Binned Scatter

Similar to a scattering plot, but with the size (or color) of each scattered point reflecting how much data is at that point. Suitable for scatter-plotting a large amount of data.

The parameter binning_algorithm is one of: Automatic, Scott, FD, Integers, Sturges, Sqrt (same as for histogram).

The parameter bin_scatter_style is one of: Automatic, Point_size, Point_alpha, Jitter, Point_colormap, Heatmap.

Functions

=============================== =========================== Function Description =============================== =========================== binscatter() 2 functions Plot a binned scatter plot. =============================== ===========================

Description ^^^^^^^^^^^

.. function:: binscatter(x, y, binning_algorithm, bin_scatter_style)

:param x: Vector<Float64>
:param y: Vector<Float64>
:param binning_algorithm: BinningAlgorithm, named parameter, default to Automatic.
:param bin_scatter_style: BinScatterStyle, named parameter, default to Automatic
:return: AxesObject

Produce a binned scatter plot using data ``x`` and ``y``.

.. function:: binscatter(x, y, nbins_x, nbins_y, binning_algorithm, bin_scatter_style)

:param x: Vector<Float64>
:param y: Vector<Float64>
:param nbins_x: Int64
:param nbins_x: Int64
:param binning_algorithm: BinningAlgorithm, named parameter, default to Automatic.
:param bin_scatter_style: BinScatterStyle, named parameter, default to Automatic
:return: AxesObject

Produce a binned scatter plot using data ``x`` and ``y``.

Examples

1. Comparison between scatter plot and binned scatter plot.

::

var r: Random = Random(0)
let x_reduced = randn(r, 1000, 0.0, 1.0)
let y_reduced = x_reduced * 2.0 + rand(r, 1000)
subplot(1, 2, 0)
scatter(x_reduced, y_reduced)
title("Scatter plot (n=1000)")

let x = randn(r, 500000, 0.0, 1.0)
let y = x * 2.0 + rand(r, 500000)
subplot(1, 2, 1)
binscatter(x, y)
axis(Tight)
title("Binned Scatter plot (n=500000)")

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_1.png

2. Comparison between different bin scatter styles.

::

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 100000, 0.0, 1.0)
let y: Vector<Float64> = x * 2.0 + rand(r, 100000)

let x_line = x[0..1000]
let y_line = y[0..1000]

subplot(2,3,0)
scatter(x_line, y_line)
title("Scatter")

subplot(2,3,1)
binscatter(x, y, bin_scatter_style:Point_size)
title("Bin Scatter: Point Size")

subplot(2,3,2)
binscatter(x, y, bin_scatter_style:Point_alpha)
title("Bin Scatter: Point Alpha")

subplot(2,3,3)
binscatter(x, y, bin_scatter_style:Point_colormap)
title("Bin Scatter: Point Colormap")

subplot(2,3,4)
binscatter(x, y, bin_scatter_style:Heatmap)
title("Bin Scatter: Heatmap")

subplot(2,3,5)
binscatter(x, y, bin_scatter_style:Jitter)
title("Bin Scatter: Jitter")

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_2.png

3. Comparison between different binning algorithm.

::

let f = gcf()
f.width(f.width() * 2)
f.height(f.height() * 2)
f.x_position(200)
f.y_position(100)

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 100000, 0.0, 1.0)
let y: Vector<Float64> = x * 2.0 + rand(r, 100000)

var b = BinScatterStyle.Automatic

subplot(2,3,0)
binscatter(x, y, binning_algorithm: BinningAlgorithm.Automatic, bin_scatter_style: b)
title("Automatic")

subplot(2,3,1)
binscatter(x, y, binning_algorithm: BinningAlgorithm.Integers, bin_scatter_style: b)
axis(Tight)
title("Integers")

subplot(2,3,2)
binscatter(x, y, binning_algorithm: BinningAlgorithm.Scott, bin_scatter_style: b)
axis(Tight)
title("Scott's rule")

subplot(2,3,3)
binscatter(x, y, binning_algorithm: BinningAlgorithm.FD, bin_scatter_style: b)
axis(Tight)
title("Freedman-Diaconis rule")

subplot(2,3,4)
binscatter(x, y, binning_algorithm: BinningAlgorithm.Sqrt, bin_scatter_style: b)
axis(Tight)
title("Square root rule")

subplot(2,3,5)
binscatter(x, y, binning_algorithm: BinningAlgorithm.Sturges, bin_scatter_style: b)
axis(Tight)
title("Sturges' rule")

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_3.png

4. Comparison between different normalization.

::

let f = gcf()
f.width(f.width() * 2)
f.height(f.height() * 2)
f.x_position(200)
f.y_position(100)

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 100000, 0.0, 1.0)
let y: Vector<Float64> = x * 2.0 + rand(r, 100000)

var b = BinScatterStyle.Heatmap
var a = BinningAlgorithm.Automatic

subplot(2,3,0)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.Count)
axis(Tight)
title("Normalization: Count")

subplot(2,3,1)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.Probability)
axis(Tight)
title("Normalization: Probability")

subplot(2,3,2)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.CumulativeCount)
axis(Tight)
title("Normalization: Cumulative count")

subplot(2,3,3)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.CountDensity)
axis(Tight)
title("Normalization: Count density")

subplot(2,3,4)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.Pdf)
axis(Tight)
title("Normalization: PDF")

subplot(2,3,5)
binscatter(x, y, binning_algorithm: a, bin_scatter_style: b, 
            normalization_alg: Normalization.Cdf)
axis(Tight)
title("Normalization: CDF")

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_4.png

5. Binned sactter plots with custom nbins_x and nbins_y.

::

let f = gcf()
f.width(f.width() * 2)
f.height(f.height() * 2)
f.x_position(200)
f.y_position(100)
f.quiet_mode(true)

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 10000, 0.0, 1.0)
let y: Vector<Float64> = randn(r, 10000, 0.0, 1.0)

subplot(2,3,0)
scatter(x, y)
title("Scatter plot")

subplot(2,3,1)
binscatter(x, y, 30, 10, bin_scatter_style: Point_size)
title("Binned scatter plot: Point size")

subplot(2, 3, 2)
binscatter(x, y, 30, 10, bin_scatter_style: Point_alpha)
title("Binned scatter plot: Point alpha")

subplot(2, 3, 3)
binscatter(x, y, 30, 10, bin_scatter_style: Jitter)
title("Binned scatter plot: Jitter")

subplot(2, 3, 4)
binscatter(x, y, 30, 10, bin_scatter_style: Point_colormap)
title("Binned scatter plot: Colormap")

subplot(2, 3, 5)
binscatter(x, y, 30, 10, bin_scatter_style: Heatmap)
title("Binned scatter plot: Heatmap")
axis(Tight)

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_5.png

6. Binned scatter plot of random normal distribution.

::

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 100000, 0.0, 1.0)
let y: Vector<Float64> = randn(r, 100000, 0.0, 1.0)

binscatter(x, y, bin_scatter_style: Point_colormap)

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_6.png

7. Binned scatter plot of random normal distribution, in heatmap style.

::

var r: Random = Random(0)
let x: Vector<Float64> = randn(r, 100000, 0.0, 1.0)
let y: Vector<Float64> = randn(r, 100000, 0.0, 1.0)

binscatter(x, y, 20, 30, bin_scatter_style: Heatmap)
axis(Tight)

Result:

.. image:: ../../../tests/imgs/bin_scatter/bin_scatter_7.png