RE: Bug in ColorFunctionScaling ???

• To: mathgroup at smc.vnet.net
• Subject: [mg39415] RE: [mg39386] Bug in ColorFunctionScaling ???
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 14 Feb 2003 03:23:22 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Cesar,

ListDensityPlot with ColorFunctionScaling -> True must be either quite fancy
or lucky because element {2,2} in your matrix is an outlier. You have such a
range of numbers in your matrix that I thought it would be better to plot
the Log of the numbers and then get rid of the outlier.

matrix2 = Map[Log, matrix, {2}];
matrix4 = ReplacePart[matrix2, -1, {2, 2}];
min = Min[matrix4];
max = Max[matrix4];

ListDensityPlot[matrix4, ColorFunctionScaling -> False,
ColorFunction -> (GrayLevel[(# - min)/(max - min)] &)];

creates a reasonable plot.

David Park

From: Cesar Guerra [mailto:guerra_cesar at yahoo.com]
To: mathgroup at smc.vnet.net

Hi math group

working with the matrix given at the end of this mail I had troubles trying
to visualize it. For instance

ListDensityPlot[matrix]

works too bad as can be seen using a 3D chart

<<Graphics`Graphics3D`

BarChart3D[matrix]

I got the correct density plot when I scaled the matrix elements by hand:

min = Min[matrix];

max = Max[matrix];

ListDensityPlot[matrix,ColorFunctionScaling->False,ColorFunction->(GrayLevel
[(#-min)/(max-min)]&)];

The question: is it a bug or I lost something in the way? A similar problem
arises with many matrices that I generated in which there are many numbres
close to zero.

Regards.. Cesar,

Well here is the matrix. Sorry because of the horrible format

matrix={{0.024880970532441947`,0.13578975670808227`,0.027812229119535358`,

0.0033045651867030673`,0.0003347493056088158`,0.000026302686284994582`,

0.00004371748398547436`,0.00003681120741920656`,0.00003087537872290685`,

0.00001905600654956626`,0.000011958703618226977`,5.517957585379249`*^-6,
1.8928075271017263`*^-6,5.269301156366419`*^-7,
6.489638911064354`*^-8},{0.13578975670808227`,0.9373917995816773`,
0.19133899349592184`,0.02294180236292207`,0.002146876534122984`,

0.00002231000770522592`,0.0001344726022920243`,0.00012287370329599313`,

0.00011865976751467771`,0.00008588847348107676`,0.0000650218873670948`,

0.00003769993910579926`,0.000017332922552971424`,7.275477707153364`*^-6,
1.801352169404378`*^-6},{0.027812229119535358`,0.19133899349592184`,
0.03906478452215391`,0.004681738877149381`,0.0004385133576867982`,
4.090272132604937`*^-6,0.000027823395408896714`,

0.000025374358467023346`,0.00002443091259330744`,0.0000176320249591744`,

0.000013309659796768249`,7.69480720132288`*^-6,3.5276710986778535`*^-6,
1.47654392225098`*^-6,3.645535247058728`*^-7},{0.0033045651867030673`,
0.02294180236292207`,0.004681738877149381`,0.0005797298493723746`,

0.000052839536129011784`,4.7226000276470905`*^-7,3.368374620650723`*^-6,
3.069745381714908`*^-6,2.952410460102803`*^-6,2.12852330993168`*^-6,
1.605032461433652`*^-6,9.269514851713523`*^-7,4.2451346697061517`*^-7,

1.7749887062983138`*^-7,4.377821687374563`*^-8},{0.0003347493056088158`,
0.002146876534122984`,0.0004385133576867982`,0.000052839536129011784`,

9.255816438202384`*^-6,4.1249326083329274`*^-8,3.0266675833749047`*^-7,
2.757224026816698`*^-7,2.650178380130713`*^-7,1.9094596136360029`*^-7,
1.43896434791398`*^-7,8.305350785567792`*^-8,3.801262097259811`*^-8,
1.588429369111028`*^-8,
3.915317215838556`*^-9},{0.000026302686284994582`,

0.00002231000770522592`,4.090272132604937`*^-6,4.7226000276470905`*^-7,

4.1249326083329274`*^-8,3.535859690725517`*^-6,2.1961201225893756`*^-8,
2.0000362799666382`*^-8,1.92152398727093`*^-8,1.3838515977742497`*^-8,

1.0424076404006913`*^-8,6.0138740883614725`*^-9,2.7512702310528075`*^-9,
1.1491658404200648`*^-9,
2.831335936719118`*^-10},{0.00004371748398547436`,

0.0001344726022920243`,0.000027823395408896714`,3.368374620650723`*^-6,

3.0266675833749047`*^-7,2.1961201225893756`*^-8,1.3721693600020958`*^-6,
1.2199036050151096`*^-9,1.17158414848564`*^-9,8.434512469918671`*^-10,
6.351128550113803`*^-10,3.6627785449735637`*^-10,
1.675069186742091`*^-10,6.993998508257666`*^-11,
1.7225733012431472`*^-11},{0.00003681120741920656`,

0.00012287370329599313`,0.000025374358467023346`,3.069745381714908`*^-6,

2.757224026816698`*^-7,2.0000362799666382`*^-8,1.2199036050151096`*^-9,

5.794192640789079`*^-7,6.135409523313631`*^-11,4.4155949418835226`*^-11,
3.3238340437588365`*^-11,1.916277391009494`*^-11,
8.760720928814635`*^-12,3.6567233858746355`*^-12,
9.003344351753371`*^-13},{0.00003087537872290685`,

0.00011865976751467771`,0.00002443091259330744`,2.952410460102803`*^-6,
2.650178380130713`*^-7,1.92152398727093`*^-8,1.17158414848564`*^-9,
6.135409523313631`*^-11,2.6403332491754`*^-7,2.0055352842629293`*^-12,

1.509195581203532`*^-12,8.698207176501544`*^-13,3.975359904169974`*^-13,
1.6587999868150363`*^-13,
4.0829224450233844`*^-14},{0.00001905600654956626`,
0.00008588847348107676`,0.0000176320249591744`,2.12852330993168`*^-6,

1.9094596136360029`*^-7,1.3838515977742497`*^-8,8.434512469918671`*^-10,

4.4155949418835226`*^-11,2.0055352842629293`*^-12,7.78759863903862`*^-8,
5.953442715856466`*^-14,3.4301675965039096`*^-14,
1.567201965631006`*^-14,6.53740694684916`*^-15,
1.6085914870370433`*^-15},{0.000011958703618226977`,

0.0000650218873670948`,0.000013309659796768249`,1.605032461433652`*^-6,
1.43896434791398`*^-7,1.0424076404006913`*^-8,6.351128550113803`*^-10,
3.3238340437588365`*^-11,1.509195581203532`*^-12,
5.953442715856466`*^-14,2.9305747143573262`*^-8,
1.1656559281957215`*^-15,5.323917587243905`*^-16,
2.2200368196954134`*^-16,
5.4608078423152933`*^-17},{5.517957585379249`*^-6,
0.00003769993910579926`,7.69480720132288`*^-6,9.269514851713523`*^-7,

8.305350785567792`*^-8,6.0138740883614725`*^-9,3.6627785449735637`*^-10,
1.916277391009494`*^-11,8.698207176501544`*^-13,

3.4301675965039096`*^-14,1.1656559281957215`*^-15,7.76299670479757`*^-9,
1.5221789994509213`*^-17,6.345037635961268`*^-18,
1.5602293071790306`*^-18},{1.8928075271017263`*^-6,
0.000017332922552971424`,3.5276710986778535`*^-6,

4.2451346697061517`*^-7,3.801262097259811`*^-8,2.7512702310528075`*^-9,

1.675069186742091`*^-10,8.760720928814635`*^-12,3.975359904169974`*^-13,
1.567201965631006`*^-14,5.323917587243905`*^-16,
1.5221789994509213`*^-17,1.6163732178696085`*^-9,
1.4386200807791453`*^-19,

3.530345878524741`*^-20},{5.269301156366419`*^-7,7.275477707153364`*^-6,
1.47654392225098`*^-6,1.7749887062983138`*^-7,1.588429369111028`*^-8,
1.1491658404200648`*^-9,6.993998508257666`*^-11,
3.6567233858746355`*^-12,1.6587999868150363`*^-13,

6.53740694684916`*^-15,2.2200368196954134`*^-16,6.345037635961268`*^-18,
1.4386200807791453`*^-19,3.740548209112563`*^-10,

6.532730362808272`*^-22},{6.489638911064354`*^-8,1.801352169404378`*^-6,
3.645535247058728`*^-7,4.377821687374563`*^-8,3.915317215838556`*^-9,
2.831335936719118`*^-10,1.7225733012431472`*^-11,
9.003344351753371`*^-13,4.0829224450233844`*^-14,
1.6085914870370433`*^-15,5.4608078423152933`*^-17,
1.5602293071790306`*^-18,3.530345878524741`*^-20,
6.532730362808272`*^-22,4.517936598686041`*^-11}}

```

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