"""
.. _Lineshapes_Example:

Lineshapes (#10)
=================
"""

# %%
# This example demonstrates how to calculate the different lineshape functions
# available in the SpinLab :mod:`spinlab.math.lineshape` module: the Gaussian,
# Lorentzian, Voigtian, and Dysonian distributions.

import spinlab as sl
import numpy as np
from spinlab.math import lineshape
from spinlab.plotting.colors import (
    primary1,
    accent,
    BrukerPacific,
    BrukerOcean,
    BrukerOrange,
    BrukerDolomite,
)

# %%
# Define a common x-axis and center/width parameters used for all lineshapes.

x = np.linspace(-10, 10, 2001)
x0 = 0.0  # center
gamma = 1.0  # Lorentzian width
sigma = 1.0  # Gaussian width

# %%
# Gaussian
# --------
# The Gaussian lineshape is calculated with :func:`spinlab.math.lineshape.gaussian`.
# Setting ``deriv=True`` returns its first derivative, which corresponds to the
# lineshape recorded with field modulation.

y_gaussian = lineshape.gaussian(x, x0, sigma)
y_gaussian_deriv = lineshape.gaussian(x, x0, sigma, deriv=True)

sl.plt.figure()
sl.plt.plot(x, y_gaussian, color=primary1, label="absorptive")
sl.plt.plot(x, y_gaussian_deriv, color=accent, label="derivative")
sl.plt.xlabel("x")
sl.plt.ylabel("Intensity (arb. u.)")
sl.plt.title("Gaussian Lineshape")
sl.plt.legend()
sl.plt.grid(ls=":")
sl.plt.show()

# %%
# Lorentzian
# ----------
# The Lorentzian lineshape is calculated with :func:`spinlab.math.lineshape.lorentzian`.
# Setting ``deriv=True`` returns its first derivative, which corresponds to the
# imaginary part of a phased EPR spectrum.

y_lorentzian = lineshape.lorentzian(x, x0, gamma)
y_lorentzian_deriv = lineshape.lorentzian(x, x0, gamma, deriv=True)

sl.plt.figure()
sl.plt.plot(x, y_lorentzian, color=primary1, label="absorptive")
sl.plt.plot(x, y_lorentzian_deriv, color=accent, label="derivative")
sl.plt.xlabel("x")
sl.plt.ylabel("Intensity (arb. u.)")
sl.plt.title("Lorentzian Lineshape")
sl.plt.legend()
sl.plt.grid(ls=":")
sl.plt.show()

# %%
# Voigtian
# --------
# The Voigtian lineshape is the convolution of a Gaussian and a Lorentzian
# distribution and is calculated with :func:`spinlab.math.lineshape.voigtian`.
# Setting ``deriv=True`` returns its first derivative (Gaussian-broadened
# imaginary part of a phased spectrum).

y_voigtian = lineshape.voigtian(x, x0, sigma, gamma)
y_voigtian_deriv = lineshape.voigtian(x, x0, sigma, gamma, deriv=True)

sl.plt.figure()
sl.plt.plot(x, y_voigtian, color=primary1, label="absorptive")
sl.plt.plot(x, y_voigtian_deriv, color=accent, label="derivative")
sl.plt.xlabel("x")
sl.plt.ylabel("Intensity (arb. u.)")
sl.plt.title("Voigtian Lineshape")
sl.plt.legend()
sl.plt.grid(ls=":")
sl.plt.show()

# %%
# Dysonian
# --------
# The Dysonian lineshape is calculated with :func:`spinlab.math.lineshape.dysonian`.
# It mixes absorption and dispersion contributions through the asymmetry
# parameter ``alpha``, which is used to describe EPR/CESR lines from
# conducting samples. ``alpha=0`` reduces the Dysonian to a symmetric
# Lorentzian. Setting ``deriv=True`` returns its first derivative.

alpha = 0.5
y_dysonian = lineshape.dysonian(x, x0, gamma, alpha)
y_dysonian_deriv = lineshape.dysonian(x, x0, gamma, alpha, deriv=True)

sl.plt.figure()
sl.plt.plot(x, y_dysonian, color=primary1, label="absorptive")
sl.plt.plot(x, y_dysonian_deriv, color=accent, label="derivative")
sl.plt.xlabel("x")
sl.plt.ylabel("Intensity (arb. u.)")
sl.plt.title(f"Dysonian Lineshape ($\\alpha$ = {alpha})")
sl.plt.legend()
sl.plt.grid(ls=":")
sl.plt.show()

# %%
# Comparison
# ----------
# All four lineshapes plotted together for direct comparison, absorptive
# shapes on the left and their derivatives on the right.

fig, (ax_abs, ax_deriv) = sl.plt.subplots(1, 2, figsize=(10, 4))

ax_abs.plot(x, y_gaussian, color=BrukerPacific, label="Gaussian")
ax_abs.plot(x, y_lorentzian, color=BrukerOrange, label="Lorentzian")
ax_abs.plot(x, y_voigtian, color=BrukerDolomite, label="Voigtian")
ax_abs.plot(x, y_dysonian, color=BrukerOcean, label=f"Dysonian ($\\alpha$ = {alpha})")
ax_abs.set_xlabel("x")
ax_abs.set_ylabel("Intensity (arb. u.)")
ax_abs.set_title("Absorptive")
ax_abs.legend()
ax_abs.grid(ls=":")

ax_deriv.plot(x, y_gaussian_deriv, color=BrukerPacific, label="Gaussian")
ax_deriv.plot(x, y_lorentzian_deriv, color=BrukerOrange, label="Lorentzian")
ax_deriv.plot(x, y_voigtian_deriv, color=BrukerDolomite, label="Voigtian")
ax_deriv.plot(
    x, y_dysonian_deriv, color=BrukerOcean, label=f"Dysonian ($\\alpha$ = {alpha})"
)
ax_deriv.set_xlabel("x")
ax_deriv.set_ylabel("Intensity (arb. u.)")
ax_deriv.set_title("Derivative")
ax_deriv.legend()
ax_deriv.grid(ls=":")

fig.suptitle("Comparison of Lineshapes")
fig.tight_layout()
sl.plt.show()