Expand

is a dyadic function or monadic operator that copies each element of the right argument a given number of times and inserts prototype elements, ordering the copies along a specified axis. Typically  is called Expand while   is called "Expand First" or an equivalent.

Expand is usually associated with Replicate, and the two functions are related to Mesh and Mask. It shares a glyph with Scan even though Expand is naturally a function and Scan must be an operator. This incongruity is sometimes resolved by making Expand an operator itself, and sometimes by function-operator overloading allowing both syntactic elements to coexist.

Examples
If the right argument is a vector, the number of positive values in the left argument must match the length of the right argument. Each positive value produces copies of the corresponding item on the right argument; a zero or negative value produces one or more prototype elements.

For Boolean left argument, Expand is the right inverse of Replicate, as Expand inserts prototype elements at the exact places which Replicate will remove:

High-rank arrays
Expand works along a particular axis, which can be specified in languages with function axis and otherwise is the first axis for, and the last axis for.

Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1.

Lessons

 * APL Cultivation

Documentation

 * Dyalog
 * APLX