"""
==================================
Rendering math equations using TeX
==================================

You can use TeX to render all of your Matplotlib text by setting
:rc:`text.usetex` to True.  This requires that you have TeX and the other
dependencies described in the :doc:`/tutorials/text/usetex` tutorial properly
installed on your system.  Matplotlib caches processed TeX expressions, so that
only the first occurrence of an expression triggers a TeX compilation. Later
occurrences reuse the rendered image from the cache and are thus faster.

Unicode input is supported, e.g. for the y-axis label in this example.
"""

import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['text.usetex'] = True


t = np.linspace(0.0, 1.0, 100)
s = np.cos(4 * np.pi * t) + 2

fig, ax = plt.subplots(figsize=(6, 4), tight_layout=True)
ax.plot(t, s)

ax.set_xlabel(r'\textbf{time (s)}')
ax.set_ylabel('\\textit{Velocity (\N{DEGREE SIGN}/sec)}', fontsize=16)
ax.set_title(r'\TeX\ is Number $\displaystyle\sum_{n=1}^\infty'
             r'\frac{-e^{i\pi}}{2^n}$!', fontsize=16, color='r')

#############################################################################
# A more complex example.

fig, ax = plt.subplots()
# interface tracking profiles
N = 500
delta = 0.6
X = np.linspace(-1, 1, N)
ax.plot(X, (1 - np.tanh(4 * X / delta)) / 2,    # phase field tanh profiles
        X, (1.4 + np.tanh(4 * X / delta)) / 4, "C2",  # composition profile
        X, X < 0, "k--")                        # sharp interface

# legend
ax.legend(("phase field", "level set", "sharp interface"),
          shadow=True, loc=(0.01, 0.48), handlelength=1.5, fontsize=16)

# the arrow
ax.annotate("", xy=(-delta / 2., 0.1), xytext=(delta / 2., 0.1),
            arrowprops=dict(arrowstyle="<->", connectionstyle="arc3"))
ax.text(0, 0.1, r"$\delta$",
        color="black", fontsize=24,
        horizontalalignment="center", verticalalignment="center",
        bbox=dict(boxstyle="round", fc="white", ec="black", pad=0.2))

# Use tex in labels
ax.set_xticks([-1, 0, 1])
ax.set_xticklabels(["$-1$", r"$\pm 0$", "$+1$"], color="k", size=20)

# Left Y-axis labels, combine math mode and text mode
ax.set_ylabel(r"\bf{phase field} $\phi$", color="C0", fontsize=20)
ax.set_yticks([0, 0.5, 1])
ax.set_yticklabels([r"\bf{0}", r"\bf{.5}", r"\bf{1}"], color="k", size=20)

# Right Y-axis labels
ax.text(1.02, 0.5, r"\bf{level set} $\phi$",
        color="C2", fontsize=20, rotation=90,
        horizontalalignment="left", verticalalignment="center",
        clip_on=False, transform=ax.transAxes)

# Use multiline environment inside a `text`.
# level set equations
eq1 = (r"\begin{eqnarray*}"
       r"|\nabla\phi| &=& 1,\\"
       r"\frac{\partial \phi}{\partial t} + U|\nabla \phi| &=& 0 "
       r"\end{eqnarray*}")
ax.text(1, 0.9, eq1, color="C2", fontsize=18,
        horizontalalignment="right", verticalalignment="top")

# phase field equations
eq2 = (r"\begin{eqnarray*}"
       r"\mathcal{F} &=& \int f\left( \phi, c \right) dV, \\ "
       r"\frac{ \partial \phi } { \partial t } &=& -M_{ \phi } "
       r"\frac{ \delta \mathcal{F} } { \delta \phi }"
       r"\end{eqnarray*}")
ax.text(0.18, 0.18, eq2, color="C0", fontsize=16)

ax.text(-1, .30, r"gamma: $\gamma$", color="r", fontsize=20)
ax.text(-1, .18, r"Omega: $\Omega$", color="b", fontsize=20)

plt.show()
