r"""
Linear Spin Wave theory
***********************

.. include:: ../../exercises/8.inc

All methods for linear spin-wave theory are grouped in the :py:class:`magnopy.LSWT` class.

To create it we require two things

* Spin Hamiltonian
* Directions of spins in the ground state
"""

import numpy as np
import magnopy

# %%
#
# An example of the cubic ferromagnet with nearest-neighbor interactions and easy
# magnetic axis along :math:`\mathbf{z}`.

spinham = magnopy.examples.cubic_ferro_nn(S=1, J_21=(0, 0, -0.5))

# Get the LSWT object from it
lswt = magnopy.LSWT(spinham=spinham, spin_directions=[[0, 0, 1]])

# %%
# Once created it can be used to compute parts of the magnon Hamiltonian
#
# Correction to the classical energy
# ==================================

print(lswt.E_2())

# %%
# Coefficients of the one-operator terms
# ======================================

print(lswt.O())

# %%
# Magnon energies
# ===============

print(lswt.omega(k=[0, 0, 0]))


# %%
# Parallelization
# ===============
#
# Typically one wants to compute magnon energies for a set of k-points. Often for a
# rather large set of k-points. Magnopy offers simple interface to parallelize the
# calculations over the k-points using multiprocessing. See
# :py:func:`magnopy.multiprocess_over_k` for details. For example, to compute magnon
# energies for the set of k-points (that are given as absolute coordinates in reciprocal
# space) using two processes use


kpoints = np.linspace([0, 0, 0], [1, 0, 0], 1000)

results = magnopy.multiprocess_over_k(
    kpoints=kpoints,
    relative=False,
    function=lswt.omega,
    number_processors=2,
)

# %%
# Note that ``results[i]`` is equivalent to ``lswt.omega(k=kpoints[i], relative=False)``.

print(results[42])

print(lswt.omega(k=kpoints[42], relative=False))


# sphinx_gallery_thumbnail_path = 'img/cat-numbers/8.png'