SparseArray
 Usage
• SparseArray[{ -> ,  -> , ... }] yields a sparse array in which values  appear at positions  .
• SparseArray[{ ,  , ... }->{ ,  , ... }] yields the same sparse array.
• SparseArray[list] yields a sparse array version of list.
• SparseArray[data, { ,  , ... }] yields a sparse array representing a  array.
• SparseArray[data, dims, val] yields a sparse array in which unspecified elements are taken to have value val.
Notes
• By default, SparseArray takes unspecified elements to be 0. • SparseArray[data, ... ] is always converted to an optimized standard form with structure SparseArray[Automatic, dims, val, ... ]. • Normal[SparseArray[ ... ]] gives the ordinary array corresponding to a sparse array object. • ArrayRules[SparseArray[ ... ]] gives the list of rules { -> ,  -> , ... }. • The elements in SparseArray need not be numeric. • The position specifications  can contain patterns. • Example: SparseArray[{{i_, i_}->1}, {d, d}] gives a  identity matrix. • With rules  :>  the  are evaluated separately for each set of indices that match  . • SparseArray[list] requires that list be a full array, with all parts at a particular level being lists of the same length. • The individual elements of a sparse array cannot themselves be lists. • SparseArray[rules] yields a sparse array with dimensions exactly large enough to include elements whose positions have been explicitly specified. • SparseArray[rules, Automatic, val] takes unspecified elements to have value val. • List and matrix operations are typically set up to work as they do on Normal[SparseArray[ ... ]]. • Functions with attribute Listable are automatically threaded over the individual elements of the ordinary arrays represented by SparseArray objects. • Part extracts specified parts of the array represented by a SparseArray object, rather than parts of the SparseArray expression itself. • Functions like Map are automatically applied to components in a SparseArray object. • SparseArray is treated as a raw object by functions like AtomQ, and for purposes of pattern matching. • Dimensions gives the dimensions of a sparse array. • The standard output format for a sparse array specified by n rules is SparseArray[<n>, dims]. • New in Version 5. • Advanced Documentation.
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