SparseArray

• 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 {pos₁->val₁, pos₂->val₂, ...}.

• The elements in SparseArray need not be numeric.

• The position specifications pos_i can contain patterns.

• SparseArray[{{i_, i_}->1}, {d, d}] gives a dd identity matrix.

• Rules of the form Band[...]->vals specify values on bands in the sparse array.

• With rules pos_i:>val_i the val_i are evaluated separately for each set of indices that match pos_i.

• 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 indicates the number of non-default elements and the total dimensions.