bandrv
==============================================

Purpose
----------------
Creates a symmetric banded matrix, given its compact form.

Format
----------------
.. function:: y = bandrv(a)

    :param a:
    :type a: KxN compact form matrix

    :return y: 

    :rtype y: KxK symmetric banded matrix

Examples
----------------

Create a diagonal matrix
+++++++++++++++++++++++++++

::

    v = { 1, 9, 6 };

    v_mat = bandrv(v);

After the above code, ``v_mat`` will equal:

::

    1  0  0
    0  9  0
    0  0  6

Create a symmetric banded matrix
++++++++++++++++++++++++++++++++++

::

    x = { 1 2 0 0,
          2 8 1 0,
          0 1 5 2,
          0 0 2 3 };

    // Create a version of 'x' in band format
    a = band(x, 1);

    // Expand the banded version of 'x' back to a full matrix
    y = bandrv(a);

After the code above:

::

             0   1       1   2   0   0          1   2   0   0
        a =  2   8   x = 2   8   1   0      y = 2   8   1   0
             1   5       0   1   5   2          0   1   5   2
             2   3       0   0   2   3          0   0   2   3

Remarks
-------

*a* is the compact form of a symmetric banded matrix, as generated by
:func:`band`. *a* stores subdiagonals right to left, with the principal diagonal
in the rightmost (Nth) column. The upper left corner of *a* is unused.
:func:`bandchol` expects a matrix of this form.

*y* is the fully expanded form of *a*, a KxK matrix with N-1 subdiagonals.

.. seealso:: Functions :func:`band`, :func:`bandchol`, :func:`bandcholsol`, :func:`bandltsol`, :func:`bandsolpd`