| Importing & Exporting |
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Mathematica automatically handles hundreds of data formats and subformats—all coherently integrated through Mathematica's uniform use of symbolic expressions. For each particular format, the correspondence between representations inside and outside Mathematica can be specified at any level of detail using Mathematica's general data elements mechanism.
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Import — import from files and URLs
Export — export data, graphics, expressions to files
ImportString, ExportString — import, export string data
SendMail — send an expression, graphic, notebook, etc. as email |
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Basic Formats »
"Table" - "List" - "String" - "Text" - "Binary" - ... |
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Raster Image Formats »
"GIF" - "JPEG" - "TIFF" - "PNG" - "BMP" - "PICT" - "WMF" - "SCT" - ...
Vector Graphics Formats »
"SVG" - "WMF" - "EPS" - "PDF" - "DXF" - ...
3D Geometry & Modeling Formats »
"PLY" - "OFF" - "OBJ" - "X3D" - "Maya" - "POV" - "LWO" - "STL" - ...
Audio Formats »
"WAV" - "AIFF" - "MIDI" - "SND" - "FLAC" - "Wave64" - ...
Multimedia Formats »
"AVI" - "FLV" - "QuickTime" - "SWF" |
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Tabular & Spreadsheet Formats »
"Table" - "CSV" - "TSV" - "XLS" - "ODS" - "SXC" - ...
Database Formats »
"MDB" - "DBF" - "DIF" - "XLS" - ... |
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Scientific & Medical Data Formats »
"HDF" - "CDF" - "FITS" - "DICOM" - "EDF" - ...
Chemical & Biomolecular Formats »
"MOL" - "SDF" - "SMILES" - "PDB" - "GenBank" - "FASTA" - ...
Geospatial Formats »
"SHP" - "USGSDEM" - "GTOPO30" - "SDTS" - "TIGER" - "SP3" - ...
Numerical Data Formats »
"XPORT" - "MAT" - "MTX" - "HarwellBoeing" - "MPS" - ...
Mathematical Data Formats »
"Graph6" - "Sparse6" - ... |
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Document Formats »
"PDF" - "HTML" - "NB" - "RTF" - "TeX" - "Text" - ...
Web Formats »
"HTML" - "GIF" - "JPEG" - "SWF" - "XHTML" - "X3D" - ...
Print Formats »
"PDF" - "EPS" - "TeX" - "SCT" - "ACO" - ... |
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XML Formats »
"XML" - "XHTML" - "MathML" - "SVG" - "X3D" - "ODS" - ...
Systems & Utility Formats »
"Directory" - "ApacheLog" - "MBOX" - "VCF" - "RSS" - ...
Compression & Archive Formats »
"Base64" - "BZIP2" - "GZIP" - "TAR" - "UUE" - "ZIP" - "WDX" - ... |
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Binary Formats »
"Bit" - "Byte" - "Integer16" - "Real32" - "TerminatedString" - ...
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Import-Export Management
$ImportFormats, $ExportFormats — lists of supported formats
FileFormat, StringFormat — test for formats of files, strings
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Lower-Level Functions
ReadList - Write - BinaryReadList - BinaryWrite |
| Numerical Data |
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Huge numerical datasets are routine for Mathematica. Its powerful array primitives make large-scale array manipulation both easy to specify and highly efficient. And its integrated collection of state-of-the-art algorithms makes a broad range of sophisticated data analysis immediately accessible. Mathematica's symbolic architecture gives a new level of flexibility in representing results in forms that can be used for further computation.
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Basic Operations
Min - Max - Total - Accumulate - Differences - Ratios
Take - Count - Select - Sort - SortBy - Union - Tally |
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Statistics »
Mean - Variance - Median - Quantile - ExpectedValue - Covariance - ...
Curve Fitting & Approximate Functions »
FindFit - Fit - Interpolation - ...
Transforms and Smoothing »
Rescale - MovingAverage - ListConvolve - Fourier - ...
Exploratory Data Analysis »
Histogram - BinCounts - FindClusters - Nearest - ... |
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Tabular Layout
Grid - Column - Row
Data Visualization »
ListPlot - ListPlot3D - ListContourPlot - ArrayPlot - ... |
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Import & Export »
Import - Export
"Table" - "CSV" - "TSV" - "XLS" - "HDF" - "HTML" - "GIF" - "WAV" - ... |
| Image Processing & Analysis |
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Mathematica provides broad and deep built-in support for both programmatic and interactive modern industrial-strength image processing—fully integrated with Mathematica's powerful mathematical and algorithmic capabilities. Mathematica's unique symbolic architecture and notebook paradigm allows images in visual form to be included and manipulated directly both interactively and in programs.
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Creating & Importing Images
Copy, Drag/Drop — copy and paste an image directly into a notebook
Import — programmatically import any standard format (TIFF, PNG, JPEG, DICOM, ...)
Image — create an image from an array of data, and represent any multichannel image
Rasterize — convert expressions, notebooks or any Mathematica object to raster form
Image Representation »
ImageData — extract the array of raster data from an image
ImageDimensions - ImageChannels - ImageType - ImageHistogram - ...
Thumbnail — display an image in thumbnail form |
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Basic Image Manipulation »
ImageCrop - ImagePad - ImageTake - ...
ImageResize - ImageRotate - ImageReflect
ImageAdjust — adjust levels, brightness, contrast, gamma, etc.
Sharpen - Blur - Lighter - Darker
ImageEffect — special image and photographic effects |
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Color Manipulation »
ColorConvert - ColorSeparate - ColorQuantize - ...
Filtering & Neighborhood Processing »
ImageFilter - ImageConvolve - ImageCorrelate
GaussianFilter - LaplacianFilter - MeanFilter - MedianFilter - MinFilter - GradientFilter - EntropyFilter - ...
Morphological Image Processing »
Dilation - Erosion - Opening - Closing
DistanceTransform - TopHatTransform - HitMissTransform - ...
MorphologicalComponents - MorphologicalPerimeter - MorphologicalEulerNumber - ... |
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Image Arithmetic
ImageAdd - ImageSubtract - ImageMultiply - ImageApply
Image Tiling & Compositing
ImagePartition - ImageAssemble - ImageCompose |
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Presenting & Exporting Images
ListAnimate - GraphicsGrid - TabView - SlideView - FlipView - Labeled
Export — export static and dynamic images to all standard display, web, print formats |
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List-Based Operations »
CellularAutomaton — apply a general cellular automaton rule
Partition - ArrayFlatten - Map ? Fourier - ... |
| Processing Textual Data |
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Mathematica has uniquely flexible capabilities for processing large volumes of textual data. Most often data represented as a string is converted to lists or other constructs which can then be manipulated using Mathematica's powerful symbolic language constructs.
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Import — import data from files or the web
"Text", "PDF", "TeX", "HTML" — pick out plain text, table data, etc.
FindList — search files for records containing particular strings |
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StringSplit — split a string into words, sentences, etc.
StringCount — count occurrences of words, etc.
StringCases — find instances of a string pattern |
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StringExpression — match symbolic string patterns
Sort — sort into alphabetical order
Tally — tally numbers of identical strings |
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Nearest — find the closest-matching string from a list
FindClusters — find clusters in string data
EditDistance — edit or Levenshtein distance |
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SequenceAlignment — find matching sequences in strings |
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Hash — find a hash code using a variety of schemes |
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DictionaryLookup — look up words in English and other dictionaries
WordData — find semantic, grammatical, morphological etc. properties of words |
| Files |
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Mathematica provides convenient and efficient system-independent functions for handling file-related constructs at all levels.
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"file" — ordinary named file
"!program" — pipe
"http:...", etc. — web-type URL |
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Complete Files
Import, Export — import and export in hundreds of formats
ReadList — read unstructured data from a file
FilePrint — display the raw contents of a file
File Searching
FindList — find strings in lists of files
FileNames — find files by name
Low-Level File Operations »
OpenRead, OpenWrite — open files
Read, Write, WriteString — read and write individual data elements
Find - Skip - SetStreamPosition - ...
Mathematica Expression Files »
Get (<<) — get Mathematica expressions from a file (.m file)
Put (>>), PutAppend (>>>) — put Mathematica expressions into a file (.m file)
Save - Splice - DumpSave - Encode
Binary Data »
BinaryReadList - BinaryRead - BinaryWrite - ... |
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File Properties & Operations »
FileDate - FileByteCount - FileNames - FileHash - CopyFile - ... |
| Date & Time |
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Mathematica has a highly flexible system for handling dates and times in almost any format, automatically converting between formats, and when necessary parsing strings representing dates.
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DateString — current or specified date as a string in many possible formats
"DateTime" - "MonthName" - "DayName" - "Hour24" - ...
$DateStringFormat — default date string format
$TimeZone — resettable current time zone |
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DateList — date elements as numbers in {y, m, d, h, m, s} format
AbsoluteTime — absolute time in seconds
Clock — real-time dynamic clock variable |
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Date Operations
DatePlus — add or subtract days, weeks, etc. to a date list or string
DateDifference — find the difference in days, weeks, etc. between two dates |
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Visualization
DateListPlot, DateListLogPlot — plot data associated with dates in any format |
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Date Import/Export
"Table" - "XLS" - "MDB" - "ApacheLog" - "MBOX" - ...
DatePattern — date pattern for string manipulation
"XLS" - "ApacheLog" - "MBOX" |
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CPU Timing »
Timing - AbsoluteTiming - TimeConstrained - SessionTime - ... |
| Handling Arrays of Data |
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Mathematica routinely handles huge arrays of numeric, symbolic, textual or any other data, with any dimension or structure. Arrays are fully integrated into Mathematica's powerful core symbolic language, making possible extremely high-level array operations that are both elegant and efficient.
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Structural Array Analysis »
Length - Dimensions - Union - Tally - Position - Count - BinCounts - ...
Parts of Arrays »
Select ? Cases ? DeleteCases ? ReplacePart ? ...
Part ([[..]]) — extract or reset elements, rows, columns, blocks, etc.
Take - Drop - Append - Join - ...
Rearranging Arrays »
Flatten - Partition - Transpose - ArrayFlatten - Sort - ...
Operations on Arrays »
{}+{}, etc. — automatically operate on corresponding elements
Map - Apply - Join - ...
Array Visualization »
ListPlot - ArrayPlot - ListDensityPlot - Grid - ...
Algorithmic Array Operations »
MovingAverage - ListConvolve - Nearest - FindClusters - ...
Creating Arrays »
Import - Table - Array - SparseArray - ... |
| Statistics |
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Mathematica provides integrated support both for classical statistics and for modern large-scale data analysis. Its symbolic character allows broader coverage, with symbolic manipulation of statistical distributions, symbolic specification of functions and models, and general symbolic representations of large-scale data properties. Incorporating the latest numerics and computational geometry algorithms, Mathematica provides high-accuracy and high-reliability statistical results for datasets of almost unlimited size.
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Statistical Quantities »
Mean - Variance - StandardDeviation - Median - Quantile - Covariance - ...
Statistical Distributions »
NormalDistribution - PoissonDistribution - ChiSquareDistribution - ...
PDF, CDF — probability density function, cumulative density function
Data Fitting »
FindFit — find a general nonlinear fit
Fit - Interpolation - LeastSquares - ...
Data Smoothing »
MovingAverage - MovingMedian - ListCorrelate - ...
Statistical Model Analysis »
LinearModelFit - NonlinearModelFit - GeneralizedLinearModelFit - ...
Exploratory Data Analysis »
Histogram - BinCounts - FindClusters - Nearest - ...
Random Sampling »
RandomReal - RandomInteger - RandomChoice - ...
Importing Data »
Import - "CSV" - "XLS" - "MDB" - ... |
| Signal Processing |
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Mathematica has powerful capabilities for explicit signal processing with large volumes of data, imported and exported in many formats, and for symbolic analysis of signal processing algorithms using state-of-the-art algebraic methods.
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Import, Export — import and export data in standard formats
"SND" - "WAV" - "AIFF" - "MAT" - "EDF" - ...
BinaryReadList - BinaryWrite - ... |
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SquareWave - TriangleWave - SawtoothWave |
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ListPlot — plot a list of values
ListPlay — play a list of amplitude values as a sound |
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Fourier, FourierDCT, FourierDST — discrete Fourier transforms
ListConvolve — convolve with a kernel
Clip ? Rescale ? MovingAverage ? ExponentialMovingAverage
Linear Algebra »
Dot(.) - LinearSolve - LeastSquares - SingularValueDecomposition - ... |
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ZTransform — symbolic Z transform for constructing filters
LaplaceTransform - FourierTransform - Sinc |
| Binary Data |
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Mathematica provides high-performance reading and writing of binary data, to both files and pipes. A convenient symbolic format representation makes it straightforward to translate published instrumentation or logging specifications to a form that can immediately be used in Mathematica.
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BinaryRead — read one binary object or block of objects
BinaryReadList — repeatedly read a binary object or block of objects
BinaryWrite — write a sequence of binary objects with specified types |
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Import, Export — import, export complete binary files |
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Binary Types
"Bit" — individual binary bits (Import, Export only)
"Byte" — 8-bit unsigned integer
"Integer8", "Integer16", ... — 8-, 16-, 24- 32-, 64-, 128-bit signed integers
"UnsignedInteger8", ... — 8-, 16-, 24-, 32-, 64-, 128-bit unsigned integers
"Real32", "Real64", "Real128" — IEEE single-, double-, quad-precision real numbers
"Complex64", "Complex128", "Complex256" — IEEE complex numbers
"Character8", "Character16" — 8- and 16-bit (Unicode) characters
"TerminatedString" — null-terminated string |
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ByteOrdering — option for byte ordering (+1 for big endian; -1 for little endian)
$ByteOrdering — native byte ordering on your computer system |
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ToCharacterCode, FromCharacterCode — character code conversion |
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Compress, Uncompress — convert expressions to and from compressed strings |
| Database Connectivity |
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Mathematica has a built-in high-level interface to all standard SQL databases, that allows immediate searching, reading and writing of arbitrary data and expressions, as well as supporting general SQL database features, including discovery, result sets and transactions.
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SQL Database Operations »
OpenSQLConnection — connect to any JDBC-compatible SQL database
SQLSelect - SQLUpdate - SQLInsert - SQLDelete - ...
SQLExecute — execute any SQL command, generating Mathematica output
SQLTableNames - SQLTableInformation - SQLDataTypeNames - ...
SQLBeginTransaction - SQLResultSetOpen - ... |
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DatabaseExplorer — use a GUI to explore databases and generate notebooks |
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Import — import entire MDB etc. databases |
| New in 7.0: Data Manipulation |
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Building on Mathematica's unified symbolic architecture, Mathematica 7 introduces several major new integrated forms of data manipulation—including large-scale support for images, for statistical models, and for geodetic data.
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New in Image Processing & Analysis »
Image — create an image from an array of data, and represent any multichannel image
ImageData - ImageDimensions - ImageChannels - ImageHistogram - ...
ImageAdjust — adjust levels, brightness, contrast, gamma, etc.
ImageCrop - ImagePad - ImageResize - ImageRotate - ImageReflect - ...
ColorConvert - ColorSeparate - ColorQuantize - ...
Sharpen - Blur - Lighter - Darker - ImageEffect - ...
ImageFilter — apply an arbitrary filter to an image
ImageConvolve - GaussianFilter - LaplacianFilter - GradientFilter - ...
Dilation, Erosion, ... — morphological transformations of an image
DistanceTransform - TopHatTransform - MorphologicalComponents - ...
ImageAdd - ImageSubtract - ImageMultiply - ImageApply
ImagePartition - ImageAssemble - ImageCompose |
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New in Statistical Model Analysis »
LinearModelFit — construct a linear regression model from data
NonlinearModelFit — construct a nonlinear regression model
GeneralizedLinearModelFit - LogitModelFit - ProbitModelFit - FittedModel
"BestFit" - "FitResiduals" - "ANOVATable" - "CookDistances" - ...
DesignMatrix — construct a design matrix from data
ConfidenceLevel - VarianceEstimatorFunction - DispersionEstimatorFunction
Standardize — shift and rescale the data to zero mean and unit variance
Median, Quartiles, QuartileDeviation, ... (modified) — use with symbolic distribution
New in Interpolation »
BezierFunction — create a function representing a Bézier manifold in any dimension
BSplineFunction — create a function representing a B-spline manifold in any dimension
BernsteinBasis - BSplineBasis - SplineClosed - SplineDegree - SplineWeights - ...
Interpolation (modified) — find interpolation at a point |
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New Import & Export Formats
"GenBank" ? "PDB" ? "SDF" ? "SMILES" ? "MMCIF" ? "MOL2"
"SHP" - "TIGER" - "SDTSDEM" - "GeoTIFF" - "SP3"
New Geodesy Functions »
GeoPosition — geodetic position specified by latitude, longitude
GeoDistance — distance between geodetic positions
GeoPositionXYZ - GeoPositionENU - GeoGridPosition - GeoDirection - ...
GeodesyData, GeoProjectionData — reference ellipsoids, datums and projections
Latitude - Longitude - DMSString - FromDMS - $GeoLocation - ... |
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