.. _Vector:

######
Vector 
######


This class simply represent a vector and provides basic linear algebra routines.
If :ref:`MPI<MPI_docs>` is available the vector is distributed across all processes, otherwise not.
In the case of shared memory (:ref:`MPI<MPI_docs>` has not been found), routines are parallelized using :ref:`openMP<openMP_docs>` if possible.

.. note::

    The syntax is equivalent for all cases.

The class is mainly used by the :ref:`ShellMatrix<ShellMatrix>` to make **matrix-free** multiplication possible.

Here is a brief example of some features:

.. code-block:: cpp

    /* Defining the type */
    using Vector=danceq::internal::Vector<double>;

    /* Initializing two vectors with are random values */
    Vector A(10);
    Vector B(10);
    A.make_random();
    B.make_random();
    std::cout << "A: " << A << std::endl;
    std::cout << "A[0] = " << A[0] << " || B[0] = " << B[0] << std::endl;

    /* Vectors can be added */
    auto C = A + B;
    std::cout << "C[0] = " << C[0] << std::endl;


    /* Vector can be scaled */
    auto D = 2. * A;
    std::cout << "D[0] = " << D[0] << std::endl;

    /* Vector can be scaled */
    auto scalar = A*A;
    std::cout << "scalar = " << scalar << std::endl;

The vector class can interact with :ref:`Petsc<Petsc_setup>` if included:

.. code-block:: cpp

    /* Defining the type */
    using Vector=danceq::internal::Vector<double>;

    /* Some Operator Hamiltonian H */
    Hamiltonian_U1 H(L,n);

    /* Retrieve Petsc Mat from H */
    Mat H_mat = H.create_PetscSparseMatrix();

    /* Retrieve Vector class from H_Mat */
    Vector V_from_mat(H_mat);


Operators that are a Lindbladian :ref:`OperatorType<OperatorTypes>` act on the space density matrices which are represented with this :ref:`Vector class<Vector>`.
In this case, the class allows you to directly extract the density matrix via: :ref:`get_density_matrix(...)<Vector_Functions_Miscellaneous_get_density_matrix>` and :ref:`get_density_matrix_in_eigen(...)<Vector_Functions_Miscellaneous_get_density_matrix_in_eigen>`.


Class content
-------------

.. toctree::
    :maxdepth: 2
    :titlesonly:


    Vector/Members.rst
    Vector/Constructors.rst
    Vector/Functions.rst
    Vector/Autodocs.rst