Replicate R←X/[K]Y

Y may be any array. X is a simple integer vector or scalar.

The axis specification is optional. If present, K must be a simple integer scalar or 1-element vector. The value of K must be an axis of Y. If absent, the last axis of Y is implied. The form R←X⌿Y implies the first axis of Y.

If Y has length 1 along the Kth (or implied) axis, it is extended along that axis to match the length of X. Otherwise, the length of X must be the length of the Kth (or implied) axis of Y. However, if X is a scalar or one-element vector, it will be extended to the length of the Kth axis.

R is composed from sub-arrays along the Kth axis of Y. If X[I] (an element of X) is positive, then the corresponding sub-array is replicated X[I] times. If X[I] is zero, then the corresponding sub-array of Y is excluded. If X[I] is negative, then the fill element of Y is replicated |X[I] times. Each of the (replicated) sub-arrays and fill items are joined along the Kth axis in the order of occurrence. The shape of R is the shape of Y except that the length of the (implied) Kth axis is +/|X (after possible extension).

This function is sometimes called Compress when X is Boolean.

Examples

      1 0 1 0 1/⍳5
1 3 5

      1 ¯2 3 ¯4 5/⍳5
1 0 0 3 3 3 0 0 0 0 5 5 5 5 5

      M
1 2 3
4 5 6

      2 0 1/M
1 1 3
4 4 6

      0 1⌿M
4 5 6

      0 1/[1]M
4 5 6

If Y is a singleton (1=×/⍴,Y) its value is notionally extended to the length of X along the specified axis. 

      1 0 1/4
4 4
      1 0 1/,3
3 3
      1 0 1/1 1⍴5
5 5