Hermitian Matrix
Hermitian Matrix
Description
The templated class hermitian_matrix<T, F1, F2,
A> is the base container adaptor for hermitian matrices.
For a (n x n )-dimensional hermitian matrix and 0
<= i < n, 0 <= j < n holds
hi, j = hj,
i-. The storage of hermitian
matrices is packed.
Example
#include <boost/numeric/ublas/hermitian.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
hermitian_matrix<std::complex<double>, lower> ml (3, 3);
for (unsigned i = 0; i < ml.size1 (); ++ i) {
for (unsigned j = 0; j < i; ++ j)
ml (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
ml (i, i) = std::complex<double> (4 * i, 0);
}
std::cout << ml << std::endl;
hermitian_matrix<std::complex<double>, upper> mu (3, 3);
for (unsigned i = 0; i < mu.size1 (); ++ i) {
mu (i, i) = std::complex<double> (4 * i, 0);
for (unsigned j = i + 1; j < mu.size2 (); ++ j)
mu (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
}
std::cout << mu << std::endl;
}
Definition
Defined in the header hermitian.hpp.
Template parameters
Parameter |
Description |
Default |
T |
The type of object stored in the matrix. |
|
F1 |
Functor describing the type of the hermitian 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<hermitian_matrix<T, F1, F2, A>
>
Members
Member |
Description |
hermitian_matrix () |
Allocates an uninitialized hermitian_matrix that
holds zero rows of zero elements. |
hermitian_matrix (size_type size) |
Allocates an uninitialized hermitian_matrix that
holds size rows of size elements. |
hermitian_matrix (const hermitian_matrix
&m) |
The copy constructor. |
template<class AE>
hermitian_matrix (const matrix_expression<AE>
&ae) |
The extended copy constructor. |
void resize (size_type size, bool preserve =
true) |
Reallocates a hermitian_matrix to hold
size rows of size elements. The existing
elements of the hermitian_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. |
hermitian_matrix &operator = (const hermitian_matrix
&m) |
The assignment operator. |
hermitian_matrix &assign_temporary (hermitian_matrix
&m) |
Assigns a temporary. May change the hermitian matrix
m . |
template<class AE>
hermitian_matrix &operator = (const matrix_expression<AE>
&ae) |
The extended assignment operator. |
template<class AE>
hermitian_matrix &assign (const matrix_expression<AE>
&ae) |
Assigns a matrix expression to the hermitian matrix. Left and
right hand side of the assignment should be independent. |
template<class AE>
hermitian_matrix &operator += (const
matrix_expression<AE> &ae) |
A computed assignment operator. Adds the matrix expression to
the hermitian matrix. |
template<class AE>
hermitian_matrix &plus_assign (const
matrix_expression<AE> &ae) |
Adds a matrix expression to the hermitian matrix. Left and
right hand side of the assignment should be independent. |
template<class AE>
hermitian_matrix &operator -= (const
matrix_expression<AE> &ae) |
A computed assignment operator. Subtracts the matrix expression
from the hermitian matrix. |
template<class AE>
hermitian_matrix &minus_assign (const
matrix_expression<AE> &ae) |
Subtracts a matrix expression from the hermitian matrix. Left
and right hand side of the assignment should be independent. |
template<class AT>
hermitian_matrix &operator *= (const AT &at) |
A computed assignment operator. Multiplies the hermitian matrix
with a scalar. |
template<class AT>
hermitian_matrix &operator /= (const AT &at) |
A computed assignment operator. Divides the hermitian matrix
through a scalar. |
void swap (hermitian_matrix &m) |
Swaps the contents of the hermitian 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 hermitian_matrix . |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the hermitian_matrix . |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning of
the hermitian_matrix . |
iterator1 end1 () |
Returns a iterator1 pointing to the end of the
hermitian_matrix . |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the hermitian_matrix . |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the hermitian_matrix . |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning of
the hermitian_matrix . |
iterator2 end2 () |
Returns a iterator2 pointing to the end of the
hermitian_matrix . |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed hermitian_matrix . |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed hermitian_matrix . |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to the
beginning of the reversed hermitian_matrix . |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to the end of
the reversed hermitian_matrix . |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed hermitian_matrix . |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed hermitian_matrix . |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to the
beginning of the reversed hermitian_matrix . |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to the end of
the reversed hermitian_matrix . |
Notes
[1]
Supported parameters for the type of the hermitian matrix are
lower and 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> .
Hermitian Adaptor
Description
The templated class hermitian_adaptor<M, F>
is a hermitian matrix adaptor for other matrices.
Example
#include <boost/numeric/ublas/hermitian.hpp>
#include <boost/numeric/ublas/io.hpp>
int main () {
using namespace boost::numeric::ublas;
matrix<std::complex<double> > m (3, 3);
hermitian_adaptor<matrix<std::complex<double> >, lower> hal (m);
for (unsigned i = 0; i < hal.size1 (); ++ i) {
for (unsigned j = 0; j < i; ++ j)
hal (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
hal (i, i) = std::complex<double> (4 * i, 0);
}
std::cout << hal << std::endl;
hermitian_adaptor<matrix<std::complex<double> >, upper> hau (m);
for (unsigned i = 0; i < hau.size1 (); ++ i) {
hau (i, i) = std::complex<double> (4 * i, 0);
for (unsigned j = i + 1; j < hau.size2 (); ++ j)
hau (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
}
std::cout << hau << std::endl;
}
Definition
Defined in the header hermitian.hpp.
Template parameters
Parameter |
Description |
Default |
M |
The type of the adapted matrix. |
|
F |
Functor describing the type of the hermitian 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<hermitian_adaptor<M, F>
>
Members
Member |
Description |
hermitian_adaptor (matrix_type &data) |
Constructs a hermitian_adaptor of a matrix. |
hermitian_adaptor (const hermitian_adaptor
&m) |
The copy constructor. |
template<class AE>
hermitian_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. |
hermitian_adaptor &operator = (const
hermitian_adaptor &m) |
The assignment operator. |
hermitian_adaptor &assign_temporary
(hermitian_adaptor &m) |
Assigns a temporary. May change the hermitian adaptor
m . |
template<class AE>
hermitian_adaptor &operator = (const
matrix_expression<AE> &ae) |
The extended assignment operator. |
template<class AE>
hermitian_adaptor &assign (const matrix_expression<AE>
&ae) |
Assigns a matrix expression to the hermitian adaptor. Left and
right hand side of the assignment should be independent. |
template<class AE>
hermitian_adaptor &operator += (const
matrix_expression<AE> &ae) |
A computed assignment operator. Adds the matrix expression to
the hermitian adaptor. |
template<class AE>
hermitian_adaptor &plus_assign (const
matrix_expression<AE> &ae) |
Adds a matrix expression to the hermitian adaptor. Left and
right hand side of the assignment should be independent. |
template<class AE>
hermitian_adaptor &operator -= (const
matrix_expression<AE> &ae) |
A computed assignment operator. Subtracts the matrix expression
from the hermitian adaptor. |
template<class AE>
hermitian_adaptor &minus_assign (const
matrix_expression<AE> &ae) |
Subtracts a matrix expression from the hermitian adaptor. Left
and right hand side of the assignment should be independent. |
template<class AT>
hermitian_adaptor &operator *= (const AT &at) |
A computed assignment operator. Multiplies the hermitian
adaptor with a scalar. |
template<class AT>
hermitian_adaptor &operator /= (const AT &at) |
A computed assignment operator. Divides the hermitian adaptor
through a scalar. |
void swap (hermitian_adaptor &m) |
Swaps the contents of the hermitian adaptors. |
const_iterator1 begin1 () const |
Returns a const_iterator1 pointing to the
beginning of the hermitian_adaptor . |
const_iterator1 end1 () const |
Returns a const_iterator1 pointing to the end of
the hermitian_adaptor . |
iterator1 begin1 () |
Returns a iterator1 pointing to the beginning of
the hermitian_adaptor . |
iterator1 end1 () |
Returns a iterator1 pointing to the end of the
hermitian_adaptor . |
const_iterator2 begin2 () const |
Returns a const_iterator2 pointing to the
beginning of the hermitian_adaptor . |
const_iterator2 end2 () const |
Returns a const_iterator2 pointing to the end of
the hermitian_adaptor . |
iterator2 begin2 () |
Returns a iterator2 pointing to the beginning of
the hermitian_adaptor . |
iterator2 end2 () |
Returns a iterator2 pointing to the end of the
hermitian_adaptor . |
const_reverse_iterator1 rbegin1 () const |
Returns a const_reverse_iterator1 pointing to the
beginning of the reversed hermitian_adaptor . |
const_reverse_iterator1 rend1 () const |
Returns a const_reverse_iterator1 pointing to the
end of the reversed hermitian_adaptor . |
reverse_iterator1 rbegin1 () |
Returns a reverse_iterator1 pointing to the
beginning of the reversed hermitian_adaptor . |
reverse_iterator1 rend1 () |
Returns a reverse_iterator1 pointing to the end of
the reversed hermitian_adaptor . |
const_reverse_iterator2 rbegin2 () const |
Returns a const_reverse_iterator2 pointing to the
beginning of the reversed hermitian_adaptor . |
const_reverse_iterator2 rend2 () const |
Returns a const_reverse_iterator2 pointing to the
end of the reversed hermitian_adaptor . |
reverse_iterator2 rbegin2 () |
Returns a reverse_iterator2 pointing to the
beginning of the reversed hermitian_adaptor . |
reverse_iterator2 rend2 () |
Returns a reverse_iterator2 pointing to the end of
the reversed hermitian_adaptor . |
Notes
[1]
Supported parameters for the type of the hermitian adaptor are
lower and 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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