Histograms

Plot histograms of a data set, used for visualizing the distribution of the data.

The examples correspond to https://alandefreitas.github.io/matplotplusplus/plot-types/data-distribution/histogram/.

Examples

1. A simple histogram.

::

var m: Random = Random(0)
let x = randn(m, 10000, 0.0, 1.0)
var h1 = hist(x)

Result:

.. image:: ../../../tests/imgs/histogram/histogram_1.png :align: center :width: 360

2. Comparison of different binning algorithms.

::

var m: Random = Random(0)
let x = randn(m, 10000, 0.0, 1.0)

subplot(2, 3, 0)
hist(x, algorithm:BinningAlgorithm.Automatic)
title("Automatic binning")

subplot(2, 3, 1)
hist(x, algorithm:Scott)
title("Scott's rule")

subplot(2, 3, 2)
hist(x, algorithm:FD)
title("Freedman-Diaconis rule")

subplot(2, 3, 3)
hist(x, algorithm:Integers)
title("Integers rule")

subplot(2, 3, 4)
hist(x, algorithm:Sturges)
title("Sturges' rule")

subplot(2, 3, 5)
hist(x, algorithm:Sqrt)
title("Square root rule")

Result:

.. image:: ../../../tests/imgs/histogram/histogram_2.png :align: center :width: 360

3. Comparison of different normalization methods.

::

var m: Random = Random(0)
let x = randn(m, 10000, 0.0, 1.0)

subplot(2, 3, 0)
hist(x, normalization_alg:Count)
title("Count (c_i)")

subplot(2, 3, 1)
hist(x, normalization_alg:Probability)
title("Probability (c_i/N)")

subplot(2, 3, 2)
hist(x, normalization_alg:CumulativeCount)
title("Cummulative count (∑_{j=1}^i c_j)")

subplot(2, 3, 3)
hist(x, normalization_alg:CountDensity)
title("Count density (c_i/w_i)")

subplot(2, 3, 4)
hist(x, normalization_alg:Pdf)
title("PDF (c_i/(N w_i))")

subplot(2, 3, 5)
hist(x, normalization_alg:Cdf)
title("CDF (∑_{j=1}^i c_j/N)")

Result:

.. image:: ../../../tests/imgs/histogram/histogram_3.png :align: center :width: 360

4. Test for values and bin edges.

::

var m: Random = Random(0)
let x = randn(m, 1000, 0.0, 1.0)
let num_bins = 25
let handle = hist(x, num_bins)
println(handle.values())
println(handle.bin_edges())

Result:

.. image:: ../../../tests/imgs/histogram/histogram_4.png :align: center :width: 360

5. Query for the number of bins.

::

var m: Random = Random(0)
let x = randn(m, 1000, 0.0, 1.0)
let handle = hist(x)
title(handle.num_bins().toString() + " bins")

Result:

.. image:: ../../../tests/imgs/histogram/histogram_5.png :align: center :width: 360

6. Custom setting of bin edges.

::

var m: Random = Random(0)
let x = randn(m, 10000, 0.0, 1.0)
let edges = vector<Float64>([
    -10.0, -2.0, -1.75, -1.5, -1.25, -1.0,
    -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75,
    1.0, 1.25, 1.5, 1.75, 2.0, 10.0
])
hist(x, edges).normalization(Normalization.CountDensity)

Result:

.. image:: ../../../tests/imgs/histogram/histogram_6.png :align: center :width: 360

7. Plotting distribution of categories.

::

let categories = [
    "no", "no", "yes", "yes", "yes", "no", "no",
    "no", "no", "undecided", "undecided", "yes", "no", "no",
    "no", "yes", "no", "yes", "no", "yes", "no",
    "no", "no", "yes", "yes", "yes", "yes"
]
hist(categories).bar_width(Float32(0.5))

Result:

.. image:: ../../../tests/imgs/histogram/histogram_7.png :align: center :width: 360

8. Illustration for probability mode.

::

var m: Random = Random(0)
let x = randn(m, 10000, 0.0, 1.0)
let handle = hist(x, normalization_alg:Normalization.Probability)
println(sum(handle.values()))  // should be 1.0

Result:

.. image:: ../../../tests/imgs/histogram/histogram_8.png :align: center :width: 360

9. Plotting two distributions (with different number of samples) in the probability mode.

::

var m: Random = Random(0)
let x = randn(m, 2000, 0.0, 1.0)
let y = randn(m, 5000, 1.0, 1.0)
let handle1 = hist(x)
hold(true)
let handle2 = hist(y)
handle1.normalization(Normalization.Probability)
handle1.bin_width(0.25)
handle2.normalization(Normalization.Probability)
handle2.bin_width(0.25)

Result:

.. image:: ../../../tests/imgs/histogram/histogram_9.png :align: center :width: 360

10. Customize face color and edge color.

::

var m: Random = Random(0)
let x = randn(m, 1000, 0.0, 1.0)
let handle = hist(x)
handle.num_bins(15)
handle.bin_edges(vector([-3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0]))
handle.face_color(0.0, 0.0, 0.5, 0.5)
handle.edge_color("r")

Result:

.. image:: ../../../tests/imgs/histogram/histogram_10.png :align: center :width: 360

11. Plotting pdf of a distribution along with a histogram of samples.

::

var m: Random = Random(0)
let x = randn(m, 5000, 5.0, 2.0)
let handle = hist(x)
handle.normalization(Normalization.Pdf)
hold(true)

fplot({x => normalPDF(x, 5.0, 2.0)}, -5.0, 15.0).line_width(1.5)

Result:

.. image:: ../../../tests/imgs/histogram/histogram_11.png :align: center :width: 360

12. Customize number of bins.

::

var m: Random = Random(0)
let x = randn(m, 1000, 0.0, 1.0)
let handle = hist(x)
handle.num_bins(5)
title(handle.num_bins().toString() + " bins")

Result:

.. image:: ../../../tests/imgs/histogram/histogram_12.png :align: center :width: 360

Methods

======================================== ================================= Method Description ======================================== ================================= hist(x, algorithm, normalization_alg) Plot a histogram. ======================================== =================================

Description

.. function:: hist(x, algorithm!, normalization_alg!)

:param x: Tensor<Float64>
:param algorithm: BinningAlgorithm
:param normalization_alg: Normalization

Plot a histogram.