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
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 ).