xpnd#

Purpose#

Expands a column vector into a symmetric matrix.

x = xpnd(v)#

Parameters:

v (Kx1 vector) – data to be expanded into a symmetric matrix.

Returns:

x (MxM matrix) –

the results of taking v and filling in a symmetric matrix with its elements.

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

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

If v does not contain the right number of elements, (that is, if \(\sqrt{1 + 8 \times K}\) 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.