"""
==============================================
Including upper and lower limits in error bars
==============================================

In matplotlib, errors bars can have "limits". Applying limits to the
error bars essentially makes the error unidirectional. Because of that,
upper and lower limits can be applied in both the y- and x-directions
via the ``uplims``, ``lolims``, ``xuplims``, and ``xlolims`` parameters,
respectively. These parameters can be scalar or boolean arrays.

For example, if ``xlolims`` is ``True``, the x-error bars will only
extend from the data towards increasing values. If ``uplims`` is an
array filled with ``False`` except for the 4th and 7th values, all of the
y-error bars will be bidirectional, except the 4th and 7th bars, which
will extend from the data towards decreasing y-values.
"""

import matplotlib.pyplot as plt
import numpy as np

# example data
x = np.array([0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0])
y = np.exp(-x)
xerr = 0.1
yerr = 0.2

# lower & upper limits of the error
lolims = np.array([0, 0, 1, 0, 1, 0, 0, 0, 1, 0], dtype=bool)
uplims = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 1], dtype=bool)
ls = 'dotted'

fig, ax = plt.subplots(figsize=(7, 4))

# standard error bars
ax.errorbar(x, y, xerr=xerr, yerr=yerr, linestyle=ls)

# including upper limits
ax.errorbar(x, y + 0.5, xerr=xerr, yerr=yerr, uplims=uplims,
            linestyle=ls)

# including lower limits
ax.errorbar(x, y + 1.0, xerr=xerr, yerr=yerr, lolims=lolims,
            linestyle=ls)

# including upper and lower limits
ax.errorbar(x, y + 1.5, xerr=xerr, yerr=yerr,
            lolims=lolims, uplims=uplims,
            marker='o', markersize=8,
            linestyle=ls)

# Plot a series with lower and upper limits in both x & y
# constant x-error with varying y-error
xerr = 0.2
yerr = np.full_like(x, 0.2)
yerr[[3, 6]] = 0.3

# mock up some limits by modifying previous data
xlolims = lolims
xuplims = uplims
lolims = np.zeros_like(x)
uplims = np.zeros_like(x)
lolims[[6]] = True  # only limited at this index
uplims[[3]] = True  # only limited at this index

# do the plotting
ax.errorbar(x, y + 2.1, xerr=xerr, yerr=yerr,
            xlolims=xlolims, xuplims=xuplims,
            uplims=uplims, lolims=lolims,
            marker='o', markersize=8,
            linestyle='none')

# tidy up the figure
ax.set_xlim((0, 5.5))
ax.set_title('Errorbar upper and lower limits')
plt.show()

# %%
#
# .. tags:: plot-type: errorbar, domain: statistics
#
# .. admonition:: References
#
#    The use of the following functions, methods, classes and modules is shown
#    in this example:
#
#    - `matplotlib.axes.Axes.errorbar` / `matplotlib.pyplot.errorbar`
