Triangular Matrix

Description

The templated class triangular_matrix<T, F1, F2, A> is the base container adaptor for triangular matrices. For a (n x n )-dimensional lower triangular matrix and 0 < = i < n, 0 < = j < n holds t_i,j = 0 , if i > j. If furthermore holds t_i,i= 1 the matrix is called unit lower triangular. For a (n x n )-dimensional lower triangular matrix and 0 < = i < n, 0 < = j < n holds t_i,j= 0 , if i < j. If furthermore holds t_i,i= 1 the matrix is called unit lower triangular. The storage of triangular matrices is packed.

Example

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

int main () {
    using namespace boost::numeric::ublas;
    triangular_matrix<double, lower> ml (3, 3);
    for (unsigned i = 0; i < ml.size1 (); ++ i)
        for (unsigned j = 0; j <= i; ++ j)
            ml (i, j) = 3 * i + j;
    std::cout << ml << std::endl;
    triangular_matrix<double, upper> mu (3, 3);
    for (unsigned i = 0; i < mu.size1 (); ++ i)
        for (unsigned j = i; j < mu.size2 (); ++ j)
            mu (i, j) = 3 * i + j;
    std::cout << mu << std::endl;
}

Please read the full triangular example for more details.

Definition

Defined in the header triangular.hpp.

Template parameters

Parameter	Description	Default
`T`	The type of object stored in the matrix.
`F1`	Functor describing the type of the triangular matrix. [1]	`lower`
`F2`	Functor describing the storage organization. [2]	`row_major`
`A`	The type of the adapted array. [3]	`unbounded_array<T>`

Model of

Matrix .

Type requirements

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

Public base classes

matrix_container<triangular_matrix<T, F1, F2, A> >

Members

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

Notes

[1] Supported parameters for the type of the triangular matrix are lower , unit_lower, upper and unit_upper .

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

[3] Supported parameters for the adapted array are unbounded_array<T> , bounded_array<T> and std::vector<T> .

Triangular Adaptor

Description

The templated class triangular_adaptor<M, F> is a triangular matrix adaptor for other matrices.

Example

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

int main () {
    using namespace boost::numeric::ublas;
    matrix<double> m (3, 3);
    triangular_adaptor<matrix<double>, lower> tal (m);
    for (unsigned i = 0; i < tal.size1 (); ++ i)
        for (unsigned j = 0; j <= i; ++ j)
            tal (i, j) = 3 * i + j;
    std::cout << tal << std::endl;
    triangular_adaptor<matrix<double>, upper> tau (m);
    for (unsigned i = 0; i < tau.size1 (); ++ i)
        for (unsigned j = i; j < tau.size2 (); ++ j)
            tau (i, j) = 3 * i + j;
    std::cout << tau << std::endl;
}

Please read the full triangular example for more details.

Definition

Defined in the header triangular.hpp.

Template parameters

Parameter	Description	Default
`M`	The type of the adapted matrix.
`F`	Functor describing the type of the triangular adaptor. [1]	`lower`

Model of

Matrix Expression .

Type requirements

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

Public base classes

matrix_expression<triangular_adaptor<M, F> >

Members

Member	Description
`triangular_adaptor (matrix_type &data)`	Constructs a `triangular_adaptor` of a matrix.
`triangular_adaptor (const triangular_adaptor &m)`	The copy constructor.
`template<class AE> triangular_adaptor (const matrix_expression<AE> &ae)`	The extended copy constructor.
`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 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.
`triangular_adaptor &operator = (const triangular_adaptor &m)`	The assignment operator.
`triangular_adaptor &assign_temporary (triangular_adaptor &m)`	Assigns a temporary. May change the triangular adaptor `m`.
`template<class AE> triangular_adaptor &operator = (const matrix_expression<AE> &ae)`	The extended assignment operator.
`template<class AE> triangular_adaptor &assign (const matrix_expression<AE> &ae)`	Assigns a matrix expression to the triangular adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> triangular_adaptor &operator += (const matrix_expression<AE> &ae)`	A computed assignment operator. Adds the matrix expression to the triangular adaptor.
`template<class AE> triangular_adaptor &plus_assign (const matrix_expression<AE> &ae)`	Adds a matrix expression to the triangular adaptor. Left and right hand side of the assignment should be independent.
`template<class AE> triangular_adaptor &operator -= (const matrix_expression<AE> &ae)`	A computed assignment operator. Subtracts the matrix expression from the triangular adaptor.
`template<class AE> triangular_adaptor &minus_assign (const matrix_expression<AE> &ae)`	Subtracts a matrix expression from the triangular adaptor. Left and right hand side of the assignment should be independent.
`template<class AT> triangular_adaptor &operator *= (const AT &at)`	A computed assignment operator. Multiplies the triangular adaptor with a scalar.
`template<class AT> triangular_adaptor &operator /= (const AT &at)`	A computed assignment operator. Divides the triangular adaptor through a scalar.
`void swap (triangular_adaptor &m)`	Swaps the contents of the triangular adaptors.
`const_iterator1 begin1 () const`	Returns a `const_iterator1` pointing to the beginning of the `triangular_adaptor`.
`const_iterator1 end1 () const`	Returns a `const_iterator1` pointing to the end of the `triangular_adaptor`.
`iterator1 begin1 ()`	Returns a `iterator1` pointing to the beginning of the `triangular_adaptor`.
`iterator1 end1 ()`	Returns a `iterator1` pointing to the end of the `triangular_adaptor`.
`const_iterator2 begin2 () const`	Returns a `const_iterator2` pointing to the beginning of the `triangular_adaptor`.
`const_iterator2 end2 () const`	Returns a `const_iterator2` pointing to the end of the `triangular_adaptor`.
`iterator2 begin2 ()`	Returns a `iterator2` pointing to the beginning of the `triangular_adaptor`.
`iterator2 end2 ()`	Returns a `iterator2` pointing to the end of the `triangular_adaptor`.
`const_reverse_iterator1 rbegin1 () const`	Returns a `const_reverse_iterator1` pointing to the beginning of the reversed `triangular_adaptor`.
`const_reverse_iterator1 rend1 () const`	Returns a `const_reverse_iterator1` pointing to the end of the reversed `triangular_adaptor`.
`reverse_iterator1 rbegin1 ()`	Returns a `reverse_iterator1` pointing to the beginning of the reversed `triangular_adaptor`.
`reverse_iterator1 rend1 ()`	Returns a `reverse_iterator1` pointing to the end of the reversed `triangular_adaptor`.
`const_reverse_iterator2 rbegin2 () const`	Returns a `const_reverse_iterator2` pointing to the beginning of the reversed `triangular_adaptor`.
`const_reverse_iterator2 rend2 () const`	Returns a `const_reverse_iterator2` pointing to the end of the reversed `triangular_adaptor`.
`reverse_iterator2 rbegin2 ()`	Returns a `reverse_iterator2` pointing to the beginning of the reversed `triangular_adaptor`.
`reverse_iterator2 rend2 ()`	Returns a `reverse_iterator2` pointing to the end of the reversed `triangular_adaptor`.

Notes

[1] Supported parameters for the type of the triangular adaptor are lower , unit_lower, upper and unit_upper .

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 ).

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

triangular.adoc

triangular.adoc

Triangular Matrix

Triangular Matrix

Description

Example

Definition

Template parameters

Model of

Type requirements

Public base classes

Members

Notes

Triangular Adaptor

Description

Example

Definition

Template parameters

Model of

Type requirements

Public base classes

Members

Notes

Files

triangular.adoc

Latest commit

History

triangular.adoc

File metadata and controls

Triangular Matrix

Triangular Matrix

Description

Example

Definition

Template parameters

Model of

Type requirements

Public base classes

Members

Notes

Triangular Adaptor

Description

Example

Definition

Template parameters

Model of

Type requirements

Public base classes

Members

Notes