# Vector

#### Description

The templated class `vector<T, A>` is the base container adaptor for dense vectors. For a n-dimensional vector and 0 <= i < n every element vi is mapped to the i-th element of the container.

#### Example

    #include <boost/numeric/ublas/vector.hpp>
    #include <boost/numeric/ublas/io.hpp>

    int main () {
        using namespace boost::numeric::ublas;
        vector<double> v (3);
        for (unsigned i = 0; i < v.size (); ++ i)
            v (i) = i;
        std::cout << v << std::endl;
    }

#### Definition

Defined in the header vector.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the vector. |
`A` | The type of the Storage array. [1] | `unbounded_array<T>`

#### Model of

Vector, RandomAccessContainer

#### Type requirements

None, except for those imposed by the requirements of Vector and RandomAccessContainer.

#### Public base classes

`vector_container<vector<T, A> >`

#### Members

Member | Where defined | Description
--- | --- | ---
`value_type` | VectorExpression |
`reference` | VectorExpression |
`const_reference` | VectorExpression |
`size_type` | VectorExpression |
`difference_type` | VectorExpression |
`const_iterator` | VectorExpression |
`iterator` | VectorExpression |
`const_reverse_iterator` | VectorExpression |
`reverse_iterator` | VectorExpression |
`array_type` | Vector |
`vector ()` | VectorExpression | Allocates an uninitialized `vector` that holds zero elements.
`vector (size_type size)` | Vector | Allocates an uninitialized `vector` that holds `size` elements.
`vector (const vector &v)` |  | The copy constructor.
`template<class AE> vector (const vector_expression<AE> &ae)` |  | The extended copy constructor.
`void resize (size_type size, bool preserve = true)` | Vector | Reallocates a `vector` to hold `size` elements. The existing elements of the `vector` are preseved when specified.
`size_type size () const` | VectorExpression | Returns the size of the `vector`.
`size_type max_size () const` | RandomAccessContainer | Returns the upper bound on the size of the `vector`.
`bool empty () const` | RandomAccessContainer | Equivilent to `size () == 0`.
`const array_type& data () const` | Vector |
`array_type& data ()` | Vector |
`const_reference operator () (size_type i) const` | VectorExpression | Returns a `const` reference of the `i` -th element.
`reference operator () (size_type i)` | VectorExpression | Returns a reference of the `i`-th element.
`const_reference operator [] (size_type i) const` | Vector | Returns a `const` reference of the `i` -th element.
`reference operator [] (size_type i)` | Vector | Returns a reference of the `i`-th element.
`vector &operator = (const vector &v)` | VectorExpression | The assignment operator.
`vector &assign_temporary (vector &v)` | VectorExpression | Assigns a temporary. May change the vector `v`.
`template<class AE> vector &operator = (const vector_expression<AE> &ae)` | VectorExpression | The extended assignment operator.
`template<class AE> vector &assign (const vector_expression<AE> &ae)` | VectorExpression | Assigns a vector expression to the vector. Left and right hand side of the assignment should be independent.
`template<class AE> vector &operator += (const vector_expression<AE> &ae)` | VectorExpression | A computed assignment operator. Adds the vector expression to the vector.
`template<class AE> vector &plus_assign (const vector_expression<AE> &ae)` | VectorExpression | Adds a vector expression to the vector. Left and right hand side of the assignment should be independent.
`template<class AE> vector &operator -= (const vector_expression<AE> &ae)` | VectorExpression | A computed assignment operator. Subtracts the vector expression from the vector.
`template<class AE> vector &minus_assign (const vector_expression<AE> &ae)` | VectorExpression | Subtracts a vector expression from the vector. Left and right hand side of the assignment should be independent.
`template<class AT> vector &operator *= (const AT &at)` | VectorExpression | A computed assignment operator. Multiplies the vector with a scalar.
`template<class AT> vector &operator /= (const AT &at)` | VectorExpression | A computed assignment operator. Divides the vector through a scalar.
`void swap (vector &v)` | VectorExpression | Swaps the contents of the vectors.
`void insert_element (size_type i, const_reference t)` | Vector | Inserts the value `t` at the `i`-th element.
`void erase_element (size_type i)` | Vector | Erases the value at the `i`-th element.
`void clear ()` | Vector | Clears the vector.
`const_iterator begin () const` | VectorExpression | Returns a `const_iterator` pointing to the beginning of the `vector`.
`const_iterator end () const` | VectorExpression | Returns a `const_iterator` pointing to the end of the `vector`.
`iterator begin ()` | VectorExpression | Returns a `iterator` pointing to the beginning of the `vector`.
`iterator end ()` | VectorExpression | Returns a `iterator` pointing to the end of the `vector`.
`const_reverse_iterator rbegin () const` | VectorExpression | Returns a `const_reverse_iterator` pointing to the beginning of the reversed `vector`.
`const_reverse_iterator rend () const` | VectorExpression | Returns a `const_reverse_iterator` pointing to the end of the reversed `vector`.
`reverse_iterator rbegin ()` | VectorExpression | Returns a `reverse_iterator` pointing to the beginning of the reversed `vector`.
`reverse_iterator rend ()` | VectorExpression | Returns a `reverse_iterator` pointing to the end of the reversed `vector`.

#### Notes

[1] Common parameters for the Storage array are `unbounded_array<T>` , `bounded_array<T>` and `std::vector<T>` .

## Unit Vector

#### Description

The templated class `unit_vector<T>` represents canonical unit vectors. For the k-th n-dimensional canonical unit vector and 0 <= i < n holds uki = 0, if i <> k, and uki = 1.

#### Example

    #include <boost/numeric/ublas/vector.hpp>
    #include <boost/numeric/ublas/io.hpp>

    int main () {
        using namespace boost::numeric::ublas;
        for (int i = 0; i < 3; ++ i) {
            unit_vector<double> v (3, i);
            std::cout << v << std::endl;
        }
    }

#### Definition

Defined in the header vector.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the vector. | `int`

#### Model of

Vector .

#### Type requirements

None, except for those imposed by the requirements of Vector .

#### Public base classes

`vector_container<unit_vector<T> >`

#### Members

Member | Description
--- | ---
`unit_vector ()` | Constructs an `unit_vector` that holds zero elements.
`unit_vector (size_type size, size_type index)` | Constructs the `index`-th `unit_vector` that holds `size` elements.
`unit_vector (const unit_vector &v)` | The copy constructor.
`void resize (size_type size, bool preserve = true)` | Resizes a `unit_vector` to hold `size` elements. Therefore the existing elements of the `unit_vector` are always preseved.
`size_type size () const` | Returns the size of the `unit_vector`.
`size_type index () const` | Returns the index of the `unit_vector`.
`const_reference operator () (size_type i) const` | Returns the value of the `i`-th element.
`const_reference operator [] (size_type i) const` | Returns the value of the `i`-th element.
`unit_vector &operator = (const unit_vector &v)` | The assignment operator.
`unit_vector &assign_temporary (unit_vector &v)` | Assigns a temporary. May change the unit vector `v` .
`void swap (unit_vector &v)` | Swaps the contents of the unit vectors.
`const_iterator begin () const` | Returns a `const_iterator` pointing to the beginning of the `unit_vector`.
`const_iterator end () const` | Returns a `const_iterator` pointing to the end of the `unit_vector`.
`const_reverse_iterator rbegin () const` | Returns a `const_reverse_iterator` pointing to the beginning of the reversed `unit_vector`.
`const_reverse_iterator rend () const` | Returns a `const_reverse_iterator` pointing to the end of the reversed `unit_vector`.

## Zero Vector

#### Description

The templated class `zero_vector<T>` represents zero vectors. For a n-dimensional zero vector and 0 <= i < n holds zi = 0.

#### Example

    #include <boost/numeric/ublas/vector.hpp>
    #include <boost/numeric/ublas/io.hpp>

    int main () {
        using namespace boost::numeric::ublas;
        zero_vector<double> v (3);
        std::cout << v << std::endl;
    }

#### Definition

Defined in the header vector.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the vector. | `int`

#### Model of

Vector .

#### Type requirements

None, except for those imposed by the requirements of Vector .

#### Public base classes

`vector_container<zero_vector<T> >`

#### Members

Member | Description
--- | ---
`zero_vector ()` | Constructs a `zero_vector` that holds zero elements.
`zero_vector (size_type size)` | Constructs a `zero_vector` that holds `size` elements.
`zero_vector (const zero_vector &v)` | The copy constructor.
`void resize (size_type size, bool preserve = true)` | Resizes a `zero_vector` to hold `size` elements. Therefore the existing elements of the `zero_vector` are always preseved.
`size_type size () const` | Returns the size of the `zero_vector`.
`const_reference operator () (size_type i) const` | Returns the value of the `i`-th element.
`const_reference operator [] (size_type i) const` | Returns the value of the `i`-th element.
`zero_vector &operator = (const zero_vector &v)` | The assignment operator.
`zero_vector &assign_temporary (zero_vector &v)` | Assigns a temporary. May change the zero vector `v` .
`void swap (zero_vector &v)` | Swaps the contents of the zero vectors.
`const_iterator begin () const` | Returns a `const_iterator` pointing to the beginning of the `zero_vector`.
`const_iterator end () const` | Returns a `const_iterator` pointing to the end of the `zero_vector`.
`const_reverse_iterator rbegin () const` | Returns a `const_reverse_iterator` pointing to the beginning of the reversed `zero_vector`.
`const_reverse_iterator rend () const` | Returns a `const_reverse_iterator` pointing to the end of the reversed `zero_vector`.

## Scalar Vector

#### Description

The templated class `scalar_vector<T>` represents scalar vectors. For a n-dimensional scalar vector and 0 <= i < n holds zi = s.

#### Example

    #include <boost/numeric/ublas/vector.hpp>
    #include <boost/numeric/ublas/io.hpp>

    int main () {
        using namespace boost::numeric::ublas;
        scalar_vector<double> v (3);
        std::cout << v << std::endl;
    }

#### Definition

Defined in the header vector.hpp.

#### Template parameters

Parameter | Description | Default
--- | --- | ---
`T` | The type of object stored in the vector. | `int`

#### Model of

Vector .

#### Type requirements

None, except for those imposed by the requirements of Vector .

#### Public base classes

`vector_container<scalar_vector<T> >`

#### Members

Member | Description
--- | ---
`scalar_vector ()` | Constructs a `scalar_vector` that holds zero elements.
`scalar_vector (size_type size, const value_type &value)` | Constructs a `scalar_vector` that holds `size` elements each of the specified value.
`scalar_vector (const scalar_vector &v)` | The copy constructor.
`void resize (size_type size, bool preserve = true)` | Resizes a `scalar_vector` to hold `size` elements. Therefore the existing elements of the `scalar_vector` are always preseved.
`size_type size () const` | Returns the size of the `scalar_vector`.
`const_reference operator () (size_type i) const` | Returns the value of the `i`-th element.
`const_reference operator [] (size_type i) const` | Returns the value of the `i`-th element.
`scalar_vector &operator = (const scalar_vector &v)` | The assignment operator.
`scalar_vector &assign_temporary (scalar_vector &v)` | Assigns a temporary. May change the scalar vector `v` .
`void swap (scalar_vector &v)` | Swaps the contents of the scalar vectors.
`const_iterator begin () const` | Returns a `const_iterator` pointing to the beginning of the `scalar_vector`.
`const_iterator end () const` | Returns a `const_iterator` pointing to the end of the `scalar_vector`.
`const_reverse_iterator rbegin () const` | Returns a `const_reverse_iterator` pointing to the beginning of the reversed `scalar_vector`.
`const_reverse_iterator rend () const` | Returns a `const_reverse_iterator` pointing to the end of the reversed `scalar_vector`.

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.