"""
Anisotropy and Rotation
=======================

The internally used (semi-) variogram
represents the isotropic case for the model.
Nevertheless, you can provide anisotropy ratios by:
"""

import gstools as gs

model = gs.Gaussian(dim=3, var=2.0, len_scale=10, anis=0.5)
print(model.anis)
print(model.len_scale_vec)


###############################################################################
# As you can see, we defined just one anisotropy-ratio
# and the second transversal direction was filled up with ``1.``.
# You can get the length-scales in each direction by
# the attribute :any:`CovModel.len_scale_vec`. For full control you can set
# a list of anistropy ratios: ``anis=[0.5, 0.4]``.
#
# Alternatively you can provide a list of length-scales:

model = gs.Gaussian(dim=3, var=2.0, len_scale=[10, 5, 4])
model.plot("vario_spatial")
print("Anisotropy representations:")
print("Anis. ratios:", model.anis)
print("Main length scale", model.len_scale)
print("All length scales", model.len_scale_vec)


###############################################################################
# Rotation Angles
# ---------------
#
# The main directions of the field don't have to coincide with the spatial
# directions :math:`x`, :math:`y` and :math:`z`. Therefore you can provide
# rotation angles for the model:

model = gs.Gaussian(dim=3, var=2.0, len_scale=[10, 2], angles=2.5)
model.plot("vario_spatial")
print("Rotation angles", model.angles)

###############################################################################
# Again, the angles were filled up with ``0.`` to match the dimension and you
# could also provide a list of angles. The number of angles depends on the
# given dimension:
#
# - in 1D: no rotation performable
# - in 2D: given as rotation around z-axis
# - in 3D: given by yaw, pitch, and roll (known as
#   `Tait–Bryan <https://en.wikipedia.org/wiki/Euler_angles#Tait-Bryan_angles>`_
#   angles)
# - in nD: See the random field example about higher dimensions