"""
Quickstart
==========

This tutorial shows how to calculate light rays between curves calculated from
scratch, meaning neither curve data nor configuration files need to be defined
prior to starting the tutorial.
"""

import numpy as np
import matplotlib.pyplot as plt
from greopy.initial_conditions import initial_conditions_calc
from greopy.orbit_calc import geodesic_calc
from greopy.emitter_observer_problem import eop_solver
from greopy.emitter_observer_solution_plot import eop_plot

# %%
# Initial conditions and the spacetime metric are supplied as a dictionary of
# the following form:

config = {
    'Curve_1': {
        'proper_times': {'time_initial': 0, 'time_final': 7000.0},
        'initial_event': {
            'x0': 0,
            'radius': 6971000.0,
            'theta': np.pi / 2,
            'phi': 0
        },
        'initial_velocity': {
            'velocity_radial': 0,
            'velocity_polar': 0,
            'velocity_azimuthal': 0.00110815,
        },
    },
    'Curve_2': {
        'proper_times': {'time_initial': 0, 'time_final': 7000.0},
        'initial_event': {
            'x0': 0,
            'radius': 7071000.0,
            'theta': np.pi / 2,
            'phi': 0
        },
        'initial_velocity': {
            'velocity_radial': 0,
            'velocity_polar': 0,
            'velocity_azimuthal': 0.00110815,
        }
    },
    'Metric': {
        'name': 'Schwarzschild',
        'params': {'multipole_moments': [398600441500000.0]},
    },
}

# %%
# The ``initial_conditions_calc`` function is used to calculate the
# four-velocities at the initial events from the given config dictionary and
# returns the events with their corresponding four-velocity:

event_1, velocity_1, event_2, velocity_2 = initial_conditions_calc(config)

# %%
# Each event with their initial four-velocity forms an initial value problem
# that is solved with the ``geodesic_calc`` function; the returned curves are
# the emitter and receiver that will be exchanging light signals:

emission_curve_data, receiver_curve_data = geodesic_calc(
    config,
    (event_1, velocity_1, event_2, velocity_2),
)

# %%
# Reduce the number of rows in the DataFrame to reduce number of light rays to
# be calculated:

emission_curve_reduced = emission_curve_data[0:600:150]

# %%
# The light signals can now be calculated via the ``eop_solver`` function,
# given the ``config`` and the two previously calculated curves:

light_rays = eop_solver(config,
                        emission_curve_reduced,
                        receiver_curve_data,
                        hypersurface_approximation=True,
                        euclidean_approximation=True)

# %%
# Optionally, the results can be visualised via the ``eop_plot`` function:

eop_plot(emission_curve_data, receiver_curve_data, light_rays)

# %%
# This plots the emission, receiver and light ray curves. From here, the plot
# can either be shown or saved via the corresponding matplotlib functions. For
# this example, the result will just be shown without saving it, which requires
# a Matplotlib backend, see
# https://matplotlib.org/stable/users/explain/figure/backends.html
# for more information:

plt.show()