Matrix

Description

The templated class matrix<T, F, A> is the base container adaptor for dense matrices. For a (m x n)-dimensional matrix and 0 ⇐ i < m, 0 ⇐ j < n every element m_i,j is mapped to the (i x n j)-th element of the container for row major orientation or the (i+ j x m)-th element of the container for column major orientation.

Example

#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 << m << std::endl;
}

Definition

Defined in the header matrix.hpp.

Template parameters

Parameter Description Default

Parameter	Description	Default
`T`	The type of object stored in the matrix.
`F`	Functor describing the storage organization. [1]	`row_major`
`A`	The type of the Storage array. [2]	`unbounded_array<T>`

T

The type of object stored in the matrix.

F

Functor describing the storage organization. [1]

row_major

A

The type of the Storage array. [2]

unbounded_array<T>

Model of

Matrix .

Type requirements

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

Public base classes

matrix_container<matrix<T, F, A> >

Members

Member Description

Member	Description
`matrix ()`	Allocates an uninitialized `matrix` that holds zero rows of zero elements.
`matrix (size_type size1, size_type size2)`	Allocates an uninitialized `matrix` that holds `size1` rows of `size2` elements.
`matrix (const matrix &m)`	The copy constructor.
`template<class AE> matrix (const matrix_expression<AE> &ae)`	The extended copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)`	Reallocates a `matrix` to hold `size1` rows of `size2` elements. The existing elements of the `matrix` are preseved when specified.
`size_type size1 () const`	Returns the number of rows.
`size_type size2 () const`	Returns the number of columns.
`const array_type& data () const`
`array_type& data ()`
`const_reference operator () (size_type i, size_type j) const`	Returns a `const` reference 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.
`matrix &operator = (const matrix &m)`	The assignment operator.
`matrix &assign_temporary (matrix &m)`	Assigns a temporary. May change the matrix `m`.
`template<class AE> matrix &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> matrix &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the matrix.
`template<class AE> matrix &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the matrix. Left and right hand side of the assignment should be independent.
`template<class AE> matrix &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the matrix.
`template<class AE> matrix &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the matrix. Left and right hand side of the assignment should be independent.
`template<class AT> matrix &operator *= (const AT &at)`	A computed assignment operator. Multiplies the matrix with a scalar.
`template<class AT> matrix &operator /= (const AT &at)`	A computed assignment operator. Divides the matrix through a scalar.
`void swap (matrix &m)`	Swaps the contents of the matrices.
`void insert_element (size_type i, size_type j, const_reference t)`	Inserts the value `t` at the `j`-th element of the `i`-th row.
`void erase_element (size_type i, size_type j)`	Erases the value at the `j`-th element of the `i`-th row.
`void clear ()`	Clears the matrix.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `matrix`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `matrix`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `matrix`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `matrix`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `matrix`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `matrix`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `matrix`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `matrix`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `matrix`.

matrix ()

Allocates an uninitialized matrix that holds zero rows of zero elements.

matrix (size_type size1, size_type size2)

Allocates an uninitialized matrix that holds size1 rows of size2 elements.

matrix (const matrix &m)

The copy constructor.

template<class AE> matrix (const matrix_expression<AE> &ae)

The extended copy constructor.

void resize (size_type size1, size_type size2, bool preserve = true)

Reallocates a matrix to hold size1 rows of size2 elements. The existing elements of the matrix are preseved when specified.

size_type size1 () const

Returns the number of rows.

size_type size2 () const

Returns the number of columns.

const array_type& data () const

array_type& data ()

const_reference operator () (size_type i, size_type j) const

Returns a const reference 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.

matrix &operator = (const matrix &m)

The assignment operator.

matrix &assign_temporary (matrix &m)

Assigns a temporary. May change the matrix m.

template<class AE> matrix &operator = (const matrix_expression<AE> &ae)

The extended assignment operator.

template<class AE> matrix &assign (const matrix_expression<AE> &ae)

Assigns a matrix expression to the matrix. Left and right hand side of the assignment should be independent.

template<class AE> matrix &operator += (const matrix_expression<AE> &ae)

A computed assignment operator. Adds the matrix expression to the matrix.

template<class AE> matrix &plus_assign (const matrix_expression<AE> &ae)

Adds a matrix expression to the matrix. Left and right hand side of the assignment should be independent.

template<class AE> matrix &operator -= (const matrix_expression<AE> &ae)

A computed assignment operator. Subtracts the matrix expression from the matrix.

template<class AE> matrix &minus_assign (const matrix_expression<AE> &ae)

Subtracts a matrix expression from the matrix. Left and right hand side of the assignment should be independent.

template<class AT> matrix &operator *= (const AT &at)

A computed assignment operator. Multiplies the matrix with a scalar.

template<class AT> matrix &operator /= (const AT &at)

A computed assignment operator. Divides the matrix through a scalar.

void swap (matrix &m)

Swaps the contents of the matrices.

void insert_element (size_type i, size_type j, const_reference t)

Inserts the value t at the j-th element of the i-th row.

void erase_element (size_type i, size_type j)

Erases the value at the j-th element of the i-th row.

void clear ()

Clears the matrix.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the matrix.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the matrix.

iterator1 begin1 ()

Returns a iterator1 pointing to the beginning of the matrix.

iterator1 end1 ()

Returns a iterator1 pointing to the end of the matrix.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the matrix.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the matrix.

iterator2 begin2 ()

Returns a iterator2 pointing to the beginning of the matrix.

iterator2 end2 ()

Returns a iterator2 pointing to the end of the matrix.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed matrix.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed matrix.

reverse_iterator1 rbegin1 ()

Returns a reverse_iterator1 pointing to the beginning of the reversed matrix.

reverse_iterator1 rend1 ()

Returns a reverse_iterator1 pointing to the end of the reversed matrix.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed matrix.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed matrix.

reverse_iterator2 rbegin2 ()

Returns a reverse_iterator2 pointing to the beginning of the reversed matrix.

reverse_iterator2 rend2 ()

Returns a reverse_iterator2 pointing to the end of the reversed matrix.

Notes

[1] Supported parameters for the storage organization are row_major and column_major.

[2] Common parameters for the storage array are unbounded_array<T> , bounded_array<T> and std::vector<T> .

Identity Matrix

Description

The templated class identity_matrix<T, ALLOC> represents identity matrices. For a (m x n)-dimensional identity matrix and 0 ⇐ i < m, 0 ⇐ j < n holds id_i,j = 0, if i <> j, and id_i,i .

Example

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>

int main () {
    using namespace boost::numeric::ublas;
    identity_matrix<double> m (3);
    std::cout << m << std::endl;
}

Definition

Defined in the header matrix.hpp.

Template parameters

Parameter Description Default

Parameter	Description	Default
`T`	The type of object stored in the matrix.	`int`
`ALLOC`	An STL Allocator for size_type and difference_type.	std::allocator

T

The type of object stored in the matrix.

int

ALLOC

An STL Allocator for size_type and difference_type.

std::allocator

Model of

Matrix .

Type requirements

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

Public base classes

matrix_container<identity_matrix<T> >

Members

Member Description

Member	Description
`identity_matrix ()`	Constructs an `identity_matrix` that holds zero rows of zero elements.
`identity_matrix (size_type size)`	Constructs an `identity_matrix` that holds `size` rows of `size` elements.
`identity_matrix (const identity_matrix &m)`	The copy constructor.
`void resize (size_type size, bool preserve = true)`	Resizes a `identity_matrix` to hold `size` rows of `size` elements. Therefore the existing elements of the `itendity_matrix` are always preseved.
`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.
`identity_matrix &operator = (const identity_matrix &m)`	The assignment operator.
`identity_matrix &assign_temporary (identity_matrix &m)`	Assigns a temporary. May change the identity matrix `m` .
`void swap (identity_matrix &m)`	Swaps the contents of the identity matrices.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `identity_matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `identity_matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `identity_matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `identity_matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `identity_matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `identity_matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `identity_matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `identity_matrix`.

identity_matrix ()

Constructs an identity_matrix that holds zero rows of zero elements.

identity_matrix (size_type size)

Constructs an identity_matrix that holds size rows of size elements.

identity_matrix (const identity_matrix &m)

The copy constructor.

void resize (size_type size, bool preserve = true)

Resizes a identity_matrix to hold size rows of size elements. Therefore the existing elements of the itendity_matrix are always preseved.

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.

identity_matrix &operator = (const identity_matrix &m)

The assignment operator.

identity_matrix &assign_temporary (identity_matrix &m)

Assigns a temporary. May change the identity matrix m .

void swap (identity_matrix &m)

Swaps the contents of the identity matrices.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the identity_matrix.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the identity_matrix.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the identity_matrix.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the identity_matrix.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed identity_matrix.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed identity_matrix.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed identity_matrix.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed identity_matrix.

Zero Matrix

Description

The templated class zero_matrix<T, ALLOC> represents zero matrices. For a (m x n)-dimensional zero matrix and 0 ⇐ i < m, 0 ⇐ j < n holds z_i,j = 0.

Example

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>

int main () {
    using namespace boost::numeric::ublas;
    zero_matrix<double> m (3, 3);
    std::cout << m << std::endl;
}

Definition

Defined in the header matrix.hpp.

Template parameters

Parameter Description Default

Parameter	Description	Default
`T`	The type of object stored in the matrix.	`int`
`ALLOC`	An STL Allocator for size_type and difference_type.	std::allocator

T

The type of object stored in the matrix.

int

ALLOC

An STL Allocator for size_type and difference_type.

std::allocator

Model of

Matrix .

Type requirements

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

Public base classes

matrix_container<zero_matrix<T> >

Members

Member Description

Member	Description
`zero_matrix ()`	Constructs a `zero_matrix` that holds zero rows of zero elements.
`zero_matrix (size_type size1, size_type size2)`	Constructs a `zero_matrix` that holds `size1` rows of `size2` elements.
`zero_matrix (const zero_matrix &m)`	The copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)`	Resizes a `zero_matrix` to hold `size1` rows of `size2` elements. Therefore the existing elements of the `zero_matrix` are always preseved.
`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.
`zero_matrix &operator = (const zero_matrix &m)`	The assignment operator.
`zero_matrix &assign_temporary (zero_matrix &m)`	Assigns a temporary. May change the zero matrix `m` .
`void swap (zero_matrix &m)`	Swaps the contents of the zero matrices.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `zero_matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `zero_matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `zero_matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `zero_matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `zero_matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `zero_matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `zero_matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `zero_matrix`.

zero_matrix ()

Constructs a zero_matrix that holds zero rows of zero elements.

zero_matrix (size_type size1, size_type size2)

Constructs a zero_matrix that holds size1 rows of size2 elements.

zero_matrix (const zero_matrix &m)

The copy constructor.

void resize (size_type size1, size_type size2, bool preserve = true)

Resizes a zero_matrix to hold size1 rows of size2 elements. Therefore the existing elements of the zero_matrix are always preseved.

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.

zero_matrix &operator = (const zero_matrix &m)

The assignment operator.

zero_matrix &assign_temporary (zero_matrix &m)

Assigns a temporary. May change the zero matrix m .

void swap (zero_matrix &m)

Swaps the contents of the zero matrices.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the zero_matrix.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the zero_matrix.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the zero_matrix.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the zero_matrix.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed zero_matrix.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed zero_matrix.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed zero_matrix.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed zero_matrix.

Scalar Matrix

Description

The templated class scalar_matrix<T, ALLOC> represents scalar matrices. For a (m x n)-dimensional scalar matrix and 0 ⇐ i < m, 0 ⇐ j < n holds z_i,j = s.

Example

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>

int main () {
    using namespace boost::numeric::ublas;
    scalar_matrix<double> m (3, 3);
    std::cout << m << std::endl;
}

Definition

Defined in the header matrix.hpp.

Template parameters

Parameter Description Default

Parameter	Description	Default
`T`	The type of object stored in the matrix.	`int`
`ALLOC`	An STL Allocator for size_type and difference_type.	std::allocator

T

The type of object stored in the matrix.

int

ALLOC

An STL Allocator for size_type and difference_type.

std::allocator

Model of

Matrix .

Type requirements

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

Public base classes

matrix_container<scalar_matrix<T> >

Members

Member Description

Member	Description
`scalar_matrix ()`	Constructs a `scalar_matrix` that holds scalar rows of zero elements.
`scalar_matrix (size_type size1, size_type size2, const value_type &value)`	Constructs a `scalar_matrix` that holds `size1` rows of `size2` elements each of the specified value.
`scalar_matrix (const scalar_matrix &m)`	The copy constructor.
`void resize (size_type size1, size_type size2, bool preserve = true)`	Resizes a `scalar_matrix` to hold `size1` rows of `size2` elements. Therefore the existing elements of the `scalar_matrix` are always preseved.
`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.
`scalar_matrix &operator = (const scalar_matrix &m)`	The assignment operator.
`scalar_matrix &assign_temporary (scalar_matrix &m)`	Assigns a temporary. May change the scalar matrix `m` .
`void swap (scalar_matrix &m)`	Swaps the contents of the scalar matrices.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `scalar_matrix`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `scalar_matrix`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `scalar_matrix`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `scalar_matrix`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `scalar_matrix`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `scalar_matrix`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `scalar_matrix`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `scalar_matrix`.

scalar_matrix ()

Constructs a scalar_matrix that holds scalar rows of zero elements.

scalar_matrix (size_type size1, size_type size2, const value_type &value)

Constructs a scalar_matrix that holds size1 rows of size2 elements each of the specified value.

scalar_matrix (const scalar_matrix &m)

The copy constructor.

void resize (size_type size1, size_type size2, bool preserve = true)

Resizes a scalar_matrix to hold size1 rows of size2 elements. Therefore the existing elements of the scalar_matrix are always preseved.

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.

scalar_matrix &operator = (const scalar_matrix &m)

The assignment operator.

scalar_matrix &assign_temporary (scalar_matrix &m)

Assigns a temporary. May change the scalar matrix m .

void swap (scalar_matrix &m)

Swaps the contents of the scalar matrices.

const_iterator1 begin1 () const

Returns a const_iterator1 pointing to the beginning of the scalar_matrix.

const_iterator1 end1 () const

Returns a const_iterator1 pointing to the end of the scalar_matrix.

const_iterator2 begin2 () const

Returns a const_iterator2 pointing to the beginning of the scalar_matrix.

const_iterator2 end2 () const

Returns a const_iterator2 pointing to the end of the scalar_matrix.

const_reverse_iterator1 rbegin1 () const

Returns a const_reverse_iterator1 pointing to the beginning of the reversed scalar_matrix.

const_reverse_iterator1 rend1 () const

Returns a const_reverse_iterator1 pointing to the end of the reversed scalar_matrix.

const_reverse_iterator2 rbegin2 () const

Returns a const_reverse_iterator2 pointing to the beginning of the reversed scalar_matrix.

const_reverse_iterator2 rend2 () const

Returns a const_reverse_iterator2 pointing to the end of the reversed scalar_matrix.

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Copyright (©) 2021 Shikhar Vashistha
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 ).