"""
Generating a Random 2D Vector Field
-----------------------------------

As a first example we are going to generate a 2d vector field with a Gaussian
covariance model on a structured grid:
"""

import numpy as np

import gstools as gs

# the grid
x = np.arange(100)
y = np.arange(100)

# a smooth Gaussian covariance model
model = gs.Gaussian(dim=2, var=1, len_scale=10)
srf = gs.SRF(model, generator="VectorField", seed=19841203)
srf((x, y), mesh_type="structured")
srf.plot()

###############################################################################
# Let us have a look at the influence of the covariance model. Choosing the
# exponential model and keeping all other parameters the same

# a rougher exponential covariance model
model2 = gs.Exponential(dim=2, var=1, len_scale=10)
srf.model = model2
srf((x, y), mesh_type="structured", seed=19841203)
srf.plot()

###############################################################################
# and we see, that the wiggles are much "rougher" than the smooth Gaussian ones.


###############################################################################
# Applications
# ~~~~~~~~~~~~
#
# One great advantage of the Kraichnan method is, that after some initializations,
# one can compute the velocity field at arbitrary points, online, with hardly any
# overhead.
# This means, that for a Lagrangian transport simulation for example, the velocity
# can be evaluated at each particle position very efficiently and without any
# interpolation. These field interpolations are a common problem for Lagrangian
# methods.