"""
==============
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* keyword argument:
"""

import datetime

import matplotlib.pyplot as plt
import numpy as np

import matplotlib.dates as mdates

fig, ax = plt.subplots(layout='constrained')
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()

# %%
# By default, the secondary axis is drawn in the Axes coordinate space.
# We can also provide a custom transform to place it in a different
# coordinate space. Here we put the axis at Y = 0 in data coordinates.

fig, ax = plt.subplots(layout='constrained')
x = np.arange(0, 10)
np.random.seed(19680801)
y = np.random.randn(len(x))
ax.plot(x, y)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_title('Random data')

# Pass ax.transData as a transform to place the axis relative to our data
secax = ax.secondary_xaxis(0, transform=ax.transData)
secax.set_xlabel('Axis at Y = 0')
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(layout='constrained')
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 one_over(x):
    """Vectorized 1/x, treating x==0 manually"""
    x = np.array(x, float)
    near_zero = np.isclose(x, 0)
    x[near_zero] = np.inf
    x[~near_zero] = 1 / x[~near_zero]
    return x


# the function "1/x" is its own inverse
inverse = one_over


secax = ax.secondary_xaxis('top', functions=(one_over, 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. Or, one axis could be a complicated nonlinear function of the
# other. In these cases we can set the forward and inverse transform functions to be
# linear interpolations from the one set of independent variables to the other.
#
# .. note::
#
#   In order to properly handle the data margins, the mapping functions
#   (``forward`` and ``inverse`` in this example) need to be defined beyond the
#   nominal plot limits. This condition can be enforced by extending the
#   interpolation beyond the plotted values, both to the left and the right,
#   see ``x1n`` and ``x2n`` below.

fig, ax = plt.subplots(layout='constrained')
x1_vals = np.arange(2, 11, 0.4)
# second independent variable is a nonlinear function of the other.
x2_vals = x1_vals ** 2
ydata = 50.0 + 20 * np.random.randn(len(x1_vals))
ax.plot(x1_vals, ydata, label='Plotted data')
ax.plot(x1_vals, x2_vals, label=r'$x_2 = x_1^2$')
ax.set_xlabel(r'$x_1$')
ax.legend()

# the forward and inverse functions must be defined on the complete visible axis range
x1n = np.linspace(0, 20, 201)
x2n = x1n**2


def forward(x):
    return np.interp(x, x1n, x2n)


def inverse(x):
    return np.interp(x, x2n, x1n)

# use axvline to prove that the derived secondary axis is correctly plotted
ax.axvline(np.sqrt(40), color="grey", ls="--")
ax.axvline(10, color="grey", ls="--")
secax = ax.secondary_xaxis('top', functions=(forward, inverse))
secax.set_xticks([10, 20, 40, 60, 80, 100])
secax.set_xlabel(r'$x_2$')

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(layout='constrained')

ax.plot(dates, temperature)
ax.set_ylabel(r'$T\ [^oC]$')
ax.xaxis.set_tick_params(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()

# %%
#
# .. admonition:: References
#
#    The use of the following functions, methods, classes and modules is shown
#    in this example:
#
#    - `matplotlib.axes.Axes.secondary_xaxis`
#    - `matplotlib.axes.Axes.secondary_yaxis`
#
# .. tags::
#
#    component: axis
#    plot-type: line
#    level: beginner