Built-in Mathematica Symbol

Histogram3D

Histogram3D[{{x₁, y₁}, {x₂, y₂}, ...}]
plots a 3D histogram of the values {x_i, y_i}.

Histogram3D[{{x₁, y₁}, {x₂, y₂}, ...}, bspec]
plots a 3D histogram with bins specified by bspec.

Histogram3D[{{x₁, y₁}, {x₂, y₂}, ...}, bspec, hspec]
plots a 3D histogram with bin heights computed according to the specification hspec.

Histogram3D[{data₁, data₂, ...}]
plots 3D histograms for multiple datasets data_i.

MORE INFORMATION

Histogram3D[data] by default plots a histogram with equal bins chosen to approximate an assumed underlying smooth distribution of the values {x_i, y_i}.

The -width of each bin is computed according to the values x_i; the -width according to the y_i.

The following bin specifications bpsec can be given:

	n	use n bins
	{w}	use bins of width w
	{min,max,w}	use bins of width w from min to max
	{{b₁,b₂,...}}	use bins [b₁, b₂), [b₂, b₃), ...
	Automatic	determine bin widths automatically
	"name"	use a named binning method
	fw	apply fw to get an explicit bin specification {b₁, b₂, ...}
	{xspec,yspec}	give different x and y specifications

Possible named binning methods include:

	"Sturges"	compute the number of bins based on the length of data
	"Scott"	asymptotically minimize the mean square error
	"FreedmanDiaconis"	twice the interquartile range divided by the cube root of sample size
	"Wand"	one-level recursive approximate Wand binning
	"Log"	logarithmic bin widths

The function fw in Histogram3D[data, fw] is applied to a list of all {x_i, y_i}, and should return an explicit bin list {{bx₁, bx₂, ...}, {by₁, by₂, ...}}. In Histogram3D[data, {fx, fy}], fx is applied to the list of x_i, and fy to the list of y_i.

Different forms of 3D histogram can be obtained by giving different bin height specifications hspec in Histogram3D[data, w, hspec]. The following forms can be used:

	"Count"	the number of values lying in each 2D bin
	"Probability"	fraction of values lying in each 2D bin
	"ProbabilityDensity"	fraction of values divided by 2D bin area
	"LogCount", "LogProbability", "LogProbabilityDensity"	logarithmic heights
	fh	heights obtained by applying fh to bins and counts

The function fh in Histogram3D[data, bspec, fh] is applied to 3 arguments: a list of bins {{bx₁, bx₂}, {bx₂, ...}, ...}, a list of bins {{by₁, by₂}, {by₂, ...}, ...}, and the corresponding 2D array of counts {{c₁₁, c₁₂, ...}, {c₂₁, ...}, ...}. The function should return an array of heights to be used for each of the c_ij.

Only values {x_i, y_i} that consist of real numbers are assigned to bins; others are taken to be missing.

In Histogram3D[{data₁, data₂, ...}, ...], automatic bin locations are determined by combining all the datasets data_i.

Histogram3D[{..., w_i[data_i, ...], ...}, ...] renders the histogram elements associated with dataset data_i according to the specification defined by the symbolic wrapper w_i.

Possible symbolic wrappers are the same as for BarChart3D, and include Style, Labeled, Legended, etc.

Histogram3D has the same options as Graphics3D with the following additions and changes:

Axes	True	whether to draw axes
BarOrigin	Bottom	origin of histogram bars
BoxRatios	{1,1,0.4}	bounding 3D box ratios
ChartBaseStyle	Automatic	overall style for bars
ChartElementFunction	Automatic	how to generate raw graphics for bars
ChartElements	Automatic	graphics to use in each of the bars
ChartLabels	None	category labels for datasets
ChartLayout	Automatic	overall layout to use
ChartLegends	None	legends for data elements and datasets
ChartStyle	Automatic	style for bars
ColorFunction	Automatic	how to color bars
ColorFunctionScaling	True	whether to normalize arguments to ColorFunction
LabelingFunction	Automatic	how to label elements
LegendAppearance	Automatic	overall appearance of legends
Lighting	"Neutral"	simulated light sources to use
Method	Automatic	methods to use
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize

Possible settings for ChartLayout include "Overlapped" and "Stacked".

The arguments supplied to ChartElementFunction are the bin region {{x_min, x_max}, {y_min, y_max}, {z_min, z_max}}, the bin values lists, and metadata {m₁, m₂, ...} from each level in a nested list of datasets.

A list of built-in settings for ChartElementFunction can be obtained from ChartElementData["Histogram3D"].

The argument supplied to ColorFunction is the height for each bin.

Style and other specifications from options and other constructs in BarChart are effectively applied in the order ChartStyle, ColorFunction, Style and other wrappers, ChartElements and ChartElementFunction, with later specifications overriding earlier ones.

EXAMPLES

CLOSE ALL

Basic Examples (4)

Generate a 3D histogram for a list of pairs:

Multiple datasets:

Generate a probability histogram for a list of values:

Use any graphic for pictorial bars:

Use procedural bars:

Generate a 3D histogram for a list of pairs:

Multiple datasets:

Generate a probability histogram for a list of values:

In[1]:=

Out[1]=

Use any graphic for pictorial bars:

Use procedural bars:

Scope (22)

Specify the number of bins to use:

Specify a different number of bins to use in x and y:

Specify the bin width:

Specify a different bin width to use in x and y:

Specify bin delimiters:

Specify different bin delimiters to use in x and y:

Specify bin delimiters as an explicit list:

Specify different bin delimiters to use in x and y:

Use different automatic binning methods:

Use logarithmically spaced bins:

Use different height specifications:

Use a height function that accumulate the bin counts over the y direction:

Bins associated with a dataset are styled the same:

Non-real data is taken to be missing:

Use different layouts to display multiple datasets:

Control the origin of bars:

Use wrappers on individual data, datasets or collections of datasets:

Wrappers can be nested:

Override the default tooltips:

Use PopupWindow to provide additional drilldown information:

Button can be used to trigger any action:

Use an explicit list of styles for the bars:

Use any gradient or indexed color schemes from ColorData:

ChartBaseStyle can be used to set an initial style for all chart elements:

Style can be used to override styles:

Use any 3D graphic for pictorial bars:

Use built-in programmatically generated bars:

For detailed settings use Palettes ► ChartElementSchemes:

Use Labeled to add a label to a dataset:

Use symbolic positions for label placement:

Provide value labels for bars by using LabelingFunction:

Add categorical legend entries for datasets:

Use Legended to add additional legend entries:

Use Placed to affect the positioning of legends:

Generalizations & Extensions (1)

Specify different bin and height specifications for each dataset:

Options (39)

Change the bar origin:

Use ChartBaseStyle to style bars:

ChartBaseStyle combines with ChartStyle:

ChartStyle may override settings for ChartBaseStyle:

ChartBaseStyle combines with Style:

Style may override settings for ChartBaseStyle:

ChartBaseStyle combines with ColorFunction:

ColorFunction may override settings for ChartBaseStyle:

Create a pictorial chart based on any Graphics3D object:

Use a different graphic for each dataset:

Graphics are used cyclically:

Styles are inherited from styles set through ChartStyle etc:

Use Style to override ChartStyle:

Explicit styles set in the graphic will override other style settings:

Get a list of built-in settings for ChartElementFunction:

For detailed settings use Palettes ► ChartElementSchemes:

ChartElementFunction appropriate to show the global scale:

Write a custom ChartElementFunction:

Built-in element function may have options, use Palettes ► ChartElementSchemes to set them:

Place dataset labels above each histogram:

Labeled wrappers around datasets will place additional labels:

Symbolic positions outside the bar:

Use different layouts to display multiple datasets:

With multiple datasets that are fairly disjoint typically "Overlapped" works better:

Generate a legend based on chart style:

Use Legended to add additional legend entries:

Use Legended to specify indvidual legend entries:

Use Placed to control the placement of legends:

Use a legend to label the layers in a stacked histogram:

Use ChartStyle to style bars:

Give a list of styles:

Use "Gradient" colors from ColorData:

Use "Indexed" colors from ColorData:

Styles are used cyclically:

Style overrides settings for ChartStyle:

ColorFunction overrides settings for ChartStyle:

ChartElements may override settings for ChartStyle:

Color by bar height:

Use ColorFunctionScaling->False, to get unscaled height values:

ColorFunction overrides styles in ChartStyle:

Use ColorFunction to combine different style effects:

By default scaled height values are used:

Use ColorFunctionScaling->False, to get unscaled height values:

Use automatic labeling by values through Tooltip and StatusArea:

Do no labeling:

Use Placed to control label placement:

Control the formatting of labels:

Use the dataset position index to generate the label:

Place complete labels as tooltips:

Generate a bar chart with interactive highlighting:

Emphasize performance, by disabling interactive behaviors:

Typically less memory is required non-interactive charts:

Applications (2)

Create a MatrixPlot from counts extracted from a histogram:

Select a subset of languages available in DictionaryLookup:

Create a histogram of word lengths of various languages:

Properties & Relations (3)

Histogram3D automatically determine bins to use based on data:

Use BinCounts to for explicit binning of data:

Display using BarChart:

Use PDF to get parametric probability density function:

Show together with Histogram of random data:

Neat Examples (2)

Overlay different bin specifications:

Vary charting options to affect display: