atompy.Hist2d.get_profile_along_x

Hist2d.get_profile_along_x(option='')

Get the x-profile.

Calculate the mean value and its error per column. Which type of error is controled with option.

Parameters:

option"", "s", "i", or "g", default ""

Control type of errors, see Notes.

• option == "": Error of the mean of all Y values

• option == "s": Standard deviation of all Y

• option == "i": See Notes

• option == "g": Error of a weighted mean for combining measurements with variances of \(w\).

Returns:

hndarray

Mean values of each Y (i.e., column)

errorsndarray

Errors of the mean values. Depends on option.

Notes

See TProfile of the ROOT Data Analysis Framework.

For a histogram \(X\) vs \(Y\), the following is calculated for each \(X\) value.

\[\begin{split}\begin{align} H(j) &= \sum w Y \\ E(j) &= \sum w Y^2 \\ W(j) &= \sum w \\ h(j) &= H(j) / W(j) \\ s(j) &= \sqrt{E(j) / W(j) - h(j)^2} \\ e(j) &= s(j) / \sqrt{W(j)} \end{align}\end{split}\]

Here, \(w\) are the counts of bin j.

Examples

import numpy as np
import atompy as ap
import matplotlib.pyplot as plt

# get some random data
gen = np.random.default_rng(42)
x_sample = gen.uniform(-1, 1, size=100_000)
y_sample = gen.normal(size=100_000)

# create a histogram
hist = ap.Hist2d(*np.histogram2d(x_sample, y_sample,
                 bins=(10, 100), range=((-1, 1), (-5, 5))))
mean, mean_errors = hist.get_profile_along_x()
_, standard_deviation = hist.get_profile_along_x("s")

# configure plots
plt.rcParams["image.cmap"] = "atom"  # works only if atompy is imported
plt.rcParams["image.interpolation"] = "none"
plt.rcParams["image.aspect"] = "auto"

_, axs = plt.subplots(1, 2)

for ax in axs.flat:
    ax.imshow(**hist.for_imshow())
    ax.set_box_aspect(1.0)

axs[0].errorbar(hist.xcenters, mean, yerr=mean_errors)
axs[0].set_title("Errorbars = Mean errors")

axs[1].errorbar(hist.xcenters, mean, yerr=standard_deviation)
axs[1].set_title("Errorbars = Standard deviation")

ap.make_me_nice()

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