Outer

Outer[f, , , ... ] gives the generalized outer product of the , forming all possible combinations of the lowest-level elements in each of them, and feeding them as arguments to f.

Outer[f, , , ... , n] treats as separate elements only sublists at level n in the .

Outer[f, , , ... , , , ... ] treats as separate elements only sublists at level in the corresponding .

Example: Outer[f,a,b,x,y] .

Outer[Times, , ] gives an outer product.

The result of applying Outer to the tensors and is the tensor with elements f[,]. Applying Outer to two tensors of ranks and gives a tensor of rank .

The heads of both must be the same, but need not necessarily be List.

The need not necessarily be cuboidal arrays.

The specifications of levels must be integers.

If only a single level specification is given, it is assumed to apply to all the . If there are several , but fewer than the number of , all levels in the remaining will be used.

Outer can be used on SparseArray objects, returning a SparseArray object when possible.

See Section 2.2.10, Section 2.4.3, Section 3.7.5 and Section 3.7.11.

See also: Inner, Distribute, Cross.

New in Version 1; modified in 3.

Further Examples