The value of zero

At several places in gstat, a result of a calculation that is very close to zero should be treated as zero. Therefor, the value of zero is set to a small positive value, and a quantity $a$ is treated as zero when $\vert a\vert < \epsilon$, with $\epsilon$ the value of zero. This applies to the following cases:

1.

when average is set, data points are averaged when their separation distance is smaller than $\epsilon$

2.

when, in sequential simulation, the absolute value of the kriging variance is smaller than $\epsilon$, it is treated as zero and ignored for simulation (i.e., the kriging prediction is returned as the simulated value).

3.

for the calculation of difference between two maps, (-e mapdiff) cell values are said to be different if they differ more than $\epsilon$.

4.

for the calculation of point-block or block-block (generalized) covariances, a block discretization point is shifted over distance $\epsilon$ when it is closer than $\epsilon$ to another (discretizing) point.

5.

for the filling of the point-point (generalized) covariance matrix during REML fitting of covariance models, an off-diagonal point-point distances in $x$, $y$ and $z$ direction will be set to ${\rm SIGN}(a)\epsilon$ when the separation distance between point pairs is smaller then $\epsilon$.