# Directly Computing \(\xi(r)\) and \(wp(rp)\)ΒΆ

For a periodic cosmological box, the 3-d auto correlation, \(\xi(r)\), and
the projected auto correlation function, \(wp(rp)\), can be directly computed
using the Natural Estimator. The relevant python wrappers are present in
`Corrfunc.theory.xi`

and `Corrfunc.theory.wp`

. See Notes on the Random-Random Term in Autocorrelations
for details on how the Natural Estimator is computed.

```
>>> import numpy as np
>>> from Corrfunc.theory.wp import wp
>>> from Corrfunc.theory.xi import xi
>>> from Corrfunc.io import read_catalog
>>> X, Y, Z = read_catalog()
>>> boxsize = 420.0
>>> nthreads = 2
>>> pimax = 40.0
>>> nbins = 10
>>> bins = np.linspace(0.1, 10.0, nbins + 1) # Note the + 1 to nbins
>>> wp_counts = wp(boxsize, pimax, nthreads, bins, X, Y, Z)
>>> xi_counts = xi(boxsize, nthreads, bins, X, Y, Z)
```

See the complete reference here `Corrfunc`

.