xpnd
==============================================

Purpose
----------------
Expands a column vector into a symmetric matrix.

Format
----------------
.. function:: x = xpnd(v)

    :param v: data to be expanded into a symmetric matrix.
    :type v: Kx1 vector

    :return x: the results of taking *v* and
        filling in a symmetric matrix with its elements.

        .. math::

            M = \frac{\sqrt{1 + 8 \times K} - 1}{2}


    :rtype x: MxM matrix

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

::

    x = { 1,
          2, 3,
          4, 5, 6,
          7, 8, 9, 10 };
    y = xpnd(x);

After the code above, the variables *x* and *y* are equal to:

::

        1
        2
        3
        4       1   2   4   7
    x = 5   y = 2   3   5   8
        6       4   5   6   9
        7       7   8   9  10
        8
        9
       10

Remarks
-------

If *v* does not contain the right number of elements, (that is, if :math:`\sqrt{1 + 8 \times K}` is not 
integral), then an error message is generated.

This function is particularly useful for hard-coding symmetric matrices,
because only about half of the matrix needs to be entered.


.. seealso:: Functions :func:`vech`