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Bivariate histogram bin counts

```
[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(___)
```

`[`

partitions the
values in `N`

,`Xedges`

,`Yedges`

]
= histcounts2(`X,Y`

)`X`

and `Y`

into 2-D bins,
and returns the bin counts, as well as 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.

`[`

partitions `N`

,`Xedges`

,`Yedges`

]
= histcounts2(`X,Y`

,`Xedges`

,`Yedges`

)`X`

and `Y`

into
bins with the bin edges specified by `Xedges`

and `Yedges`

.

`N(i,j)`

counts the value `[X(k),Y(k)]`

if `Xedges(i)`

≤ `X(k)`

< `Xedges(i+1)`

and `Yedges(j)`

≤ `Y(k)`

< `Yedges(j+1)`

.
The last bins in each dimension also include the last (outer) edge.
For example, `[X(k),Y(k)]`

falls into the `i`

th
bin in the last row if `Xedges(end-1)`

≤ `X(k)`

≤ `Xedges(end)`

and `Yedges(i)`

≤ `Y(k)`

< `Yedges(i+1)`

.

`[`

uses
additional options specified by one or more `N`

,`Xedges`

,`Yedges`

]
= histcounts2(___,`Name,Value`

)`Name,Value`

pair
arguments using any of the input arguments in previous syntaxes. For
example, you can specify `'BinWidth'`

and a two-element
vector to adjust the width of the bins in each dimension.

`[`

also returns index arrays `N`

,`Xedges`

,`Yedges`

,`binX`

,`binY`

]
= histcounts2(___)`binX`

and `binY`

,
using any of the previous syntaxes. `binX`

and `binY`

are
arrays of the same size as `X`

and `Y`

whose
elements are the bin indices for the corresponding elements in `X`

and `Y`

.
The number of elements in the `(i,j)`

th bin is equal
to `nnz(binX==i & binY==j)`

, which is the same
as `N(i,j)`

if `Normalization`

is `'count'`

.

`discretize`

| `fewerbins`

| `histcounts`

| `histogram`

| `histogram2`

| `morebins`