Square root of positive real data

Let

$\displaystyle z_i=\sqrt{x_i}, \; 1\leq i \leq N.$

Then, the Jacobian is

$\displaystyle \frac{\partial z_i}{\partial x_i} = \frac{1}{2} x_i^{-1/2},$

so

$\displaystyle \log J = - \sum_{i=1}^N \log (2 z_i).$

Inversion is trivial: $ x_i=z_i^2.$ For more information, refer to the software module software/module_sqrt.m.



Baggenstoss 2017-05-19