Data Visualizationwith Mathematica Philadelphia Math + Science Coalition www.philaedfund.org/programs/advancing-education/philadelphia-math-science- coalition United Way Building 1709 Benjamin Franklin Parkway, Suite 700 Philadelphia, PA 19103 March 8, 2010 Edward Bujak
[email protected] Goals : To explore and dynamically interact easily with large real-time data sets visually, graphically, algebraically. Manipulate data and its creative presentation to maximize information transfer utilizing numeric, textual, and/or image representa- tions. 2 Methods : Import[ ] function allows us to process data from personal files. <Name>Data[ ] functions allow us to manipulate large amounts of real-world data into Mathematica from Wolfram's Integrated Data Sources (Curated Data Sources). Notes : With data we have values, not functions. So the data is discrete, not continuous. In Mathematica the data can be anything, not just numbers. Mathematica Mathematica files are notebooks (.NB). Each notebook is organized by grouped cells indicated by nested brackets on the right. Cells can be collapsed/expanded. Almost any type of object can be copied/pasted anywhere or saved as a file. Ther are numerous types of help: palettes, application (live) documentation, online (live) documentation, support. The documentation is live and written in Mathematica. Deployment options: 1. Notebook Player - I can share this interactivity with anyone who does not have Mathematica. User needs to download the free Mathematica Player - www.wolfram.com/products/player. The author needs to publish the notebook (.NB) into a notebook player (.NBP) file with Wolfram Mathematica Player: Online Conversion - www.wolfram.com/solutions/interactivedeployment/publish 2. Slideshow generator via "Slide Show palette" - dynamic, live - need the free Notebook Player if you do not have Mathemat- ica. 3. “Demonstration” - dynamic interactivity with Manipulate[] to create virtual manipulatives that can be hosted at Wolfram's Demonstrations site - http://demonstrations.wolfram.com 4. Can save almost anything (including cell, selections) as static RTF, PDF, HTML, TeX, TXT, PS, XML, package, GIF, JPG, PNG, TIFF, BMP, WMF, L A T E X, MathML 5. Quiz generator. Mathematica Syntax Mathematica is symbolic. As in all CAS (Computer Algebrais Systems], the presentation of the mathematical results may some- times look non "traditional." Sometimes may want TraditionalForm[] or set a system preference to always display tradtional form.. [ ] function { } lists and sets ( ) grouping [[ ]] indexing = assignment == logical equal := function definition x3 is a "rule," read as x gets 3 Mathematica functions are mixed-case and start upper-case. Do-Loop Construct 2 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ?Table Ta ble [expr, ¦i max ¦] ge ne ra t e s a lis t of i max copie s of expr. Ta ble [expr, ¦i, i max ¦] ge ne ra t e s a lis t of t he va lue s of expr whe n i runs from 1 t o i max . Ta ble [expr, ¦i, i min , i max ¦] s t a rt s wit h i i min . Ta ble [expr, ¦i, i min , i max , di¦] us e s s t e ps di. Ta ble [expr, ¦i, ¦i 1 , i 2 , …¦¦] us e s t he s ucce s s ive va lue s i 1 , i 2 , …. Ta ble [expr, ¦i, i min , i max ¦, ¦ j, j min , j max ¦, …] give s a ne s t e d lis t . The lis t a s s ocia t e d wit h i is out e rmos t . Table [2 x 1, {x, 1, 6}] ¦3, 5, 7, 9, 11, 13¦ Table ]]x, 2 x, 2 x 5, 2 x 4 ¦, {x, 1, 6}| 1 2 7 2 2 4 9 32 3 6 11 162 4 8 13 512 5 10 15 1250 6 12 17 2592 Many more such as conditionals (if), user-defined functions. Can program procedurally, functionally, and/or rule-based. Built in mathematical algorithm selection is optimally chosen for problem, but can be over-ridden. Parallel computing - within one CPU across cores and/or across CPUs - this is great for multi-core CPUs, during time-consuming operations to allow you to do other work on the file. Mathematica Visualization Capabilities Looking at some visualization capbabilities. Remember that data is discrete so the Mathematica functions that utilize a mathemati- cal function can only be used after the data is modeled with a function. sizeImageNotebook 200; Plot[Sin[x], {x, 0, 2 Π}, ImageSize sizeImageNotebook] 1 2 3 4 5 6 1.0 0.5 0.5 1.0 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 3 Plot3D]Sin]x y 2 |, {x, 3, 3}, {y, 2, 2}, ImageSize sizeImageNotebook| 2 0 2 2 1 0 1 2 1.0 0.5 0.0 0.5 1.0 ContourPlot]Sin]x y 2 |, {x, 3, 3}, {y, 2, 2}, ImageSize sizeImageNotebook| 3 2 1 0 1 2 3 2 1 0 1 2 DiscretePlot[Prime[k], {k, 1, 50}, ImageSize sizeImageNotebook] 10 20 30 40 50 50 100 150 200 Everything can be changed, decorated, annotated via options (PlotStyle is a graphic option) and directives. This can be easily accessed from the "Chart Element Schemes" and the "Color Schemes"palettes. Hover cursor over any point to be shown the data value in the tooltip. 4 Dat a Vis ualiz at ion wit h Mat he m at ica. nb data1 ListPlot[Tooltip[{3, 4, 5}], PlotStyle {PointSize[0.025], Red}, ImageSize sizeImageNotebook] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 data2 ListLinePlot[{3, 4, 5}, PlotStyle {Dashed, Magenta}, ImageSize sizeImageNotebook] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Can combine many graphs: Show[data1, data2] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 5 ListLinePlot[Accumulate[RandomReal[{1, 1}, 250]], ColorFunction "Rainbow", Filling Axis, ImageSize sizeImageNotebook] 50 100 150 200 250 5 10 15 starData Table[{Cos[k 2 Pi/7], Sin[k 2 Pi/7]}, {k, 0, 21, 3}] 1 0 cos| Π 7 ] sin| Π 7 ] sin| 3 Π 14 | cos| 3 Π 14 | sin| Π 14 ] cos| Π 14 ] sin| Π 14 ] cos| Π 14 ] sin| 3 Π 14 | cos| 3 Π 14 | cos| Π 7 ] sin| Π 7 ] 1 0 N[starData] 1. 0. 0.900969 0.433884 0.62349 0.781831 0.222521 0.974928 0.222521 0.974928 0.62349 0.781831 0.900969 0.433884 1. 0. ListLinePlot[Tooltip[starData], Frame True, Axes False, ImageSize sizeImageNotebook] 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0 6 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ListPlot3D[{{0, 0, 1}, {1, 0, 0}, {0, 1, 0}}, Mesh All, ImageSize sizeImageNotebook] 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 dataSteps Table[Sin[j^2 i], {i, 0, Pi, Pi/5}, {j, 0, Pi, Pi/5}] 0 sin| Π 2 25 | sin| 4 Π 2 25 | sin| 9 Π 2 25 | sin| 16 Π 2 25 | sin|Π 2 ] 5 8 5 8 sin| Π 5 Π 2 25 | sin| Π 5 4 Π 2 25 | sin| Π 5 9 Π 2 25 | sin| Π 5 16 Π 2 25 | sin| Π 5 Π 2 ] 5 8 5 8 cos| Π 10 Π 2 25 | cos| Π 10 4 Π 2 25 | cos| Π 10 9 Π 2 25 | cos| Π 10 16 Π 2 25 | cos| Π 10 Π 2 ] 5 8 5 8 cos| Π 10 Π 2 25 | cos| Π 10 4 Π 2 25 | cos| Π 10 9 Π 2 25 | cos| Π 10 16 Π 2 25 | cos| Π 10 Π 2 ] 5 8 5 8 sin| Π 5 Π 2 25 | sin| Π 5 4 Π 2 25 | sin| Π 5 9 Π 2 25 | sin| Π 5 16 Π 2 25 | sin| Π 5 Π 2 ] 0 sin| Π 2 25 | sin| 4 Π 2 25 | sin| 9 Π 2 25 | sin| 16 Π 2 25 | sin|Π 2 ] ListPlot3D[dataSteps, Mesh None, InterpolationOrder 0, ColorFunction "SouthwestColors", ImageSize sizeImageNotebook] 2 4 6 2 4 6 1.0 0.5 0.0 0.5 1.0 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 7 ParametricPlot[{Sin[2 u], Sin[3 u]}, {u, 0, 2 Pi}, ImageSize sizeImageNotebook] 1.0 0.5 0.5 1.0 1.0 0.5 0.5 1.0 ParametricPlot[r^2 { Sqrt[t] Cos[t], Sin[t]}, {t, 0, 3 Pi/2}, {r, 1, 2}, ImageSize sizeImageNotebook] 6 4 2 0 2 4 2 0 2 4 8 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ParametricPlot3D] ¦t Cos[t] 10 , t Sin[t] 10 , t 10 ¦, {t, 6 Π, 6 Π}, ImageSize sizeImageNotebook, PlotStyle {Thick, Red} | 1 0 1 1 0 1 1 0 1 ParametricPlot3D[{1.16^v Cos[v] (1 Cos[u]), 1.16^v Sin[v] (1 Cos[u]), 2 1.16^v (1 Sin[u])}, {u, 0, 2 Pi}, {v, 15, 6}, Mesh None, PlotStyle Opacity[0.6], PlotRange All, PlotPoints 25, ImageSize sizeImageNotebook] 2 0 2 4 2 0 2 4 5 0 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 9 PolarPlot[Sin[5 t], {t, 0, Π}, ImageSize sizeImageNotebook] 0.5 0.5 0.5 0.5 1.0 ReliefPlot[Table[i Sin[i^2 j^2], {i, 4, 4, .03}, {j, 4, 4, .03}], ColorFunction "SunsetColors", ImageSize sizeImageNotebook] 10 Dat a Vis ualiz at ion wit h Mat he m at ica. nb GraphPlot[Table[i Mod[i^2, 102], {i, 0, 102}]] A 100-node random graph with 1% of possible edges filled in: GraphPlot[RandomChoice[{0.01, 0.99} {1, 0}, {100, 100}]] Layered graphs. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 11 LayeredGraphPlot[{1 2, 1 3, 2 3, 1 4, 2 4, 1 5}, VertexLabeling True, ImageSize sizeImageNotebook] 1 2 3 4 5 LayeredGraphPlot[ {"John" "plants", "lion" "John", "tiger" "John", "tiger" "deer", "lion" "deer", "deer" "plants", "mosquito" "lion", "frog" "mosquito", "mosquito" "tiger", "John" "cow", "cow" "plants", "mosquito" "deer", "mosquito" "John", "snake" "frog", "vulture" "snake"}, Left, VertexLabeling True, ImageSize 700] John lion tiger deer mosquito frog cow snake vulture And many more: ListPlot, DateListPlot, ListLogPlot, RegionPlot, RegionPlot3D, DensityPlot, Lis t De ns it yPlot , ContourPlot, ArrayPlot, RegionPlot, StreamPlot, VectorPlot, StreamDensi- tyPlot, VectordensityPlot, St r e a mPlot Ve ct or Plot St r e a mDe ns it yPlot Ve ct or De ns it yPlot RevolutionPlot3D, ParametricPlot3D, TreePlot Import [ ] and Fitting Model to Data 12 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Import [ ] and Fitting Model to Data Import and Export can handle not only tabular data, but also data corresponding to graphics, sounds, expressions and even whole documents. Import and Export can often deduce the appropriate format for data simply by looking at the extension of the file name for the file in which the data is being stored. "Exporting Graphics and Sounds" and "Importing and Exporting Files" discuss in more detail how Import and Export work. Note that you can also use Import and Export to manipulate raw files of binary data. $ImportFormats ¦3DS, ACO, AIFF, ApacheLog, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDED, CDF, Character16, Character8, Complex128, Complex256, Complex64, CSV, CUR, DBF, DICOM, DIF, Directory, DXF, EDF, ExpressionML, FASTA, FITS, FLAC, GenBank, GeoTIFF, GIF, Graph6, GTOPO30, GZIP, HarwellBoeing, HDF, HDF5, HTML, ICO, Integer128, Integer16, Integer24, Integer32, Integer64, Integer8, JPEG, JPEG2000, JVX, LaTeX, List, LWO, MAT, MathML, MBOX, MDB, MGF, MMCIF, MOL, MOL2, MPS, MTP, MTX, MX, NB, NetCDF, NOFF, OBJ, ODS, OFF, Package, PBM, PCX, PDB, PDF, PGM, PLY, PNG, PNM, PPM, PXR, QuickTime, RawBitmap, Real128, Real32, Real64, RIB, RSS, RTF, SCT, SDF, SDTS, SDTSDEM, SHP, SMILES, SND, SP3, Sparse6, STL, String, SXC, Table, TAR, TerminatedString, Text, TGA, TIFF, TIGER, TSV, UnsignedInteger128, UnsignedInteger16, UnsignedInteger24, UnsignedInteger32, UnsignedInteger64, UnsignedInteger8, USGSDEM, UUE, VCF, WAV, Wave64, WDX, XBM, XHTML, XHTMLMathML, XLS, XML, XPORT, XYZ, ZIP¦ $ExportFormats ¦3DS, ACO, AIFF, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDF, Character16, Character8, Complex128, Complex256, Complex64, CSV, DICOM, DIF, DXF, EMF, EPS, ExpressionML, FASTA, FITS, FLAC, FLV, GIF, Graph6, GZIP, HarwellBoeing, HDF, HDF5, HTML, Integer128, Integer16, Integer24, Integer32, Integer64, Integer8, JPEG, JPEG2000, JVX, List, LWO, MAT, MathML, Maya, MGF, MIDI, MOL, MOL2, MTX, MX, NB, NetCDF, NOFF, OBJ, OFF, Package, PBM, PCX, PDB, PDF, PGM, PLY, PNG, PNM, POV, PPM, PXR, RawBitmap, Real128, Real32, Real64, RIB, RTF, SCT, SDF, SND, Sparse6, STL, String, SVG, SWF, Table, TAR, TerminatedString, TeX, Text, TGA, TIFF, TSV, UnsignedInteger128, UnsignedInteger16, UnsignedInteger24, UnsignedInteger32, UnsignedInteger64, UnsignedInteger8, UUE, VRML, WAV, Wave64, WDX, WMF, X3D, XBM, XHTML, XHTMLMathML, XLS, XML, XYZ, ZIP, ZPR¦ ?Import Import [" file"] import s da t a from a file , re t urning a comple t e Mathematica ve rs ion of it . Import [" file", elements] import s t he s pe cifie d e le me nt s from a file . Import ["ht t p: llurl", …] a nd Import ["ft p: llurl", …] import s from a ny a cce s s ible URL. ?Fit Fit [data, funs, vars] finds a le a s t -s qua re s fit t o a lis t of da t a a s a line a r combina t ion of t he funct ions funs of va ria ble s vars. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 13 ?FindFit FindFit [data, expr, pars, vars] finds nume rica l va lue s of t he pa ra me t e rs pars t ha t ma ke expr give a be s t fit t o data a s a funct ion of vars. The da t a ca n ha ve t he form ¦¦x 1 , y 1 , …, f 1 ¦, ¦x 2 , y 2 , …, f 2 ¦, …¦, whe re t he numbe r of coordina t e s x, y, … is e qua l t o t he numbe r of va ria ble s in t he lis t vars. The da t a ca n a ls o be of t he form ¦ f 1 , f 2 , …¦, wit h a s ingle coordina t e a s s ume d t o t a ke va lue s 1, 2, …. FindFit [data, ¦expr, cons¦, pars, vars] finds a be s t fit s ubje ct t o t he pa ra me t e r cons t ra int s cons. $DataDirectory ToFileName[{NotebookDirectory[], "Data"}]; $DataDirectory J:\presentations\Data Visualization with Mathematica\Data\ AppendTo[$Path, $DataDirectory]; $Path ¦C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Links, C:\Documents and Settings\Ed\Application Data\Mathematica\Kernel, C:\Documents and Settings\Ed\Application Data\Mathematica\Autoload, C:\Documents and Settings\Ed\Application Data\Mathematica\Applications, C:\Documents and Settings\All Users\Application Data\Mathematica\Kernel, C:\Documents and Settings\All Users\Application Data\Mathematica\Autoload, C:\Documents and Settings\All Users\Application Data\Mathematica\Applications, ., C:\Documents and Settings\Ed, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Packages, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\LegacyPackages, C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Autoload, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Autoload, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Applications, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\ExtraPackages, C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Kernel\Packages, C:\Program Files\Wolfram Research\Mathematica\7.0\Documentation\English\System, J:\presentations\Data Visualization with Mathematica\Data\¦ Fitting a model to a series of (x,y) data values: 14 Dat a Vis ualiz at ion wit h Mat he m at ica. nb dataLinear Import["data.xls", {"Data", 1}]; dataPlotLinear ListPlot[Tooltip[dataLinear], PlotStyle {PointSize[0.02], Green}] 2 4 6 8 10 30 40 50 Fit the data to the model a x b. Clear [a, b]; fitLinear FindFit[dataLinear, a x b, {a, b}, x] ¦a 4.61415, b 8.924¦ Display the fit function together with the data. Show[dataPlotLinear, Plot[a x b /. fitLinear, {x, 0, 10}, PlotStyle Red]] 2 4 6 8 10 30 40 50 Fitting non-linear data. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 15 dataNoisy Import["noisydata.xls", {"Data", 1}]; dataNoisyPlot ListPlot[dataNoisy] 1 2 3 4 5 6 1.0 0.5 0.5 1.0 Fit the data to the model Αsin(x ΒΓ sin(∆ x)). fit FindFit[dataNoisy, Α Sin[Β x Γ Sin[∆ x]], {Α, Β, Γ, ∆}, x] ¦Α 0.00718779, Β 1.00277, Γ 1.41681, ∆ 0.999737¦ Display the fit function together with the data. Show[dataNoisyPlot, Plot[Α Sin[Β x Γ Sin[∆ x]] /. fit, {x, 0, 6.3}, PlotStyle Red]] 1 2 3 4 5 6 1.0 0.5 0.5 1.0 The next example fits a nonlinear model to some astronomical data. This imports a data file consisting of timing residuals for the pulsar PSR1257+12 spanning a three-year period (kindly supplied by Alex Wolszczan). dataPulsar Import["pulsar1257.dat", "Table"]; Display the pulsar data: 16 Dat a Vis ualiz at ion wit h Mat he m at ica. nb dataPulsar 0.687021 0.0188495 0.719811 0.335115 0.730804 0.52507 0.796315 0.257191 0.845486 2.15298 0.861925 2.10726 0.952068 2.59551 0.95484 2.62171 0.973977 2.32315 0.976714 2.22064 1.20073 0.568935 1.21987 0.150349 1.30188 0.488403 1.30455 0.494481 1.31002 0.469674 1.39201 1.94947 1.39477 1.97185 1.44655 0.0107999 1.44664 0.0066815 1.55317 0.0770058 1.55587 0.128978 1.59684 2.46479 1.59966 2.52511 1.63513 1.86379 1.67874 0.689795 1.68151 0.815304 1.6897 1.12602 1.70062 1.37461 1.71974 1.37764 1.76346 0.223993 1.76619 0.155781 1.80171 0.231833 1.80456 0.218089 1.80735 0.19759 1.82358 0.02412 1.82634 0.0089064 1.8509 0.22583 1.85364 0.222086 1.86456 0.150962 1.88094 0.176626 1.88366 0.253788 1.90829 1.07285 1.91101 1.16397 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 17 1.91379 1.24854 1.91918 1.40647 1.92192 1.46948 1.96838 1.15017 1.99029 0.019696 2.06935 1.89477 2.12112 1.7299 2.13467 2.39416 2.15652 2.67063 2.15925 2.63692 2.18661 1.47038 2.19189 1.12811 2.19464 0.939938 2.26282 1.63623 2.29831 0.571845 2.30105 0.467178 2.3038 0.370373 2.30653 0.27104 2.30923 0.185139 2.31196 0.100059 2.31473 0.0191635 2.31741 0.0613637 2.32012 0.135984 2.32288 0.193437 2.32562 0.262972 2.33105 0.3573 2.3336 0.386537 2.38549 0.108196 2.3882 0.0782136 2.41802 0.0979297 2.41909 0.116686 2.4208 0.139112 2.49979 1.2944 2.50256 1.23173 2.55708 1.44589 2.55979 1.58387 2.57344 2.143 2.57619 2.21118 2.66331 1.77407 2.66602 1.93837 2.72048 2.01038 2.7232 1.85777 2.75059 0.0428941 2.75592 0.405188 2.75867 0.595059 2.78859 1.85679 2.79134 1.89844 18 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 2.79134 1.89844 2.83763 0.804781 2.84038 0.68503 2.87312 0.49313 2.87584 0.550665 2.91669 0.564317 2.96028 0.154039 2.96302 0.17036 3.02575 1.16419 3.02851 1.17307 3.08589 0.619972 3.08867 0.764877 3.12139 2.11591 3.1706 0.76415 3.17332 0.576337 3.23625 2.80614 3.2389 2.80191 3.26894 1.70996 3.2717 1.52628 3.27441 1.34718 3.27716 1.15426 3.27988 0.958417 3.2826 0.752647 3.28539 0.542753 3.28809 0.337932 3.29353 0.0750401 3.29624 0.274558 3.299 0.47054 3.30172 0.667524 3.30445 0.851145 3.30719 1.02325 3.31267 1.34591 3.3154 1.48888 3.31809 1.61345 3.32085 1.73499 3.3263 1.91916 3.32906 1.9923 3.33182 2.04945 3.33455 2.09106 3.38369 0.774774 3.38643 0.647009 3.43013 0.938914 3.4312 0.951182 3.43291 0.967501 3.47933 0.531234 3.48206 0.479443 3.52028 0.222164 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 19 3.52028 0.222164 3.54214 0.516191 3.54486 0.560826 3.55033 0.649746 3.55852 0.771456 3.56671 0.857604 3.56947 0.87025 3.57219 0.882395 3.57496 0.889598 3.58044 0.873126 3.58584 0.832191 3.5886 0.800181 3.5914 0.757595 3.59404 0.708435 3.59676 0.654172 3.59952 0.585253 3.60227 0.513836 3.60496 0.43218 3.60775 0.345518 3.6241 0.303461 3.62692 0.430591 3.63231 0.679269 3.63502 0.809463 3.63778 0.929009 3.64049 1.05495 3.64323 1.18237 3.64596 1.30095 3.65144 1.5187 3.65414 1.6279 3.65689 1.70974 3.65962 1.79757 3.66236 1.87084 3.6651 1.93 3.71426 0.703003 3.71701 0.515862 3.76086 2.36768 3.76342 2.46275 dataPulsarPlot ListPlot]dataPulsar, AspectRatio 1 2 , PlotStyle Red| 1.5 2.0 2.5 3.0 3.5 2 1 1 2 3 Here is the nonlinear model we will use for the fit. Ε + Β cos(t Θ) + ∆ cos(t Φ) + Α sin(t Θ) + Γ sin(t Φ) This computes the regression using nondefault starting values for the parameters. 20 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Here is the nonlinear model we will use for the fit. Ε + Β cos(t Θ) + ∆ cos(t Φ) + Α sin(t Θ) + Γ sin(t Φ) This computes the regression using nondefault starting values for the parameters. params FindFit[dataPulsar, Α Sin[Θ t] Β Cos[Θ t] Γ Sin[Φ t] ∆ Cos[Φ t] Ε, {{Α, 1}, {Β, 1}, {Γ, 1}, {∆, 0}, {Θ, 23.31}, {Φ, 34.64}, {Ε, 0}}, t] ¦Α 0.46115, Β 1.33261, Γ 1.29803, ∆ 0.209533, Θ 23.3869, Φ 34.5111, Ε 0.0769581¦ This plot shows the quality of the nonlinear fit. Show[Plot[Α Sin[Θ t] Β Cos[Θ t] Γ Sin[Φ t] ∆ Cos[Φ t] Ε /. params, {t, 0.68, 3.76}], dataPulsarPlot] 1.5 2.0 2.5 3.0 3.5 2 1 1 2 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 21 xxxxData[] - Curated Data Sources - Integrated Data Sources - What Kind of Data Collections? xxxxData[] functions : An efficient load-on-demand mechanism makes hundreds of gigabytes of carefully curated and continually updated data immedi- ately available inside Mathematica for use in computations. This data, curated at Wolfram Research, can be accessed and pro- cessed in a coherent way. These data functions cover: math, science, politics, geography, finance, ... Examples include: LatticeData, WeatherData, Physical and chemical data: ElementData, ChemicalData, IsotopeData, ParticleData, » Earth and astronomical data: WeatherData, GeodesyData, CityData, CountryData, GeoDistance, AstronomicalData, » Life science data: GenomeData, GenomeLookup, SequenceAlignment, ProteinData, » Finance and economic data: FinancialData, CountryData, » Mathematical data: FiniteGroupData, GraphData, KnotData, LatticeData, PolyhedronData, » Linguistic data: DictionaryLookup, WordData, ExampleData, » Prot e inDa t a[" prot"] give s t he re fe re nce a mino a cid s e que nce for t he prot e in prot. Prot e inDa t a[" prot", " property"] give s t he va lue of t he s pe cifie d prope rt y for t he prot e in prot. What Kind of Data and Meta-Data within Collection? ?ElementData Ele me nt Da t a["name", " property"] give s t he va lue of t he s pe cifie d prope rt y for t he che mica l e le me nt "name". Ele me nt Da t a[n, " property"] give s t he s pe cifie d prope rt y for t he n t h che mica l e le me nt . List the ElementData[] collections: ElementData[] ¦Hydrogen, Helium, Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, Neon, Sodium, Magnesium, Aluminum, Silicon, Phosphorus, Sulfur, Chlorine, Argon, Potassium, Calcium, Scandium, Titanium, Vanadium, Chromium, Manganese, Iron, Cobalt, Nickel, Copper, Zinc, Gallium, Germanium, Arsenic, Selenium, Bromine, Krypton, Rubidium, Strontium, Yttrium, Zirconium, Niobium, Molybdenum, Technetium, Ruthenium, Rhodium, Palladium, Silver, Cadmium, Indium, Tin, Antimony, Tellurium, Iodine, Xenon, Cesium, Barium, Lanthanum, Cerium, Praseodymium, Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium, Ytterbium, Lutetium, Hafnium, Tantalum, Tungsten, Rhenium, Osmium, Iridium, Platinum, Gold, Mercury, Thallium, Lead, Bismuth, Polonium, Astatine, Radon, Francium, Radium, Actinium, Thorium, Protactinium, Uranium, Neptunium, Plutonium, Americium, Curium, Berkelium, Californium, Einsteinium, Fermium, Mendelevium, Nobelium, Lawrencium, Rutherfordium, Dubnium, Seaborgium, Bohrium, Hassium, Meitnerium, Darmstadtium, Roentgenium, Ununbium, Ununtrium, Ununquadium, Ununpentium, Ununhexium, Ununseptium, Ununoctium¦ 22 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ElementData[1] Hydrogen Length[ElementData[]] 118 ElementData["Properties"] ¦Abbreviation, AbsoluteBoilingPoint, AbsoluteMeltingPoint, AdiabaticIndex, AllotropeNames, AllotropicMultiplicities, AlternateNames, AlternateStandardNames, AtomicNumber, AtomicRadius, AtomicWeight, Block, BoilingPoint, BrinellHardness, BulkModulus, CASNumber, Color, CommonCompoundNames, CovalentRadius, CriticalPressure, CriticalTemperature, CrustAbundance, CrystalStructure, CuriePoint, DecayMode, Density, DiscoveryCountries, DiscoveryYear, ElectricalConductivity, ElectricalType, ElectronAffinity, ElectronConfiguration, ElectronConfigurationString, Electronegativity, ElectronShellConfiguration, FusionHeat, GasAtomicMultiplicities, Group, HalfLife, HumanAbundance, IconColor, IonizationEnergies, IsotopeAbundances, KnownIsotopes, LatticeAngles, LatticeConstants, Lifetime, LiquidDensity, MagneticType, MassMagneticSusceptibility, MeltingPoint, Memberships, MeteoriteAbundance, MohsHardness, MolarMagneticSusceptibility, MolarVolume, Name, NeelPoint, NeutronCrossSection, NeutronMassAbsorption, OceanAbundance, Period, Phase, PoissonRatio, QuantumNumbers, Radioactive, RefractiveIndex, Resistivity, ShearModulus, SolarAbundance, SoundSpeed, SpaceGroupName, SpaceGroupNumber, SpecificHeat, StableIsotopes, StandardName, SuperconductingPoint, ThermalConductivity, ThermalExpansion, UniverseAbundance, Valence, VanDerWaalsRadius, VaporizationHeat, VickersHardness, VolumeMagneticSusceptibility, YoungModulus¦ ElementData can be indexed by full name, number, or abbreviation: ElementData["Hydrogen", "MeltingPoint"] 259.14 ElementData[1, "MeltingPoint"] 259.14 ElementData["H", "MeltingPoint"] 259.14 What are the units of Hydrogen's MeltingPoint? ElementData["H", "MeltingPoint", "Units"] DegreesCelsius ElementData["H", "MeltingPoint", "UnitsNotation"] °C Sample Visualization Development Dat a Vis ualiz at ion wit h Mat he m at ica. nb 23 Sample Visualization Development ?ListLinePlot Lis t Line Plot [¦y 1 , y 2 , …¦] plot s a line t hrough a lis t of va lue s, a s s ume d t o corre s pond t o x coordina t e s 1, 2, …. Lis t Line Plot [¦¦x 1 , y 1 ¦, ¦x 2 , y 2 ¦, …¦] plot s a line t hrough s pe cific x a nd y pos it ions. Lis t Line Plot [¦list 1 , list 2 , …¦] plot s s e ve ra l line s. Table[ElementData[z, "MeltingPoint"], {z, 1, 118}] |259.14, —, 180.54, 1287., 2075., 3550., 210.1, 218.3, 219.6, 248.59, 97.72, 650., 660.32, 1414., 44.2, 115.21, 101.5, 189.3, 63.38, 842., 1541., 1668., 1910., 1907., 1246., 1538., 1495., 1455., 1084.62, 419.53, 29.76, 938.3, 817., 221., 7.3, 157.36, 39.31, 777., 1526., 1855., 2477., 2623., 2157., 2334., 1964., 1554.9, 961.78, 321.07, 156.6, 231.93, 630.63, 449.51, 113.7, 111.8, 28.44, 727., 920., 798., 931., 1021., 1.1 10 3 , 1072., 822., 1313., 1356., 1412., 1474., 1497., 1545., 819., 1663., 2233., 3017., 3422., 3186., 3033., 2466., 1768.3, 1064.18, 38.83, 304., 327.46, 271.3, 254., 302., 71., —, 7.010 2 , 1050., 1750., 1572., 1135., 644., 640., 1176., 1345., 1050., 900., 860., 1527., 827., 827., 1627., —, —, —, —, —, —, —, —, —, —, —, —, —, —, —| ListLinePlot[Table[ElementData[z, "MeltingPoint"], {z, 1, 118}]] 20 40 60 80 100 500 1000 1500 2000 2500 3000 3500 ?ListPlot Lis t Plot [¦y 1 , y 2 , …¦] plot s point s corre s ponding t o a lis t of va lue s, a s s ume d t o corre s pond t o x coordina t e s 1, 2, …. Lis t Plot [¦¦x 1 , y 1 ¦, ¦x 2 , y 2 ¦, …¦] plot s a lis t of point s wit h s pe cifie d x a nd y coordina t e s. Lis t Plot [¦list 1 , list 2 , …¦] plot s s e ve ra l lis t s of point s. 24 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ListPlot[Table[ElementData[z, "MeltingPoint"], {z, 1, 118}]] 20 40 60 80 100 500 1000 1500 2000 2500 3000 3500 Table[ElementData[z, "MeltingPoint"], {z, 118}] |259.14, —, 180.54, 1287., 2075., 3550., 210.1, 218.3, 219.6, 248.59, 97.72, 650., 660.32, 1414., 44.2, 115.21, 101.5, 189.3, 63.38, 842., 1541., 1668., 1910., 1907., 1246., 1538., 1495., 1455., 1084.62, 419.53, 29.76, 938.3, 817., 221., 7.3, 157.36, 39.31, 777., 1526., 1855., 2477., 2623., 2157., 2334., 1964., 1554.9, 961.78, 321.07, 156.6, 231.93, 630.63, 449.51, 113.7, 111.8, 28.44, 727., 920., 798., 931., 1021., 1.1 10 3 , 1072., 822., 1313., 1356., 1412., 1474., 1497., 1545., 819., 1663., 2233., 3017., 3422., 3186., 3033., 2466., 1768.3, 1064.18, 38.83, 304., 327.46, 271.3, 254., 302., 71., —, 7.010 2 , 1050., 1750., 1572., 1135., 644., 640., 1176., 1345., 1050., 900., 860., 1527., 827., 827., 1627., —, —, —, —, —, —, —, —, —, —, —, —, —, —, —| dataMeltingPointElement Table[{ElementData[z, "MeltingPoint"], ElementData[z]}, {z, 118}] 259.14 Hydrogen — Helium 180.54 Lithium 1287. Beryllium 2075. Boron 3550. Carbon 210.1 Nitrogen 218.3 Oxygen 219.6 Fluorine 248.59 Neon 97.72 Sodium 650. Magnesium 660.32 Aluminum 1414. Silicon 44.2 Phosphorus Dat a Vis ualiz at ion wit h Mat he m at ica. nb 25 44.2 Phosphorus 115.21 Sulfur 101.5 Chlorine 189.3 Argon 63.38 Potassium 842. Calcium 1541. Scandium 1668. Titanium 1910. Vanadium 1907. Chromium 1246. Manganese 1538. Iron 1495. Cobalt 1455. Nickel 1084.62 Copper 419.53 Zinc 29.76 Gallium 938.3 Germanium 817. Arsenic 221. Selenium 7.3 Bromine 157.36 Krypton 39.31 Rubidium 777. Strontium 1526. Yttrium 1855. Zirconium 2477. Niobium 2623. Molybdenum 2157. Technetium 2334. Ruthenium 1964. Rhodium 1554.9 Palladium 961.78 Silver 321.07 Cadmium 156.6 Indium 231.93 Tin 630.63 Antimony 449.51 Tellurium 113.7 Iodine 111.8 Xenon 28.44 Cesium 727. Barium 920. Lanthanum 798. Cerium 931. Praseodymium 1021. Neodymium 1.1 10 3 Promethium 26 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 1.1 10 3 Promethium 1072. Samarium 822. Europium 1313. Gadolinium 1356. Terbium 1412. Dysprosium 1474. Holmium 1497. Erbium 1545. Thulium 819. Ytterbium 1663. Lutetium 2233. Hafnium 3017. Tantalum 3422. Tungsten 3186. Rhenium 3033. Osmium 2466. Iridium 1768.3 Platinum 1064.18 Gold 38.83 Mercury 304. Thallium 327.46 Lead 271.3 Bismuth 254. Polonium 302. Astatine 71. Radon — Francium 7.0 10 2 Radium 1050. Actinium 1750. Thorium 1572. Protactinium 1135. Uranium 644. Neptunium 640. Plutonium 1176. Americium 1345. Curium 1050. Berkelium 900. Californium 860. Einsteinium 1527. Fermium 827. Mendelevium 827. Nobelium 1627. Lawrencium — Rutherfordium — Dubnium — Seaborgium Bohrium Dat a Vis ualiz at ion wit h Mat he m at ica. nb 27 — Bohrium — Hassium — Meitnerium — Darmstadtium — Roentgenium — Ununbium — Ununtrium — Ununquadium — Ununpentium — Ununhexium — Ununseptium — Ununoctium ?Dimensions Dime ns ions[expr] give s a lis t of t he dime ns ions of expr. Dime ns ions[expr, n] give s a lis t of t he dime ns ions of expr down t o le ve l n. Dimensions[dataMeltingPointElement] ¦118, 2¦ Length[dataMeltingPointElement] 118 dataMeltingPointElement[[1]] ¦259.14, Hydrogen¦ dataMeltingPointElement[[1]][[2]] Hydrogen ListLinePlot[Table[ElementData[z, "MeltingPoint"], {z, 1, 118}]] 20 40 60 80 100 500 1000 1500 2000 2500 3000 3500 28 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ListLinePlot] Tooltip[Table[ElementData[z, "MeltingPoint"], {z, 1, 118}]], PlotLabel "Melting Point vs Atomic Number", AxesLabel ]"Atomic\nNumber", "Melting\nPoint [°C]"¦, LabelStyle Directive[Blue, Bold], GridLines Automatic| 20 40 60 80 500 1000 1500 2000 2500 3000 3500 Melting Point °C Melting Point vs Atomic Number dataMpBp Table[{ElementData[z, "MeltingPoint"], ElementData[z, "BoilingPoint"]}, {z, 1, 118}]; Dat a Vis ualiz at ion wit h Mat he m at ica. nb 29 ListLinePlot[dataMpBp] 500 1000 1500 2000 2500 3000 3500 1000 2000 3000 4000 5000 ListPlot[dataMpBp] 500 1000 1500 2000 2500 3000 3500 1000 2000 3000 4000 5000 The data points can have tool tips with information when the mouse hovers over a data point. ?Tooltip Toolt ip[expr, label] dis pla ys label a s a t oolt ip while t he mous e point e r is in t he a re a whe re expr is dis pla ye d. 30 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ListPlot[Tooltip[dataMpBp]] 500 1000 1500 2000 2500 3000 3500 1000 2000 3000 4000 5000 ElementData["Properties"] ¦Abbreviation, AbsoluteBoilingPoint, AbsoluteMeltingPoint, AdiabaticIndex, AllotropeNames, AllotropicMultiplicities, AlternateNames, AlternateStandardNames, AtomicNumber, AtomicRadius, AtomicWeight, Block, BoilingPoint, BrinellHardness, BulkModulus, CASNumber, Color, CommonCompoundNames, CovalentRadius, CriticalPressure, CriticalTemperature, CrustAbundance, CrystalStructure, CuriePoint, DecayMode, Density, DiscoveryCountries, DiscoveryYear, ElectricalConductivity, ElectricalType, ElectronAffinity, ElectronConfiguration, ElectronConfigurationString, Electronegativity, ElectronShellConfiguration, FusionHeat, GasAtomicMultiplicities, Group, HalfLife, HumanAbundance, IconColor, IonizationEnergies, IsotopeAbundances, KnownIsotopes, LatticeAngles, LatticeConstants, Lifetime, LiquidDensity, MagneticType, MassMagneticSusceptibility, MeltingPoint, Memberships, MeteoriteAbundance, MohsHardness, MolarMagneticSusceptibility, MolarVolume, Name, NeelPoint, NeutronCrossSection, NeutronMassAbsorption, OceanAbundance, Period, Phase, PoissonRatio, QuantumNumbers, Radioactive, RefractiveIndex, Resistivity, ShearModulus, SolarAbundance, SoundSpeed, SpaceGroupName, SpaceGroupNumber, SpecificHeat, StableIsotopes, StandardName, SuperconductingPoint, ThermalConductivity, ThermalExpansion, UniverseAbundance, Valence, VanDerWaalsRadius, VaporizationHeat, VickersHardness, VolumeMagneticSusceptibility, YoungModulus¦ dataMpBp2 Table[{ElementData[z, "MeltingPoint"], ElementData[z, "BoilingPoint"]}, {z, 1, 118}] 259.14 252.87 — 268.93 180.54 1342. 1287. 2470. 2075. 4000. 3550. 4027. 210.1 195.79 218.3 182.9 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 31 218.3 182.9 219.6 188.12 248.59 246.08 97.72 883. 650. 1090. 660.32 2519. 1414. 2.910 3 44.2 280.5 115.21 444.72 101.5 34.04 189.3 185.8 63.38 759. 842. 1484. 1541. 2830. 1668. 3287. 1910. 3407. 1907. 2671. 1246. 2061. 1538. 2861. 1495. 2927. 1455. 2913. 1084.62 2927. 419.53 907. 29.76 2204. 938.3 2820. 817. 614. 221. 685. 7.3 59. 157.36 153.22 39.31 688. 777. 1382. 1526. 3345. 1855. 4409. 2477. 4744. 2623. 4639. 2157. 4265. 2334. 4150. 1964. 3695. 1554.9 2963. 961.78 2162. 321.07 767. 156.6 2072. 231.93 2602. 630.63 1587. 449.51 988. 113.7 184.3 111.8 108. 32 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 111.8 108. 28.44 671. 727. 1870. 920. 3464. 798. 3360. 931. 3290. 1021. 3.110 3 1.1 10 3 3.010 3 1072. 1803. 822. 1527. 1313. 3250. 1356. 3230. 1412. 2567. 1474. 2700. 1497. 2868. 1545. 1950. 819. 1196. 1663. 3402. 2233. 4603. 3017. 5458. 3422. 5555. 3186. 5596. 3033. 5012. 2466. 4428. 1768.3 3825. 1064.18 2856. 38.83 356.73 304. 1473. 327.46 1749. 271.3 1564. 254. 962. 302. — 71. 61.7 — — 7.0 10 2 1737. 1050. 3200. 1750. 4820. 1572. 4000. 1135. 3927. 644. 4.010 3 640. 3230. 1176. 2011. 1345. 3110. 1050. — 900. — 860. — 1527. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 33 1527. — 827. — 827. — 1627. — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — Creating a Dynamic Interactive Manipulative to Huge Data Set Manipulate[ plotType[Table[ {ElementData[z, prop1], ElementData[z, prop2]}, {z, 1, 118}]], {plotType, {ListPlot, ListLinePlot, ListLogPlot, ListLogLinearPlot}}, {prop1, ElementData["Properties"]}, {prop2, ElementData["Properties"]} ] 34 Dat a Vis ualiz at ion wit h Mat he m at ica. nb plot Type Lis t Plot Lis t Line Plot Lis t LogPlot Lis t LogLine a rPlot prop1 At omicNumbe r prop2 At omicRa dius 20 40 60 80 100 150 200 250 300 Capabilities - Only the Beginning Plot the closing prices for Google stock since its initial public offering on August 19, 2004. DateListPlot[ Tooltip[FinancialData["GOOG", "August 19 2004"]], Joined True] 2005 2006 2007 2008 2009 2010 100 200 300 400 500 600 700 This creates a plot comparing the closing stock price over the year 2006 for three companies: General Electric, Akamai, and Microsoft. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 35 DateListPlot[Tooltip[ {FinancialData["GE", "2006"], FinancialData["AKAM", "2006"], FinancialData["MSFT", "2006"]}], Joined True] 2006 2007 2008 2009 2010 10 20 30 40 50 60 AstronomicalData["Earth", "Image"] 36 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Tooltip[AstronomicalData[, "Image"], AstronomicalData[, "Name"]] & / AstronomicalData["Planet"] ¦ , , , , , , , , ¦ Make a graphic of solar system orbit paths with tooltips displaying images of each planet. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 37 Graphics3D[{LightGray, Tooltip[AstronomicalData[, "OrbitPath"], AstronomicalData[, "Image"]] & / AstronomicalData["Planet"]}, Background Black] Varying distance of planets from Earth in 2009: AstronomicalData["Earth", "Distance", "Units"] Meters DateListPlot[ Tooltip[Table[{DateList[{2009, 1, i}], AstronomicalData[, {"Distance", DateList[{2009, 1, i}]}]}, {i, 1, 365.25, 10}], ] & / {"Mercury", "Venus", "Mars", "Jupiter", "Saturn"}, Joined True, GridLines Automatic] Jan Apr Jul Oct Jan 0 5.010 11 1.010 12 1.510 12 38 Dat a Vis ualiz at ion wit h Mat he m at ica. nb ProteinData["SP1", "MoleculePlot"] Import a PDB file. Import["ExampleData/1PPT.pdb"] Import a PDB file by setting various options. Dat a Vis ualiz at ion wit h Mat he m at ica. nb 39 Import["ExampleData/1PPT.pdb", "PDB", Background GrayLevel[0.15], ImageSize Medium, "Rendering" "Wireframe"] Get the title of this PDB file. Import["ExampleData/1PPT.pdb", {"PDB", "Title"}] XRAY ANALYSIS(1.4ANGSTROMS RESOLUTION) OF AVIANPANCREATIC POLYPEPTIDE. SMALL GLOBULARPROTEIN HORMONE Get the name of the organism referenced in this file. Import["ExampleData/1PPT.pdb", {"PDB", {"Organism", "DepositionDate"}}] ¦¦MOL_ID 1, ORGANISM_SCIENTIFIC MELEAGRIS GALLOPAVO¦, ¦1981, 1, 16, 0, 0, 0.¦¦ Import the residue sequence. Import["ExampleData/1PPT.pdb", {{"Residues"}}] ( Gly Pro Ser Gln Pro Thr Tyr Pro Gly Asp Asp Ala Pro Val Glu Asp Leu Ile Arg Phe Tyr Asp Asn Leu Gln Gln ) 40 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Import a 3D molecule model as a ball-and-stick model. Import["ExampleData/aspirin.mol"] Dat a Vis ualiz at ion wit h Mat he m at ica. nb 41 Show the bonds of the same molecule using spacefilling rendering. Import["ExampleData/aspirin.mol", "Rendering" "Spacefilling"] 42 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Import a 3D molecule model as a wireframe model. Import["ExampleData/aspirin.mol", "Rendering" "Wireframe"] When importing a molfile that contains a 2 D representation of a molecule, Mathematica automatically renders it as a chemical structure diagram. Import[ "ExampleData/fluoxetine.mol"] OO NN F F F This gives the atom types and their 2D coordinates for the structure diagram. Import["ExampleData/fluoxetine.mol", {{"VertexTypes", "VertexCoordinates"}}] C C O C C C C C ¦98.28, 75.86¦ ¦98.28, 7.24¦ ¦25.86, 117.59¦ ¦170.69, 117.59¦ ¦171.03, 48.97¦ ¦26.21, 48.97¦ ¦46.21, 75.86¦ ¦242.41 Dat a Vis ualiz at ion wit h Mat he m at ica. nb 43 This creates a molfile from the previous output. molstr ExportString[ , {"MOL", {"VertexTypes", "VertexCoordinates"}}] 44 Dat a Vis ualiz at ion wit h Mat he m at ica. nb Created by Wolfram Mathematica 7.0 : www.wolfram.com 22 0 0 0 0 999 V2000 0.9828 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0 0.9828 0.0724 0.0000 C 0 0 0 0 0 0 0 0 0 0.2586 1.1759 0.0000 O 0 0 0 0 0 0 0 0 0 1.7069 1.1759 0.0000 C 0 0 0 0 0 0 0 0 0 1.7103 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0 0.2621 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0 0.4621 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0 2.4241 0.7621 0.0000 C 0 0 0 0 0 0 0 0 0 1.7103 1.3241 0.0000 C 0 0 0 0 0 0 0 0 0 0.2621 1.3241 0.0000 C 0 0 0 0 0 0 0 0 0 0.4621 0.0724 0.0000 C 0 0 0 0 0 0 0 0 0 1.1828 1.1759 0.0000 C 0 0 0 0 0 0 0 0 0 3.1483 1.1793 0.0000 N 0 0 0 0 0 0 0 0 0 0.9828 1.7414 0.0000 C 0 0 0 0 0 0 0 0 0 1.1793 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0 1.9035 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0 3.8690 0.7621 0.0000 C 0 0 0 0 0 0 0 0 0 1.9035 0.0759 0.0000 C 0 0 0 0 0 0 0 0 0 2.6241 0.4931 0.0000 C 0 0 0 0 0 0 0 0 0 3.4000 0.8690 0.0000 F 0 0 0 0 0 0 0 0 0 2.9724 0.0966 0.0000 F 0 0 0 0 0 0 0 0 0 2.2172 1.1621 0.0000 F 0 0 0 0 0 0 0 0 0 M END Dat a Vis ualiz at ion wit h Mat he m at ica. nb 45 ImportString[molstr, {"MOL", "VertexTypes"}] ¦C, C, O, C, C, C, C, C, C, C, C, C, N, C, C, C, C, C, C, F, F, F¦ ImportString[molstr, {"MOL", "VertexCoordinates"}] 98.28 75.86 98.28 7.24 25.86 117.59 170.69 117.59 171.03 48.97 26.21 48.97 46.21 75.86 242.41 76.21 171.03 132.41 26.21 132.41 46.21 7.24 118.28 117.59 314.83 117.93 98.28 174.14 117.93 48.97 190.35 75.86 386.9 76.21 190.35 7.59 262.41 49.31 340. 86.9 297.24 9.66 221.72 116.21 Initializations sizeImageNotebook 200; 46 Dat a Vis ualiz at ion wit h Mat he m at ica. nb