Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

Histogram3D

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

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 .

Details and OptionsDetails and Options

• Histogram3D[data] by default plots a histogram with equal bins chosen to approximate an assumed underlying smooth distribution of the values .
• 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 <|k1e1,k2e2,…|> 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 ; the width according to the .
• 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 Automatic determine bin widths automatically "name" use a named binning method {"Log",bspec} apply binning bspec on log-transformed data fb apply fb to get an explicit bin specification {xspec,yspec} give different x and y specifications
• The binning specification 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 , and should return an explicit bin list . In Histogram3D[data,{fx,fy}], fx is applied to the list of , and fy to the list of .
• Different forms of 3D histogram can be obtained by giving different bin height specifications hspec in Histogram3D[data,bspec,hspec]. The following forms can be used:
•  "Count" the number of values lying in each bin "CumulativeCount" cumulative counts "SurvivalCount" survival counts "Probability" fraction of values lying in each bin "PDF" probability density function "CDF" cumulative distribution function "SF" survival function "HF" hazard function "CHF" cumulative hazard function {"Log",hspec} log-transformed height specification fh heights 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 , a list of bins , and the corresponding 2D array of counts . The function should return an array of heights to be used for each of the .
• Only values 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 .
• Histogram3D[{,wi[datai,],},] renders the histogram elements associated with dataset according to the specification defined by the symbolic wrapper .
• 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 PlotTheme \$PlotTheme overall theme for the plot ScalingFunctions None how to scale individual coordinates TargetUnits Automatic units to display in the chart
• Possible settings for ChartLayout include and .
• The arguments supplied to ChartElementFunction are the bin region , the bin values lists, and metadata from each level in a nested list of datasets.
• A list of built-in settings for ChartElementFunction can be obtained from .
• The argument supplied to ColorFunction is the height for each bin.
• With ScalingFunctions->{sx,sy,sz}, the coordinate is scaled using 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.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Generate a 3D histogram for a list of pairs:

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Multiple datasets:

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Generate a probability histogram for a list of values:

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Use any graphic for pictorial bars:

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Use procedural bars:

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