Histogram3D

Histogram3D[{{x1,y1},{x2,y2},}]

plots a 3D histogram of the values {xi,yi}.

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 datai.

Details and Options

  • Histogram3D[data] by default plots a histogram with equal bins chosen to approximate an assumed underlying smooth distribution of the values {xi,yi}.
  • Data elements for Histogram3D can be given in the following forms:
  • {xi,yi}a pure value pair
    {Quantity[xi,unit],Quantity[xi,unit]}value pair with units
  • Data for Histogram3D can be given in the following forms:
  • {e1,e2,}list of elements with or without wrappers
    <|k1e1,k2e2,|>association of keys and elements
    TimeSeries[],EventSeries[],TemporalData[]time series, event series, and temporal data
    WeightedData[],EventData[]augmented datasets
    w[{e1,e2,},]wrapper applied to a whole dataset
    w[{data1,data1,},]wrapper applied to all datasets
  • The width of each bin is computed according to the values xi; the width according to the yi.
  • The following bin specifications bpsec can be given:
  • nuse 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),
    Automaticdetermine bin widths automatically
    "name"use a named binning method
    {"Log",bspec}apply binning bspec on log-transformed data
    fbapply fb to get an explicit bin specification {b1,b2,}
    {xspec,yspec}give different x and y specifications
  • The binning specification "Log" is taken to use the Automatic underlying binning method.
  • 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
    "Knuth"balance likelihood and prior probability of a piecewise uniform model
    "Wand"one-level recursive approximate Wand binning
  • The function fb in Histogram3D[data,fb] is applied to a list of all {xi,yi}, and should return an explicit bin list {{bx1,bx2,},{by1,by2,}}. In Histogram3D[data,{fx,fy}], fx is applied to the list of xi, and fy to the list of yi.
  • Different forms of 3D histograms can be obtained by giving different bin height specifications hspec in Histogram3D[data,bspec,hspec]. The following forms can be used:
  • "Count"number of elements in each bin
    "CumulativeCount"cumulative counts
    "SurvivalCount"survival counts
    "Probability"fraction of values lying in each bin
    "Intensity"count divided by bin area
    "PDF"probability density function
    "CDF"cumulative distribution function
    "SF"survival function
    "HF"hazard function
    "CHF"cumulative hazard function
    {"Log",hspec}log-transformed height specification
    fhheights obtained by applying fh to bins and counts
  • The function fh in Histogram3D[data,bspec,fh] is applied to three 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 cij.
  • Only values {xi,yi} 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 datai.
  • Histogram3D[{,wi[datai,],},] renders the histogram elements associated with dataset datai according to the specification defined by the symbolic wrapper wi.
  • 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:
  • AxesTruewhether to draw axes
    BarOriginBottomorigin of histogram bars
    BoxRatios{1,1,0.4}bounding 3D box ratios
    ChartBaseStyleAutomaticoverall style for bars
    ChartElementFunctionAutomatichow to generate raw graphics for bars
    ChartElementsAutomaticgraphics to use in each of the bars
    ChartLabelsNonecategory labels for datasets
    ChartLayoutAutomaticoverall layout to use
    ChartLegendsNonelegends for data elements and datasets
    ChartStyleAutomaticstyle for bars
    ColorFunctionAutomatichow to color bars
    ColorFunctionScalingTruewhether to normalize arguments to ColorFunction
    LabelingFunctionAutomatichow to label elements
    LegendAppearanceAutomaticoverall appearance of legends
    Lighting"Neutral"simulated light sources to use
    MethodAutomaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotTheme$PlotThemeoverall theme for the plot
    ScalingFunctionsNonehow to scale individual coordinates
    TargetUnitsAutomaticunits to display in the chart
  • Possible settings for ChartLayout include "Overlapped" and "Stacked".
  • The arguments supplied to ChartElementFunction are the bin region {{xmin,xmax},{ymin,ymax},{zmin,zmax}}, 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.
  • With ScalingFunctions->{sx,sy,sz}, the coordinate is scaled using sx etc.
  • 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

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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:

Scope  (30)

Data and Layouts  (18)

Specify the number of bins to use:

Specify a different number of bins to use in and :

Specify the bin width:

Specify a different bin width to use in and :

Specify bin delimiters:

Specify different bin delimiters to use in and :

Specify bin delimiters as an explicit list:

Specify different bin delimiters to use in and :

Use different automatic binning methods:

Use logarithmically spaced bins:

Use different height specifications:

Use a height function that accumulates the bin counts over the direction:

Bins associated with a dataset are styled the same:

Nonreal data is taken to be missing:

The data may include units:

Specify units to use:

Specify binning spec with units:

The values in an association are used as elements:

Associations can be nested:

Use the keys as labels:

Use the keys as legends:

The time stamps in TimeSeries, EventSeries, and TemporalData are ignored:

Weights in WeightedData affect the shape of the histogram:

Use different layouts to display multiple datasets:

Control the origin of bars:

Wrappers  (2)

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:

Styling and Appearance  (4)

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 a monochrome theme in a gray tone:

Labeling and Legending  (6)

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:

Options  (43)

BarOrigin  (1)

Change the bar origin:

ChartBaseStyle  (4)

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:

ChartElements  (5)

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:

ChartElementFunction  (4)

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 functions may have options; use Palettes ChartElementSchemes to set them:

ChartLabels  (2)

Place dataset labels above each histogram:

Labeled wrappers around datasets will place additional labels:

Symbolic positions outside the bar:

ChartLayout  (2)

Use different layouts to display multiple datasets:

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

ChartLegends  (3)

Generate a legend based on chart style:

Use Legended to add additional legend entries:

Use Legended to specify individual legend entries:

Use Placed to control the placement of legends:

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

ChartStyle  (5)

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:

ColorFunction  (4)

Color by bar height:

Use ColorFunctionScaling->False to get unscaled height values:

ColorFunction overrides styles in ChartStyle:

Use ColorFunction to combine different style effects:

ColorFunctionScaling  (2)

By default, scaled height values are used:

Use ColorFunctionScaling->False to get unscaled height values:

LabelingFunction  (6)

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:

PerformanceGoal  (1)

Generate a bar chart with interactive highlighting:

Emphasize performance by disabling interactive behaviors:

Typically, less memory is required for noninteractive charts:

PlotTheme  (4)

Use a theme with guiding grid lines:

Change the color scheme:

Use a theme with minimal styling:

Add legends to the chart:

Applications  (3)

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:

Histogram for a multivariate slice of a random process:

Properties & Relations  (3)

Histogram3D automatically determines bins to use based on data:

Use BinCounts for explicit binning of data:

Display using BarChart3D:

Use PDF to get parametric probability density function:

Show together with Histogram of random data:

Neat Examples  (1)

Vary charting options to affect display:

Introduced in 2008
 (7.0)
 |
Updated in 2010
 (8.0)
2012
 (9.0)
2014
 (10.0)
2015
 (10.2)