"""
.. _atomic_orbitals_example:

Plot Atomic Orbitals
--------------------
Visualize the wave functions (orbitals) of the hydrogen atom.

"""

# %%
# Import
# ~~~~~~
# Import the applicable libraries.
#
# .. note::
#    This example is modeled off of `Matplotlib: Hydrogen Wave Function
#    <http://staff.ustc.edu.cn/~zqj/posts/Hydrogen-Wavefunction/>`_.
#
#    This example requires `sympy <https://www.sympy.org/>`_. Install it with:
#
#    .. code-block:: bash
#
#       pip install sympy
import numpy as np
import pyvista as pv
from pyvista import examples

# %%
# Generate the Dataset
# ~~~~~~~~~~~~~~~~~~~~
# Generate the dataset by evaluating the analytic hydrogen wave function from
# ``sympy``.
#
# .. math::
#    \begin{equation}
#        \psi_{n\ell m}(r,\theta,\phi)
#        =
#        \sqrt{
#            \left(\frac{2}{na_0}\right)^3\, \frac{(n-\ell-1)!}{2n[(n+\ell)!]}
#        }
#        e^{-r / na_0}
#        \left(\frac{2r}{na_0}\right)^\ell
#        L_{n-\ell-1}^{2\ell+1} \cdot Y_\ell^m(\theta, \phi)
#    \end{equation}
#
# See `Hydrogen atom <https://en.wikipedia.org/wiki/Hydrogen_atom>`_ for more
# details.
#
# This dataset evaluates this function for the hydrogen orbital
# :math:`3d_{xy}`, with the following quantum numbers:
#
# * Principal quantum number: ``n=3``
# * Azimuthal quantum number: ``l=2``
# * Magnetic quantum number: ``m=-2``

grid = examples.load_hydrogen_orbital(3, 2, -2)
grid


# %%
# Plot the Orbital
# ~~~~~~~~~~~~~~~~
# Plot the orbital using :func:`add_volume() <pyvista.Plotter.add_volume>` and
# using the default scalars contained in ``grid``, ``real_wf``. This way we
# can plot more than just the probability of the electron, but also the phase
# of the electron wave function.
#
# .. note::
#    Since the real value of evaluated wave function for this orbital varies
#    between ``[-<value>, <value>]``, we cannot use the default opacity
#    ``opacity='linear'``. Instead, we use ``[1, 0, 1]`` since we would like
#    the opacity to be proportional to the absolute value of the scalars.

# sphinx_gallery_start_ignore
# volume rendering does not work in interactive plots currently
PYVISTA_GALLERY_FORCE_STATIC = True
# sphinx_gallery_end_ignore

pl = pv.Plotter()
vol = pl.add_volume(grid, cmap='magma', opacity=[1, 0, 1])
vol.prop.interpolation_type = 'linear'
pl.camera.zoom(2)
pl.show_axes()
pl.show()


# %%
# Plot the Orbital Contours as an Isosurface
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Generate the contour plot for the orbital by determining when the orbital
# equals 10% the maximum value of the orbital. This effectively captures the
# most likely locations of the electron for this orbital.
#
# Note how we use the absolute value of the scalars when evaluating
# :func:`contour() <pyvista.DataSetFilters.contour>` to capture where the
# positive and negative phases cross ``eval_at``.

eval_at = grid['real_wf'].max() * 0.1
contours = grid.contour(
    [eval_at],
    scalars=np.abs(grid['real_wf']),
    method='marching_cubes',
)
contours = contours.interpolate(grid)
contours.plot(
    smooth_shading=True,
    show_scalar_bar=False,
)


# %%
# Volumetric Plot: Plot the Orbitals using RGBA
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Let's now combine some of the best parts of the two above plots. The
# volumetric plot is great for showing the probability of the "electron cloud"
# orbitals, but the colormap doesn't quite match reality as well as the
# isosurface plot.
#
# For this example we're going to use an RGBA colormap to tightly control the
# way the orbitals are plotted. For this, the opacity will be mapped to the
# probability of the electron being at a location in the grid, which we can do
# by taking the absolute value squared of the orbital's wave function. We can
# set the color of the orbital based on the phase, which we can get simply
# with ``orbital['real_wf'] < 0``.
#
# Let's start with a simple one, the :math:`3p_z` orbital.

# sphinx_gallery_start_ignore
# volume rendering does not work in interactive plots currently
PYVISTA_GALLERY_FORCE_STATIC = True
# sphinx_gallery_end_ignore


def plot_orbital(orbital, cpos='iso', clip_plane='x'):
    """Plot an electron orbital using an RGBA colormap."""
    neg_mask = orbital['real_wf'] < 0
    rgba = np.zeros((orbital.n_points, 4), np.uint8)
    rgba[neg_mask, 0] = 255
    rgba[~neg_mask, 1] = 255

    # normalize opacity
    opac = np.abs(orbital['real_wf']) ** 2
    opac /= opac.max()
    rgba[:, -1] = opac * 255

    orbital['plot_scalars'] = rgba

    pl = pv.Plotter()
    vol = pl.add_volume(
        orbital,
        scalars='plot_scalars',
    )
    vol.prop.interpolation_type = 'linear'
    if clip_plane:
        pl.add_volume_clip_plane(
            vol,
            normal=clip_plane,
            normal_rotation=False,
        )
    pl.camera_position = cpos
    pl.camera.zoom(1.5)
    pl.show_axes()
    return pl.show()


hydro_orbital = examples.load_hydrogen_orbital(3, 1, 0)
plot_orbital(hydro_orbital, clip_plane='-x')


# %%
# Volumetric Plot: :math:`4d_{z^2}` orbital
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# sphinx_gallery_start_ignore
# volume rendering does not work in interactive plots currently
PYVISTA_GALLERY_FORCE_STATIC = True
# sphinx_gallery_end_ignore
hydro_orbital = examples.load_hydrogen_orbital(4, 2, 0)
plot_orbital(hydro_orbital, clip_plane='-y')


# %%
# Volumetric Plot: :math:`4d_{xz}` orbital
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# sphinx_gallery_start_ignore
# volume rendering does not work in interactive plots currently
PYVISTA_GALLERY_FORCE_STATIC = True
# sphinx_gallery_end_ignore
hydro_orbital = examples.load_hydrogen_orbital(4, 2, -1)
plot_orbital(hydro_orbital, clip_plane='-y')


# %%
# Plot an Orbital Using a Density Plot
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# We can also plot atomic orbitals using a 3D density plot. For this, we will
# use :func:`numpy.random.choice` to sample all the points of our
# :class:`pyvista.ImageData` based on the probability of the electron being
# at that coordinate.

# Seed rng for reproducibility
rng = np.random.default_rng(seed=0)

# Generate the orbital and sample based on the square of the probability of an
# electron being within a particular volume of space.
hydro_orbital = examples.load_hydrogen_orbital(4, 2, 0, zoom_fac=0.5)
prob = np.abs(hydro_orbital['real_wf']) ** 2
prob /= prob.sum()
indices = rng.choice(hydro_orbital.n_points, 10000, p=prob)

# add a small amount of noise to these coordinates to remove the "grid like"
# structure present in the underlying ImageData
points = hydro_orbital.points[indices]
points += rng.random(points.shape) - 0.5

# Create a point cloud and add the phase as the active scalars
point_cloud = pv.PolyData(points)
point_cloud['phase'] = hydro_orbital['real_wf'][indices] < 0

# Turn the point cloud into individual spheres. We do this so we can improve
# the plot by enabling surface space ambient occlusion (SSAO)
dplot = point_cloud.glyph(
    geom=pv.Sphere(theta_resolution=8, phi_resolution=8),
    scale=False,
    orient=False,
)

# be sure to enable SSAO here. This makes the "points" that are deeper within
# the density plot darker.
pl = pv.Plotter()
pl.add_mesh(
    dplot,
    smooth_shading=True,
    show_scalar_bar=False,
    cmap=['red', 'green'],
    ambient=0.2,
)
pl.enable_ssao(radius=10)
pl.enable_anti_aliasing()
pl.camera.zoom(2)
pl.background_color = 'w'
pl.show()


# %%
# Density Plot - Gaussian Points Representation
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Finally, let's plot the same data using the "Gaussian points" representation.


# sphinx_gallery_start_ignore
# volume rendering does not work in interactive plots currently
PYVISTA_GALLERY_FORCE_STATIC = True
# sphinx_gallery_end_ignore

point_cloud.plot(
    style='points_gaussian',
    render_points_as_spheres=False,
    point_size=3,
    emissive=True,
    background='k',
    show_scalar_bar=False,
    cpos='xz',
    zoom=2,
)
