r"""
A Very Simple Example
---------------------

We are going to start with a very simple example of a spatial random field
with an isotropic Gaussian covariance model and following parameters:

- variance :math:`\sigma^2=1`
- correlation length :math:`\lambda=10`

First, we set things up and create the axes for the field. We are going to
need the :any:`SRF` class for the actual generation of the spatial random field.
But :any:`SRF` also needs a covariance model and we will simply take the
:any:`Gaussian` model.
"""

import gstools as gs

x = y = range(100)

###############################################################################
# Now we create the covariance model with the parameters :math:`\sigma^2` and
# :math:`\lambda` and hand it over to :any:`SRF`. By specifying a seed,
# we make sure to create reproducible results:

model = gs.Gaussian(dim=2, var=1, len_scale=10)
srf = gs.SRF(model, seed=20170519)

###############################################################################
# With these simple steps, everything is ready to create our first random field.
# We will create the field on a structured grid (as you might have guessed from
# the `x` and `y`), which makes it easier to plot.

field = srf.structured([x, y])
srf.plot()

###############################################################################
# Wow, that was pretty easy!