Inverse empirical cumulative distribution function

Quantile function or inverse-ECDF of some data-sample. Data is finite and the ECDF from which the inverse is taken is discontiuous.

Quantile function for an empirical cumulative distribution function (ECDF), i.e. inverse-ECDF, of some (finite) data-sample. The ECDF (F) is thus discontinuous and the quantile function (Q) at q is computed as:
Q(q) = inf{x: q<=F(x)}.

Simple problem, frequently discussed online, for which however a clean matlab code seems not to be available.