Triangular Matrix
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
ti, j = 0 , if i >
j. If furthermore holds ti, i= 1
the matrix is called unit lower triangular. For a (n x n
)-dimensional upper triangular matrix and 0 <= i <
n,0 <= j < n holds ti,
j = 0 , if i < j. If furthermore
holds ti, 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;
}
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;
}
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
).
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