Bivariate histogram plot
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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
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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
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| logical
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, thenhistogram2
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
andYedges
withBinMethod
,BinWidth
, orNumBins
,histogram2
only honors the bin edges and the bin edges must be specified last.If you specify
Xedges
withXBinLimits
,histogram2
only honors theXedges
and theXedges
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
andXedges
withBinMethod
,BinWidth
, orNumBins
,histogram2
only honors the bin edges and the bin edges must be specified last.If you specify
Yedges
withYBinLimits
,histogram2
only honors theYedges
and theYedges
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
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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
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Color and Styling
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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 |
---|---|
'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 |
'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.
|
Example: histogram2(X,Y,'FaceLighting','none')
turns off the lighting of the histogram bars.
Output Arguments
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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
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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
Plot a bivariate histogram of 1,000 pairs of random numbers sorted into 25 equally spaced bins, using 5 bins in each dimension.
x = randn(1000,1);y = randn(1000,1);nbins = 5;h = histogram2(x,y,nbins)
h = Histogram2 with properties: Data: [1000x2 double] Values: [5x5 double] NumBins: [5 5] XBinEdges: [-4 -2.4000 -0.8000 0.8000 2.4000 4] YBinEdges: [-4 -2.4000 -0.8000 0.8000 2.4000 4] BinWidth: [1.6000 1.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0.1500 0.1500 0.1500] Use GET to show all properties
Find the resulting bin counts.
counts = h.Values
counts = 5×5 0 2 3 1 0 2 40 124 47 4 1 119 341 109 10 1 32 117 33 1 0 4 8 1 0
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 = 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
andfewerbins
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
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R2023b: Normalize using percentages
You can create histograms with percentages on the vertical axis by setting the Normalization
name-value argument to 'percentage'
.
See Also
Histogram2 Properties | bar3 | discretize | fewerbins | morebins | histcounts2 | histcounts
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