"""
==============
Secondary Axis
==============

Sometimes we want a secondary axis on a plot, for instance to convert
radians to degrees on the same plot.  We can do this by making a child
axes with only one axis visible via `.axes.Axes.secondary_xaxis` and
`.axes.Axes.secondary_yaxis`.  This secondary axis can have a different scale
than the main axis by providing both a forward and an inverse conversion
function in a tuple to the ``functions`` kwarg:
"""

import matplotlib.pyplot as plt
import numpy as np
import datetime
import matplotlib.dates as mdates
from matplotlib.ticker import AutoMinorLocator

fig, ax = plt.subplots(constrained_layout=True)
x = np.arange(0, 360, 1)
y = np.sin(2 * x * np.pi / 180)
ax.plot(x, y)
ax.set_xlabel('angle [degrees]')
ax.set_ylabel('signal')
ax.set_title('Sine wave')


def deg2rad(x):
    return x * np.pi / 180


def rad2deg(x):
    return x * 180 / np.pi


secax = ax.secondary_xaxis('top', functions=(deg2rad, rad2deg))
secax.set_xlabel('angle [rad]')
plt.show()

###########################################################################
# Here is the case of converting from wavenumber to wavelength in a
# log-log scale.
#
# .. note ::
#
#   In this case, the xscale of the parent is logarithmic, so the child is
#   made logarithmic as well.

fig, ax = plt.subplots(constrained_layout=True)
x = np.arange(0.02, 1, 0.02)
np.random.seed(19680801)
y = np.random.randn(len(x)) ** 2
ax.loglog(x, y)
ax.set_xlabel('f [Hz]')
ax.set_ylabel('PSD')
ax.set_title('Random spectrum')


def forward(x):
    return 1 / x


def inverse(x):
    return 1 / x


secax = ax.secondary_xaxis('top', functions=(forward, inverse))
secax.set_xlabel('period [s]')
plt.show()

###########################################################################
# Sometime we want to relate the axes in a transform that is ad-hoc from
# the data, and is derived empirically.  In that case we can set the
# forward and inverse transforms functions to be linear interpolations from the
# one data set to the other.

fig, ax = plt.subplots(constrained_layout=True)
xdata = np.arange(1, 11, 0.4)
ydata = np.random.randn(len(xdata))
ax.plot(xdata, ydata, label='Plotted data')

xold = np.arange(0, 11, 0.2)
# fake data set relating x coordinate to another data-derived coordinate.
# xnew must be monotonic, so we sort...
xnew = np.sort(10 * np.exp(-xold / 4) + np.random.randn(len(xold)) / 3)

ax.plot(xold[3:], xnew[3:], label='Transform data')
ax.set_xlabel('X [m]')
ax.legend()


def forward(x):
    return np.interp(x, xold, xnew)


def inverse(x):
    return np.interp(x, xnew, xold)


secax = ax.secondary_xaxis('top', functions=(forward, inverse))
secax.xaxis.set_minor_locator(AutoMinorLocator())
secax.set_xlabel('$X_{other}$')

plt.show()

###########################################################################
# A final example translates np.datetime64 to yearday on the x axis and
# from Celsius to Fahrenheit on the y axis.  Note the addition of a
# third y axis, and that it can be placed using a float for the
# location argument

dates = [datetime.datetime(2018, 1, 1) + datetime.timedelta(hours=k * 6)
         for k in range(240)]
temperature = np.random.randn(len(dates)) * 4 + 6.7
fig, ax = plt.subplots(constrained_layout=True)

ax.plot(dates, temperature)
ax.set_ylabel(r'$T\ [^oC]$')
plt.xticks(rotation=70)


def date2yday(x):
    """Convert matplotlib datenum to days since 2018-01-01."""
    y = x - mdates.date2num(datetime.datetime(2018, 1, 1))
    return y


def yday2date(x):
    """Return a matplotlib datenum for *x* days after 2018-01-01."""
    y = x + mdates.date2num(datetime.datetime(2018, 1, 1))
    return y


secax_x = ax.secondary_xaxis('top', functions=(date2yday, yday2date))
secax_x.set_xlabel('yday [2018]')


def celsius_to_fahrenheit(x):
    return x * 1.8 + 32


def fahrenheit_to_celsius(x):
    return (x - 32) / 1.8


secax_y = ax.secondary_yaxis(
    'right', functions=(celsius_to_fahrenheit, fahrenheit_to_celsius))
secax_y.set_ylabel(r'$T\ [^oF]$')


def celsius_to_anomaly(x):
    return (x - np.mean(temperature))


def anomaly_to_celsius(x):
    return (x + np.mean(temperature))


# use of a float for the position:
secax_y2 = ax.secondary_yaxis(
    1.2, functions=(celsius_to_anomaly, anomaly_to_celsius))
secax_y2.set_ylabel(r'$T - \overline{T}\ [^oC]$')


plt.show()

#############################################################################
#
# ------------
#
# References
# """"""""""
#
# The use of the following functions and methods is shown in this example:

import matplotlib

matplotlib.axes.Axes.secondary_xaxis
matplotlib.axes.Axes.secondary_yaxis