes

matrix_expression<C>

Members

Member	Description
`const container_type &operator () () const`	Returns a `const` reference of the container.
`container_type &operator () ()`	Returns a reference of the container.

Matrix References

Reference

Description

The templated class matrix_reference<E> contains a reference to a matrix expression.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

Parameter	Description	Default
`E`	The type of the matrix expression.

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<matrix_reference<E> >

Members

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.

Matrix Operations

Unary Operation Description

Description

The templated classes matrix_unary1<E, F> and matrix_unary2<E, F> describe unary matrix operations.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

Parameter	Description	Default
`E`	The type of the matrix expression.
`F`	The type of the operation.

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<matrix_unary1<E, F> > and matrix_expression<matrix_unary2<E, F> > resp.

Members

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.

Unary Operations

Prototypes

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);

Description

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.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

E is a model of Matrix Expression .

Preconditions

None.

Complexity

Quadratic depending from the size of the matrix expression.

Examples

#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;
}

Binary Operation Description

Description

The templated class matrix_binary<E1, E2, F> describes a binary matrix operation.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

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.

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<matrix_binary<E1, E2, F> >.

Members

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.

Binary Operations

Prototypes

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);

Description

operator + computes the sum of two matrix expressions. operator - computes the difference of two matrix expressions.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

E1 is a model of Matrix Expression .
E2 is a model of Matrix Expression .

Preconditions

e1 ().size1 () == e2 ().size1 ()
e1 ().size2 () == e2 ().size2 ()

Complexity

Quadratic depending from the size of the matrix expressions.

Examples

#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;
}

Scalar Matrix Operation Description

Description

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.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

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.

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<matrix_binary_scalar1<E1, E2, F> > and matrix_expression<matrix_binary_scalar2<E1, E2, F> > resp.

Members

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.

Scalar Matrix Operations

Prototypes

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);

Description

operator * computes the product of a scalar and a matrix expression. operator / multiplies the matrix with the reciprocal of the scalar.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

T1/T2 is a model of Scalar Expression .
E2/E1 is a model of Matrix Expression .

Preconditions

None.

Complexity

Quadratic depending from the size of the matrix expression.

Examples

#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;
}

Matrix Vector Operations

Binary Operation Description

Description

The templated classes matrix_vector_binary1<E1, E2, F> and matrix_vector_binary2<E1, E2, F> describe binary matrix vector operations.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

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.

Model of

Vector Expression .

Type requirements

None, except for those imposed by the requirements of Vector Expression .

Public base classes

vector_expression<matrix_vector_binary1<E1, E2, F> > and vector_expression<matrix_vector_binary2<E1, E2, F> > resp.

Members

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.

Binary Operations

Prototypes

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);

Description

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.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

E1 is a model of Matrix Expression or Vector Expression .
E2 is a model of Vector Expression or Matrix Expression .

Preconditions

e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()

Complexity

Quadratic depending from the size of the matrix expression.

Examples

#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;
}

Triangular Solver

Prototypes

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);

Description

solve solves a linear equation for lower or upper (unit) triangular matrices.

Definition

Defined in the header triangular.hpp.

Type requirements

E1 is a model of Matrix Expression or Vector Expression .
E2 is a model of Vector Expression or Matrix Expression .

Preconditions

e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size ()
e1 ().size () == e2 ().size1 ()
e2 ().size1 () == e2 ().size2 ()

Complexity

Quadratic depending from the size of the matrix expression.

Examples

#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;
}

Matrix Matrix Operations

Binary Operation Description

Description

The templated class matrix_matrix_binary<E1, E2, F> describes a binary matrix operation.

Definition

Defined in the header matrix_expression.hpp.

Template parameters

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.

Model of

Matrix Expression .

Type requirements

None, except for those imposed by the requirements of Matrix Expression .

Public base classes

matrix_expression<matrix_matrix_binary<E1, E2, F> > .

Members

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.

Binary Operations

Prototypes

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);

Description

prod computes the product of the matrix expressions. prec_prod computes the double precision product of the matrix expressions.

Definition

Defined in the header matrix_expression.hpp.

Type requirements

E1 is a model of Matrix Expression .
E2 is a model of Matrix Expression .

Preconditions

e1 ().size2 () == e2 ().size1 ()

Complexity

Cubic depending from the size of the matrix expression.

Examples

#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;
}

Triangular Solvers

Prototypes

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);

Description

solve solves a linear equation for lower or upper (unit) triangular matrices.

Definition

Defined in the header triangular.hpp.

Type requirements

E1 is a model of Matrix Expression .
E2 is a model of Matrix Expression .

Preconditions

e1 ().size1 () == e1 ().size2 ()
e1 ().size2 () == e2 ().size1 ()

Complexity

Cubic depending from the size of the matrix expressions.

Examples

#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
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