# binScatterPlot

Scatter plot of bins for tall arrays

## Syntax

## Description

`binScatterPlot(`

creates a binned
scatter plot of the data in `X,Y`

)`X`

and `Y`

. The
`binScatterPlot`

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.

`binScatterPlot(`

specifies additional options with one or more name-value pair arguments using any of
the previous syntaxes. For example, you can specify `X,Y`

,`Name,Value`

)`'Color'`

and a
valid color option to change the color theme of the plot, or
`'Gamma'`

with a positive scalar to adjust the level of
detail.

returns a `h`

= binScatterPlot(___)`Histogram2`

object. Use this object to inspect
properties of the plot.

## Examples

### Binned Scatter Plot of Normally Distributed Random Data

Create two tall vectors of random data. Create a binned scatter plot for the data.

When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. To run the example using the local MATLAB session when you have Parallel Computing Toolbox, change the global execution environment by using the `mapreducer`

function.

mapreducer(0) X = tall(randn(1e5,1)); Y = tall(randn(1e5,1)); binScatterPlot(X,Y)

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 2: Completed in 0.5 sec - Pass 2 of 2: Completed in 0.12 sec Evaluation completed in 1.3 sec Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.13 sec Evaluation completed in 0.19 sec

The resulting figure contains a slider to adjust the level of detail in the image.

### Specify Number of Scatter Plot Bins

Specify a scalar value as the third input argument to use the same number of bins in each dimension, or a two-element vector to use a different number of bins in each dimension.

When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. To run the example using the local MATLAB session when you have Parallel Computing Toolbox, change the global execution environment by using the `mapreducer`

function.

mapreducer(0)

Plot a binned scatter plot of random data sorted into 100 bins in each dimension.

X = tall(randn(1e5,1)); Y = tall(randn(1e5,1)); binScatterPlot(X,Y,100)

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.22 sec Evaluation completed in 0.41 sec Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.11 sec Evaluation completed in 0.16 sec

Use 20 bins in the *x*-dimension and continue to use 100 bins in the *y*-dimension.

binScatterPlot(X,Y,[20 100])

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.08 sec Evaluation completed in 0.15 sec Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.096 sec Evaluation completed in 0.13 sec

### Specify Bin Edges for Scatter Plot

Plot a binned scatter plot of random data with specific bin edges. Use bin edges of `Inf`

and `-Inf`

to capture outliers.

When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. To run the example using the local MATLAB session when you have Parallel Computing Toolbox, change the global execution environment by using the `mapreducer`

function.

mapreducer(0)

Create a binned scatter plot with 100 bin edges between `[-2 2]`

in each dimension. The data outside the specified bin edges is not included in the plot.

X = tall(randn(1e5,1)); Y = tall(randn(1e5,1)); Xedges = linspace(-2,2); Yedges = linspace(-2,2); binScatterPlot(X,Y,Xedges,Yedges)

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.54 sec Evaluation completed in 0.72 sec

Use coarse bins extending to infinity on the edges of the plot to capture outliers.

Xedges = [-Inf linspace(-2,2) Inf]; Yedges = [-Inf linspace(-2,2) Inf]; binScatterPlot(X,Y,Xedges,Yedges)

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.14 sec Evaluation completed in 0.21 sec

### Adjust Plot Color Theme

Plot a binned scatter plot of random data, specifying `'Color'`

as `'c'`

.

`mapreducer`

function.

mapreducer(0) X = tall(randn(1e5,1)); Y = tall(randn(1e5,1)); binScatterPlot(X,Y,'Color','c')

Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 2: Completed in 0.52 sec - Pass 2 of 2: Completed in 0.12 sec Evaluation completed in 1.4 sec Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.14 sec Evaluation completed in 0.2 sec

## Input Arguments

`X,Y`

— Data to distribute among bins (as separate arguments)

tall vectors | tall matrices | tall multidimensional arrays

Data to distribute among bins, specified as separate arguments of tall
vectors, matrices, or multidimensional arrays. `X`

and
`Y`

must be the same size. If `X`

and
`Y`

are not vectors, then
`binScatterPlot`

treats them as single column
vectors, `X(:)`

and `Y(:)`

.

Corresponding elements in `X`

and `Y`

specify the *x* and *y* coordinates of 2-D
data points, `[X(k),Y(k)]`

. The underlying data types of
`X`

and `Y`

can be different, but
`binScatterPlot`

concatenates these inputs into a
single `N`

-by-`2`

tall matrix of the
dominant underlying data type.

`binScatterPlot`

ignores all `NaN`

values. Similarly, `binScatterPlot`

ignores
`Inf`

and `-Inf`

values, unless the
bin edges explicitly specify `Inf`

or
`-Inf`

as a bin edge.

**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 bin edges.`binScatterPlot`

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

scalar | vector

Number of bins in each dimension, specified as a positive scalar integer
or two-element vector of positive integers. If you do not specify
`nbins`

, then `binScatterPlot`

automatically calculates how many bins to use based on the values in
`X`

and `Y`

.

If

`nbins`

is a scalar, then`binScatterPlot`

uses that many bins in each dimension.If

`nbins`

is a vector, then`nbins(1)`

specifies the number of bins in the*x*-dimension and`nbins(2)`

specifies the number of bins in the*y*-dimension.

**Example: **`binScatterPlot(X,Y,20)`

uses 20 bins in each
dimension.

**Example: **`binScatterPlot(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.
`Xedges(1)`

is the first edge of the first bin in the
*x*-dimension, and `Xedges(end)`

is
the outer edge of the last bin.

The value `[X(k),Y(k)]`

is in the
`(i,j)`

th bin 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)`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

`Yedges`

— Bin edges in *y*-dimension

vector

Bin edges in *y*-dimension, specified as a vector.
`Yedges(1)`

is the first edge of the first bin in the
*y*-dimension, and `Yedges(end)`

is
the outer edge of the last bin.

The value `[X(k),Y(k)]`

is in the
`(i,j)`

th bin 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)`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

### 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: **`binScatterPlot(X,Y,'BinWidth',[5 10])`

`BinMethod`

— Binning algorithm

`'auto'`

(default) | `'scott'`

| `'integers'`

Binning algorithm, specified as the comma-separated pair consisting of
`'BinMethod'`

and one of these values.

Value | Description |
---|---|

`'auto'` | The default `'auto'` algorithm uses
a maximum of 100 bins and chooses a bin width to cover
the data range and reveal the shape of the underlying
distribution. |

`'scott'` | Scott’s rule is optimal if the data is close to being
jointly normally distributed. This rule is appropriate
for most other distributions, as well. It uses a bin
size of ```
[3.5*std(X)*numel(X)^(-1/4),
3.5*std(Y)*numel(Y)^(-1/4)]
``` . |

`'integers'` | The integer rule is useful with integer data, as it
creates a bin for each integer. It uses a bin width of 1
and places bin edges halfway between integers. To avoid
accidentally creating too many bins, you can use this
rule to create a limit of 65536 bins (2^{16}). If the data range is greater than
65536, then the integer rule uses wider bins
instead. |

**Note**

The `BinMethod`

property of the resulting
`Histogram2`

object always has a value of
`'manual'`

.

`BinWidth`

— Width of bins in each dimension

scalar | vector

Width of bins in each dimension, specified as the comma-separated pair
consisting of `'BinWidth'`

and a scalar or two-element
vector of positive integers, `[xWidth yWidth]`

. A
scalar value indicates the same bin width for each dimension.

If you specify `BinWidth`

, then
`binScatterPlot`

can use a maximum of 1024 bins (2^{10}) along each dimension. If instead the specified bin
width requires more bins, then `binScatterPlot`

uses
a larger bin width corresponding to the maximum number of bins.

**Example: **`binScatterPlot(X,Y,'BinWidth',[5 10])`

uses
bins with size `5`

in the
`x`

-dimension and size `10`

in the
`y`

-dimension.

`Color`

— Plot color theme

`'b'`

(default) | `'y'`

| `'m'`

| `'c'`

| `'r'`

| `'g'`

| `'k'`

Plot color theme, specified as the comma-separated pair consisting of
`'Color'`

and one of these options.

Option | Description |
---|---|

`'b'` | Blue |

`'m'` | Magenta |

`'c'` | Cyan |

`'r'` | Red |

`'g'` | Green |

`'y'` | Yellow |

`'k'` | Black |

`Gamma`

— Gamma correction

`1`

(default) | positive scalar

Gamma correction, specified as the comma-separated pair consisting of
`'Gamma'`

and a positive scalar. Use this option to
adjust the brightness and color intensity to affect the amount of detail
in the image.

`gamma < 1`

— As gamma decreases, the shading of bins with smaller bin counts becomes progressively darker, including more detail in the image.`gamma > 1`

— As gamma increases, the shading of bins with smaller bin counts becomes progressively lighter, removing detail from the image.The default value of 1 does not apply any correction to the display.

`XBinLimits`

— Bin limits in *x*-dimension

vector

Bin limits in *x*-dimension, specified as the
comma-separated pair consisting of `'XBinLimits'`

and a
two-element vector, `[xbmin,xbmax]`

. The vector
indicates the first and last bin edges in the
*x*-dimension.

`binScatterPlot`

only plots data that falls within
the bin limits inclusively, ```
Data(Data(:,1)>=xbmin &
Data(:,1)<=xbmax)
```

.

`YBinLimits`

— Bin limits in *y*-dimension

vector

Bin limits in *y*-dimension, specified as the
comma-separated pair consisting of `'YBinLimits'`

and a
two-element vector, `[ybmin,ybmax]`

. The vector
indicates the first and last bin edges in the
*y*-dimension.

`binScatterPlot`

only plots data that falls within
the bin limits inclusively, ```
Data(Data(:,2)>=ybmin &
Data(:,2)<=ybmax)
```

.

## Output Arguments

`h`

— Binned scatter plot

`Histogram2`

object

Binned scatter plot, returned as a `Histogram2`

object.
For more information, see Histogram2 Properties.

## Extended Capabilities

### Tall Arrays

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

The
`binScatterPlot`

function fully supports tall arrays. For more information,
see Tall Arrays.

## Version History

**Introduced in R2016b**

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