# 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;
}
```

#### 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>`

#### 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>` .

#### 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);
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;
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;
}
```

#### Template parameters

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

#### 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`.