correlated.</p>
<p><code>euclid_type</code> Details: Let \(D\) be a matrix of Euclidean distances,
\(r = D / range\), and \(I\) be an identity matrix. Then parametric
forms for elements of \(R(ze)\) are given below:</p><ul><li><p>exponential: \(exp(- r )\)</p></li>
<li><p>spherical: \((1 - 1.5r + 0.5r^3) * (r &lt;= 1)\)</p></li>
<li><p>gaussian: \(exp(- r^2 )\)</p></li>
<li><p>cubic: \((1 - 7r^2 + 8.75r^3 - 3.5r^5 + 0.75r^7) * (r &lt;= 1)\)</p></li>
<li><p>pentaspherical: \((1 - 1.875r + 1.25r^3 - 0.375r^5)