Mathematica Asked on February 6, 2021
I’m trying to create a 3d histogram/ matrix plot pair. My data is in the form
{{TTR1,TBF1},{TTR2,TBF2},....}
What I would like is to modify the Histogram3D so instead of having the counts of each bin on the z axis I would have the sum of TTR in that bin. I would also like the modify the matrix plot in the same way.
I’ve hacked an example in the help to get this far;
hist := Histogram3D[Log[10, dateFilter[[All, 2]]], {-4, 4, 0.25},
Function[{xbins, ybins, counts}, Sow[counts]],
AxesLabel -> {Style["TTR (log(hours))", 16],
Style["TBF (log(hours))", 16]}, ImageSize -> Large,
PlotLabel -> Style["Dryer 1 TBF and TTR Counts", 18],
ChartStyle -> RGBColor[27/255, 121/255, 169/255],
ViewPoint -> {Pi, Pi, 2}];
{g, {binCounts}} = Reap[hist];
mPlot := MatrixPlot[First@binCounts, ImageSize -> Large]
Row[{g, mPlot}]
In this case my data list is
dateFilter[[All, 2]]={{TTR1,TBF1},{TTR2,TBF2}....}
I would also like to fix this axis on the MatrixPlot so it has the same range labels as the histogram.
Also is there a better way to do the log axes on the Histogram? I’ve just taken the Log of the data but it would be better if I could just modify the axes to show 1,10,100,….
Edit
I’ve re-plotted by data using kgulers code. The function I used was
Histogram3D[Log[10, dateFilter[[All, 2]]], {-4, 4, 0.25},
heightF[dateFilter[[All, 2]]][Total, First], styles,
AxesLabel -> {Style["TTR (log(hours))", 16],
Style["TBF (log(hours))", 16], Style["Sum TTR (hours)", 16]},
ViewPoint -> {Pi, Pi, 2}]
It looks like my data has stratified into 3 groups of TTR (which may be what is really going on). I was kind of expecting the same plot with different z values but if that’s what’s going on then that’s what’s going on.
Thanks kguler and belisarius. Give me a day to check that this is all ok and I’ll tick this one off.
For the Histogram, you could do something like:
data = RandomReal[NormalDistribution[0, 1], {200, 2}];
Histogram3D[data, {.5},
Function[{xbs, ybs, c},
Table[Total[ Select[data, x[[1]] <= #[[1]] < x[[2]] && y[[1]] <= #[[2]] < y[[2]] &][[All, 1]]],
{x, xbs}, {y, ybs}]
]
]
Answered by Dr. belisarius on February 6, 2021
A custom height function for Histogram3D
:
Key ideas: (1) get the list of data points in each bin using BinLists
, (2) Map func2
to each 2D data point and func1
to the results to define the heights for each bin:
ClearAll[binListF, heightF];
binListF[data_][bins_, counts_] := BinLists[data, {bins[[1]]}, {bins[[2]]}];
heightF[data_][func1_: Total, func2_: First, binning_: Automatic] :=
Map[func1, Map[func2,
HistogramList[data, binning, binListF[data]][[2]] /. {} -> {0, 0}, {-2}], {-2}] &
Data and styles:
data = RandomVariate[NormalDistribution[0, 1], {100, 2}];
styles = Sequence @@ {BoxRatios -> 1, ImageSize -> 300, ChartStyle -> Opacity[.6],
ChartElementFunction -> ChartElementDataFunction["SegmentScaleCube",
"Segments" -> 12, "ColorScheme" -> 46]};
Usage examples:
Histogram3D[data, Automatic, heightF[data][Total, First], styles] (* OP's example *)
Bin specifications:
Row[Column[{Style[Row[{"binning: ", #}], 18, "Panel"],
Histogram3D[data, #, heightF[data][Total, First, #], styles]}, Center] & /@
{{{-2, 2, 0.5}, {-3, 3,1.5}}, "Knuth", "Sturges", "FreedmanDiaconis", "Scott", "Wand"}]
Aggregation functions:
Row[Column[{Style[Row[{"heightF[data][", #[[1]], ", ", #[[2]], "]"}], 18, "Panel"],
Histogram3D[data, Automatic, heightF[data][#[[1]], #[[2]]], styles]}, Center] & /@
{{Total, Last}, {Total, Mean}, {Max, Mean}, {Min, Mean}, {Max, Min}, {Min, Max}}]
Answered by kglr on February 6, 2021
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