Bivariate histogram plot

expand all in page

Description

Bivariate histograms are a type of bar plot for numeric data that group the data into 2-D bins. After you create a Histogram2 object, you can modify aspects of the histogram by changing its property values. This is particularly useful for quickly modifying the properties of the bins or changing the display.

Creation

Syntax

histogram2(X,Y)

histogram2(X,Y,nbins)

histogram2(X,Y,Xedges,Yedges)

histogram2('XBinEdges',Xedges,'YBinEdges',Yedges,'BinCounts',counts)

histogram2(___,Name,Value)

histogram2(ax,___)

h = histogram2(___)

Description

example

histogram2(X,Y) creates a bivariate histogram plot of X and Y. The histogram2 function uses an automatic binning algorithm that returns bins with a uniform area, chosen to cover the range of elements in X and Y and reveal the underlying shape of the distribution. histogram2 displays the bins as 3-D rectangular bars such that the height of each bar indicates the number of elements in the bin.

example

histogram2(X,Y,nbins) specifies the number of bins to use in each dimension.

example

histogram2(X,Y,Xedges,Yedges) sorts X and Y into bins with the bin edges for each dimension specified in vectors.

histogram2('XBinEdges',Xedges,'YBinEdges',Yedges,'BinCounts',counts) plots the specified bin counts and does not do any data binning.

example

histogram2(___,Name,Value) specifies additional parameters using one or more name-value arguments for any of the previous syntaxes. For example, specify Normalization to use a different type of normalization. For a list of properties, see Histogram2 Properties.

histogram2(ax,___) plots into the specified axes instead of into the current axes (gca). ax can precede any of the input argument combinations in the previous syntaxes.

example

h = histogram2(___) returns a Histogram2 object. Use this to inspect and adjust properties of the bivariate histogram. For a list of properties, see Histogram2 Properties.

Input Arguments

expand all

`X,Y` — Data to distribute among bins (as separate arguments)
vectors | matrices | multidimensional arrays

Data to distribute among bins, specified as separate arguments of vectors, matrices, or multidimensional arrays. X and Y must be the same size. histogram2 treats matrix or multidimensional array data as single column vectors, X(:) and Y(:), and plots a single histogram.

Corresponding elements in X and Y specify the x and y coordinates of 2-D data points, [X(k),Y(k)]. The data types of X and Y can be different, but histogram2 concatenates these inputs into a single N-by-2 matrix of the dominant data type.

histogram2 ignores all NaN values. Similarly, histogram2 ignores Inf and -Inf values, unless the bin edges explicitly specify Inf or -Inf as a bin edge. Although NaN, Inf, and -Inf values are typically not plotted, they are still included in normalization calculations that include the total number of data elements, such as 'probability'.

Note

If X or Y contain integers of type int64 or uint64 that are larger than flintmax, then it is recommended that you explicitly specify the histogram bin edges.histogram2 automatically bins the input data using double precision, which lacks integer precision for numbers greater than flintmax.

`nbins` — Number of bins in each dimension
positive integer scalar | two-element vector of positive integers

Number of bins in each dimension, specified as a positive integer scalar or two-element vector of positive integers.

If nbins is a scalar, then histogram2 uses that many bins in each dimension.
If nbins is a vector, then the first element gives the number of bins in the x-dimension, and the second element gives the number of bins in the y-dimension.

If you do not specify nbins, then histogram2 automatically calculates how many bins to use based on the values in X and Y.

If you specify nbins with BinMethod or BinWidth, histogram2 only honors the last parameter.

Example: histogram2(X,Y,20) uses 20 bins in each dimension.

Example: histogram2(X,Y,[10 20]) uses 10 bins in the x-dimension and 20 bins in the y-dimension.

`Xedges` — Bin edges in x-dimension
vector

Bin edges in x-dimension, specified as a vector. The first element specifies the leading edge of the first bin in the x-dimension. The last element specifies the trailing edge of the last bin in the x-dimension. The trailing edge is only included for the last bin.

If you specify Xedges and Yedges with BinMethod, BinWidth, or NumBins, histogram2 only honors the bin edges and the bin edges must be specified last.
If you specify Xedges with XBinLimits, histogram2 only honors the Xedges and the Xedges must be specified last.

`Yedges` — Bin edges in y-dimension
vector

Bin edges in y-dimension, specified as a vector. The first element specifies the leading edge of the first bin in the y-dimension. The last element specifies the trailing edge of the last bin in the y-dimension. The trailing edge is only included for the last bin.

If you specify Yedges and Xedges with BinMethod, BinWidth, or NumBins, histogram2 only honors the bin edges and the bin edges must be specified last.
If you specify Yedges with YBinLimits, histogram2 only honors the Yedges and the Yedges must be specified last.

`counts` — Bin counts
matrix

Bin counts, specified as a matrix. Use this input to pass bin counts to histogram2 when the bin counts calculation is performed separately and you do not want histogram2 to do any data binning.

counts must be a matrix of size [length(XBinEdges)-1 length(YBinEdges)-1] so that it specifies a bin count for each bin.

Example: histogram2('XBinEdges',-1:1,'YBinEdges',-2:2,'BinCounts',[1 2 3 4; 5 6 7 8])

`ax` — Axes object
object

Axes object. If you do not specify an axes, then the histogram2 function uses the current axes (gca).

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: histogram2(X,Y,BinWidth=[5 10])

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: histogram2(X,Y,'BinWidth',[5 10])

Note

The properties listed here are only a subset. For a complete list, see Histogram2 Properties.

Bins

expand all

`XBinLimits` — Bin limits in x-dimension
two-element vector

Bin limits in x-dimension, specified as a two-element vector, [xbmin,xbmax]. The first element indicates the first bin edge in the x-dimension. The second element indicates the last bin edge in the x-dimension.

This option only bins data that falls within the bin limits inclusively, X>=xbmin & X<=xbmax.

`XBinLimitsMode` — Selection mode for bin limits in `x`-dimension
`'auto'` (default) | `'manual'`

Selection mode for bin limits in x-dimension, specified as 'auto' or 'manual'. The default value is 'auto', so that the bin limits automatically adjust to the data along the x-axis.

If you explicitly specify either XBinLimits or XBinEdges, then XBinLimitsMode is set automatically to 'manual'. In that case, specify XBinLimitsMode as 'auto' to rescale the bin limits to the data.

`YBinLimits` — Bin limits in y-dimension
two-element vector

Bin limits in y-dimension, specified as a two-element vector, [ybmin,ybmax]. The first element indicates the first bin edge in the y-dimension. The second element indicates the last bin edge in the y-dimension.

This option only bins data that falls within the bin limits inclusively, Y>=ybmin & Y<=ybmax.

`YBinLimitsMode` — Selection mode for bin limits in y-dimension
`'auto'` (default) | `'manual'`

Selection mode for bin limits in y-dimension, specified as 'auto' or 'manual'. The default value is 'auto', so that the bin limits automatically adjust to the data along the y-axis.

If you explicitly specify either YBinLimits or YBinEdges, then YBinLimitsMode is set automatically to 'manual'. In that case, specify YBinLimitsMode as 'auto' to rescale the bin limits to the data.

`ShowEmptyBins` — Toggle display of empty bins
`'off'` (default) | `'on'`

Toggle display of empty bins, specified as either 'off' or 'on'. The default value is 'off'.

Example: histogram2(X,Y,'ShowEmptyBins','on') turns on the display of empty bins.

Data

expand all

Color and Styling

expand all

`DisplayStyle` — Histogram display style
`'bar3'` (default) | `'tile'`

Histogram display style, specified as either 'bar3' or 'tile'.

'bar3' — Display the histogram using 3-D bars.
'tile' — Display the histogram as a rectangular array of tiles with colors indicating the bin values.

Example: histogram2(X,Y,'DisplayStyle','tile') plots the histogram as a rectangular array of tiles.

`FaceLighting` — Lighting effect on histogram bars
`'lit'` (default) | `'flat'` | `'none'`

Lighting effect on histogram bars, specified as one of these values.

Value Description

Value	Description
`'lit'`	Histogram bars display a pseudo-lighting effect, where the sides of the bars use darker colors relative to the tops. The bars are unaffected by other light sources in the axes. This is the default value when `DisplayStyle` is `'bar3'`.
`'flat'`	Histogram bars are not lit automatically. In the presence of other light objects, the lighting effect is uniform across the bar faces.
`'none'`	Histogram bars are not lit automatically, and lights do not affect the histogram bars. `FaceLighting` can only be `'none'` when `DisplayStyle` is `'tile'`.

'lit'

Histogram bars display a pseudo-lighting effect, where the sides of the bars use darker colors relative to the tops. The bars are unaffected by other light sources in the axes.

This is the default value when DisplayStyle is 'bar3'.

'flat'

Histogram bars are not lit automatically. In the presence of other light objects, the lighting effect is uniform across the bar faces.

'none'

Histogram bars are not lit automatically, and lights do not affect the histogram bars.

FaceLighting can only be 'none' when DisplayStyle is 'tile'.

Example: histogram2(X,Y,'FaceLighting','none') turns off the lighting of the histogram bars.

Output Arguments

expand all

`h` — Bivariate histogram
object

Bivariate histogram, returned as an object. For more information, see Histogram2 Properties.

Properties

Histogram2 Properties

Bivariate histogram appearance and behavior

Object Functions

morebins	Increase number of histogram bins
fewerbins	Decrease number of histogram bins

Examples

collapse all

Histogram of Vectors

Open Live Script

Generate 10,000 pairs of random numbers and create a bivariate histogram. The histogram2 function automatically chooses an appropriate number of bins to cover the range of values in x and y and show the shape of the underlying distribution.

x = randn(10000,1);y = randn(10000,1);h = histogram2(x,y)

h = Histogram2 with properties: Data: [10000x2 double] Values: [25x28 double] NumBins: [25 28] XBinEdges: [-3.9000 -3.6000 -3.3000 -3 -2.7000 -2.4000 -2.1000 -1.8000 -1.5000 -1.2000 -0.9000 -0.6000 -0.3000 0 0.3000 0.6000 0.9000 1.2000 1.5000 1.8000 2.1000 2.4000 2.7000 3.0000 3.3000 3.6000] YBinEdges: [-4.2000 -3.9000 -3.6000 -3.3000 -3.0000 -2.7000 -2.4000 -2.1000 -1.8000 -1.5000 -1.2000 -0.9000 -0.6000 -0.3000 0 0.3000 0.6000 0.9000 1.2000 1.5000 1.8000 2.1000 2.4000 2.7000 3 3.3000 3.6000 3.9000 4.2000] BinWidth: [0.3000 0.3000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

xlabel('x')ylabel('y')

When you specify an output argument to the histogram2 function, it returns a histogram2 object. You can use this object to inspect the properties of the histogram, such as the number of bins or the width of the bins.

Find the number of histogram bins in each dimension.

nXnY = h.NumBins

nXnY = 1×2 25 28

Specify Number of Histogram Bins

Open Live Script

Adjust Number of Histogram Bins

Open Live Script

Generate 1,000 pairs of random numbers and create a bivariate histogram.

x = randn(1000,1);y = randn(1000,1);h = histogram2(x,y)

h = Histogram2 with properties: Data: [1000x2 double] Values: [15x15 double] NumBins: [15 15] XBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] YBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] BinWidth: [0.5000 0.5000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

Use the morebins function to coarsely adjust the number of bins in the x dimension.

nbins = morebins(h,'x');nbins = morebins(h,'x')

nbins = 1×2 19 15

Use the fewerbins function to adjust the number of bins in the y dimension.

nbins = fewerbins(h,'y');nbins = fewerbins(h,'y')

nbins = 1×2 19 11

Adjust the number of bins at a fine grain level by explicitly setting the number of bins.

h.NumBins = [20 10];

Color Histogram Bars by Height

Open Live Script

Create a bivariate histogram using 1,000 normally distributed random numbers with 12 bins in each dimension. Specify FaceColor as 'flat' to color the histogram bars by height.

h = histogram2(randn(1000,1),randn(1000,1),[12 12],'FaceColor','flat');colorbar

Tiled Histogram View

Open Live Script

Generate random data and plot a bivariate tiled histogram. Display the empty bins by specifying ShowEmptyBins as 'on'.

x = 2*randn(1000,1)+2;y = 5*randn(1000,1)+3;h = histogram2(x,y,'DisplayStyle','tile','ShowEmptyBins','on');

Specify Bin Edges of Histogram

Open Live Script

Generate 1,000 pairs of random numbers and create a bivariate histogram. Specify the bin edges using two vectors, with infinitely wide bins on the boundary of the histogram to capture all outliers that do not satisfy $| x | < 2$ .

x = randn(1000,1);y = randn(1000,1);Xedges = [-Inf -2:0.4:2 Inf];Yedges = [-Inf -2:0.4:2 Inf];h = histogram2(x,y,Xedges,Yedges)

h = Histogram2 with properties: Data: [1000x2 double] Values: [12x12 double] NumBins: [12 12] XBinEdges: [-Inf -2 -1.6000 -1.2000 -0.8000 -0.4000 0 0.4000 0.8000 1.2000 1.6000 2 Inf] YBinEdges: [-Inf -2 -1.6000 -1.2000 -0.8000 -0.4000 0 0.4000 0.8000 1.2000 1.6000 2 Inf] BinWidth: 'nonuniform' Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

When the bin edges are infinite, histogram2 displays each outlier bin (along the boundary of the histogram) as being double the width of the bin next to it.

Specify the Normalization property as 'countdensity' to remove the bins containing the outliers. Now the volume of each bin represents the frequency of observations in that interval.

h.Normalization = 'countdensity';

Normalized Histogram

Open Live Script

Generate 1,000 pairs of random numbers and create a bivariate histogram using the 'probability' normalization.

x = randn(1000,1);y = randn(1000,1);h = histogram2(x,y,'Normalization','probability')

h = Histogram2 with properties: Data: [1000x2 double] Values: [15x15 double] NumBins: [15 15] XBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] YBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] BinWidth: [0.5000 0.5000] Normalization: 'probability' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

Compute the total sum of the bar heights. With this normalization, the height of each bar is equal to the probability of selecting an observation within that bin interval, and the heights of all of the bars sum to 1.

S = sum(h.Values(:))

S = 1

Histogram Using Percentages

Open Live Script

Generate 100,000 normally distributed random vectors. Use a standard deviation of 15 and means of 100 and 85.

x = [100 85] + 15*randn(1e5,2);

Plot a histogram of the random vectors. Scale and label the z-axis as percentages.

edges = 40:15:145;histogram2(x(:,1),x(:,2),edges,edges,Normalization="percentage")ztickformat("percentage")

Adjust Histogram Properties

Open Live Script

Generate 1,000 pairs of random numbers and create a bivariate histogram. Return the histogram object to adjust the properties of the histogram without recreating the entire plot.

x = randn(1000,1);y = randn(1000,1);h = histogram2(x,y)

h = Histogram2 with properties: Data: [1000x2 double] Values: [15x15 double] NumBins: [15 15] XBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] YBinEdges: [-3.5000 -3 -2.5000 -2 -1.5000 -1 -0.5000 0 0.5000 1 1.5000 2 2.5000 3 3.5000 4] BinWidth: [0.5000 0.5000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

Color the histogram bars by height.

h.FaceColor = 'flat';

Change the number of bins in each direction.

h.NumBins = [10 25];

Display the histogram as a tile plot.

h.DisplayStyle = 'tile';view(2)

Saving and Loading Histogram2 Objects

Open Live Script

Use the savefig function to save a histogram2 figure.

histogram2(randn(100,1),randn(100,1));savefig('histogram2.fig');close gcf

Use openfig to load the histogram figure back into MATLAB®. openfig also returns a handle to the figure, h.

h = openfig('histogram2.fig');

Use the findobj function to locate the correct object handle from the figure handle. This allows you to continue manipulating the original histogram object used to generate the figure.

y = findobj(h,'type','histogram2')

y = Histogram2 with properties: Data: [100x2 double] Values: [7x6 double] NumBins: [7 6] XBinEdges: [-3 -2 -1 0 1 2 3 4] YBinEdges: [-3 -2 -1 0 1 2 3] BinWidth: [1 1] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties

Tips

Histogram plots created using histogram2 have a context menu in plot edit mode that enables interactive manipulations in the figure window. For example, you can use the context menu to interactively change the number of bins, align multiple histograms, or change the display order.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with the limitations:

Some input options are not supported. The allowedoptions are:
- 'BinWidth'
- 'XBinLimits'
- 'YBinLimits'
- 'Normalization'
- 'DisplayStyle'
- 'BinMethod' — The 'auto' and 'scott' binmethods are the same. The 'fd' bin method is notsupported.
- 'EdgeAlpha'
- 'EdgeColor'
- 'FaceAlpha'
- 'FaceColor'
- 'LineStyle'
- 'LineWidth'
- 'Orientation'
Additionally, there is a cap on the maximum numberof bars. The default maximum is 100.
The morebins and fewerbins methodsare not supported.
Editing properties of the histogram object that requirerecomputing the bins is not supported.

For more information, see Tall Arrays for Out-of-Memory Data.

Version History

Introduced in R2015b

expand all

R2023b: Normalize using percentages

You can create histograms with percentages on the vertical axis by setting the Normalization name-value argument to 'percentage'.

MATLAB Command

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

Americas

América Latina (Español)
Canada (English)
United States (English)

Europe

Belgium (English)
Denmark (English)
Deutschland (Deutsch)
España (Español)
Finland (English)
France (Français)
Ireland (English)
Italia (Italiano)
Luxembourg (English)

Netherlands (English)
Norway (English)
Österreich (Deutsch)
Portugal (English)
Sweden (English)
Switzerland
- Deutsch
- English
- Français
United Kingdom (English)

Asia Pacific

Australia (English)
India (English)
New Zealand (English)
中国
- 简体中文
- English
日本 (日本語)
한국 (한국어)

Contact your local office

Bivariate histogram plot - MATLAB (2024)

Description

Creation

Syntax

Description

Input Arguments

X,Y — Data to distribute among bins (as separate arguments)vectors | matrices | multidimensional arrays

nbins — Number of bins in each dimension positive integer scalar | two-element vector of positive integers

Xedges — Bin edges in x-dimension vector

Yedges — Bin edges in y-dimension vector

counts — Bin counts matrix

ax — Axes object object

XBinLimits — Bin limits in x-dimension two-element vector

XBinLimitsMode — Selection mode for bin limits in x-dimension'auto' (default) | 'manual'

YBinLimits — Bin limits in y-dimensiontwo-element vector

YBinLimitsMode — Selection mode for bin limits in y-dimension 'auto' (default) | 'manual'

ShowEmptyBins — Toggle display of empty bins 'off' (default) | 'on'

DisplayStyle — Histogram display style 'bar3' (default) | 'tile'

FaceLighting — Lighting effect on histogram bars 'lit' (default) | 'flat' | 'none'

Output Arguments

h — Bivariate histogramobject

Properties

Object Functions

Examples

Histogram of Vectors

Specify Number of Histogram Bins

Adjust Number of Histogram Bins

Color Histogram Bars by Height

Tiled Histogram View

Specify Bin Edges of Histogram

Normalized Histogram

Histogram Using Percentages

Adjust Histogram Properties

Saving and Loading Histogram2 Objects

Tips

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

Version History

R2023b: Normalize using percentages

See Also

MATLAB Command

Americas

Europe

Asia Pacific

`X,Y` — Data to distribute among bins (as separate arguments)
vectors | matrices | multidimensional arrays

`nbins` — Number of bins in each dimension
positive integer scalar | two-element vector of positive integers

`Xedges` — Bin edges in x-dimension
vector

`Yedges` — Bin edges in y-dimension
vector

`counts` — Bin counts
matrix

`ax` — Axes object
object

`XBinLimits` — Bin limits in x-dimension
two-element vector

`XBinLimitsMode` — Selection mode for bin limits in `x`-dimension
`'auto'` (default) | `'manual'`

`YBinLimits` — Bin limits in y-dimension
two-element vector

`YBinLimitsMode` — Selection mode for bin limits in y-dimension
`'auto'` (default) | `'manual'`

`ShowEmptyBins` — Toggle display of empty bins
`'off'` (default) | `'on'`

`DisplayStyle` — Histogram display style
`'bar3'` (default) | `'tile'`

`FaceLighting` — Lighting effect on histogram bars
`'lit'` (default) | `'flat'` | `'none'`

`h` — Bivariate histogram
object

Tall Arrays
Calculate with arrays that have more rows than fit in memory.