Bivariate histogram bin counts - MATLAB histcounts2 - MathWorks France (2024)

Bivariate histogram bin counts

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Syntax

[N,Xedges,Yedges]= histcounts2(X,Y)

[N,Xedges,Yedges]= histcounts2(X,Y,nbins)

[N,Xedges,Yedges]= histcounts2(X,Y,Xedges,Yedges)

[N,Xedges,Yedges]= histcounts2(___,Name,Value)

[N,Xedges,Yedges,binX,binY]= histcounts2(___)

Description

example

[N,Xedges,Yedges]= histcounts2(X,Y) partitions the values in X and Y into 2-D bins and returns the bin counts and the bin edges in each dimension. The histcounts2 function uses an automatic binning algorithm that returns uniform bins chosen to cover the range of values in X and Y and reveal the underlying shape of the distribution.

example

[N,Xedges,Yedges]= histcounts2(X,Y,nbins) specifiesthe number of bins to use in each dimension.

example

[N,Xedges,Yedges]= histcounts2(X,Y,Xedges,Yedges) partitions X and Y intobins with the bin edges specified by Xedges and Yedges.

example

[N,Xedges,Yedges]= histcounts2(___,Name,Value) specifies additional parameters using one or more name-value arguments for any of the previous syntaxes. For example, specify BinWidth as a two-element vector to adjust the width of the bins in each dimension.

example

[N,Xedges,Yedges,binX,binY]= histcounts2(___) also returns bin indices for the corresponding elements in X and Y.

Examples

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Bin Counts and Bin Edges

Open Live Script

Distribute 100 pairs of random numbers into bins. histcounts2 automatically chooses an appropriate bin width to reveal the underlying distribution of the data.

x = randn(100,1);y = randn(100,1);[N,Xedges,Yedges] = histcounts2(x,y)
N = 7×6 0 0 0 2 0 0 1 2 10 4 0 0 1 4 9 9 5 0 1 4 10 11 5 1 1 4 6 3 1 1 0 0 1 2 0 0 0 0 1 0 1 0
Xedges = 1×8 -3 -2 -1 0 1 2 3 4
Yedges = 1×7 -3 -2 -1 0 1 2 3

Specify Number of Bins in Each Dimension

Open Live Script

Distribute 10 pairs of numbers into 12 bins. Specify 3 bins in the x-dimension, and 4 bins in the y-dimension.

x = [1 1 2 3 2 2 1 1 2 3];y = [5 6 3 8 9 1 2 7 5 1];nbins = [3 4];[N,Xedges,Yedges] = histcounts2(x,y,nbins)
Xedges = 1×4 0.6000 1.4000 2.2000 3.0000
Yedges = 1×5 0 2.3000 4.6000 6.9000 9.2000

Specify Bin Edges

Open Live Script

Distribute 1,000 pairs of random numbers into bins. Define the bin edges with two vectors: one each for the x and y dimensions. The first element in each vector specifies the first edge of the first bin, and the last element is the last edge of the last bin.

x = randn(1000,1);y = randn(1000,1);Xedges = -5:5;Yedges = [-5 -4 -2 -1 -0.5 0 0.5 1 2 4 5];N = histcounts2(x,y,Xedges,Yedges)
N = 10×10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 5 5 3 5 1 2 0 0 0 2 19 23 29 25 26 20 5 0 0 10 36 51 59 71 54 46 10 0 0 7 43 46 79 64 60 46 9 0 0 3 12 18 21 23 19 9 6 0 0 0 5 3 2 8 2 2 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Normalized Bin Counts

Open Live Script

Distribute 1,000 pairs of random numbers into bins. Specify Normalization as 'probability' to normalize the bin counts such that sum(N(:)) is 1. That is, each bin count represents the probability that an observation falls within that bin.

x = randn(1000,1);y = randn(1000,1);[N,Xedges,Yedges] = histcounts2(x,y,6,'Normalization','probability')
N = 6×6 0 0 0.0020 0.0020 0 0 0 0.0110 0.0320 0.0260 0.0070 0.0010 0.0010 0.0260 0.1410 0.1750 0.0430 0.0060 0 0.0360 0.1620 0.1940 0.0370 0.0040 0 0.0040 0.0300 0.0370 0.0100 0.0010 0 0.0030 0.0040 0.0040 0.0010 0
Xedges = 1×7 -4.0000 -2.7000 -1.4000 -0.1000 1.2000 2.5000 3.8000
Yedges = 1×7 -4.0000 -2.7000 -1.4000 -0.1000 1.2000 2.5000 3.8000

Determine Bin Placement

Open Live Script

Distribute 1,000 random integer pairs between -10 and 10 into bins, and specify BinMethod as 'integers' to use unit-width bins centered on integers. Specify five outputs for histcounts2 to return vectors representing the bin placement of the data.

x = randi([-10,10],1000,1);y = randi([-10,10],1000,1);[N,Xedges,Yedges,binX,binY] = histcounts2(x,y,'BinMethod','integers');

Determine which bin the value (x(3),y(3)) falls into.

[x(3),y(3)]
ans = 1×2 -8 10
bin = [binX(3) binY(3)]
bin = 1×2 3 21

Input Arguments

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

Data to distribute among bins, specified as separate argumentsof vectors, matrices, or multidimensional arrays. X and Y musthave the same size.

Corresponding elements in X and Y specifythe x and y coordinates of 2-Ddata points, [X(k),Y(k)]. The data types of X and Y canbe different.

histcounts2 ignores all NaN values.Similarly, histcounts2 ignores Inf and -Inf valuesunless the bin edges explicitly specify Inf or -Inf asa bin edge.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

nbinsNumber 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 histcounts2 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 histcounts2 automatically calculates how many bins to use based on the values in X and Y.

If you specify nbins with BinMethod or BinWidth, histcounts2 only honors the last parameter.

Example: [N,Xedges,Yedges] = histcounts2(X,Y,15) uses 15 bins in the x-dimension and in the y-dimension.

Example: [N,Xedges,Yedges] = histcounts2(X,Y,[15 20]) uses 15 bins in the x-dimension and 20 bins in the y-dimension.

XedgesBin 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, histcounts2 only honors the bin edges and the bin edges must be specified last.

  • If you specify Xedges with XBinLimits, histcounts2 only honors the Xedges and the Xedges must be specified last.

YedgesBin 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, histcounts2 only honors the bin edges and the bin edges must be specified last.

  • If you specify Yedges with YBinLimits, histcounts2 only honors the Yedges and the Yedges must be specified last.

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.

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

Example: [N,Xedges,Yedges] = histcounts2(X,Y,'Normalization','probability') normalizesthe bin counts in N, such that sum(N) is1.

XBinLimitsBin 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.

YBinLimitsBin 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.

Output Arguments

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N — Bin counts
array

Bin counts, returned as an array.

The binning scheme includes the leading x-dimension and y-dimension edge of each bin as well as the trailing edge for the last bins along the x-dimension and y-dimension.

Bivariate histogram bin counts - MATLAB histcounts2- MathWorks France (1)

For example, the (1,1) bin includes values that fall on the first edge in each dimension, and the last bin in the bottom right includes values that fall on any of its edges.

Xedges — Bin edges in x-dimension
vector

Bin edges in x-dimension, returned as a vector. The first element is the leading edge of the first bin in the x-dimension. The last element is the trailing edge of the last bin in the x-dimension.

Yedges — Bin edges in y-dimension
vector

Bin edges in y-dimension, returned as a vector. The first element is the leading edge of the first bin in the y-dimension. The last element is the trailing edge of the last bin in the y-dimension.

binX — Bin index in x-dimension
array

Bin index in x-dimension, returned as an array of the same size as X. Corresponding elements in binX and binY describe which numbered bin contains the corresponding values in X and Y. A value of 0 in binX or binY indicates an element that does not belong to any of the bins (such as a NaN value).

For example, binX(1) and binY(1) describethe bin placement for the value [X(1),Y(1)].

binY — Bin index in y-dimension
array

Bin index in y-dimension, returned as an array of the same size as Y. Corresponding elements in binX and binY describe which numbered bin contains the corresponding values in X and Y. A value of 0 in binX or binY indicates an element that does not belong to any of the bins (such as a NaN value).

For example, binX(1) and binY(1) describethe bin placement for the value [X(1),Y(1)].

Extended Capabilities

Version History

Introduced in R2015b

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You can normalize histogram values as percentages by specifying the Normalization name-value argument as 'percentage'.

See Also

histogram | histcounts | discretize | histogram2 | morebins | fewerbins

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Bivariate histogram bin counts - MATLAB histcounts2- MathWorks France (2)

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Bivariate histogram bin counts - MATLAB histcounts2
- MathWorks France (2024)
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