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 h_i,j= h_j,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

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>`

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

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`.

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

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

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

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`.

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
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 ).