Dilate
From NARS2000


X is an optional numeric singleton axis with X∊⍳1+⍴⍴R. If [X] is omitted, the operation applies to the last axis plus one.  
R is an arbitrary Real or Hypercomplex numeric array — otherwise, DOMAIN ERROR.  
Z is the corresponding array of Real numbers of shape ((=R),⍴R)[⍋⍋X≠⍳1+⍴⍴R] where =R is the Hypercomplex dimension of R as in (=R)∊1 2 4 8. 
For example,
⍴⎕←>23 23 1 ⍴⎕←>[1] 23 23 1 ⍴⎕←>2 2⍴⍳4 1 2 3 4 2 2 1 ⍴⎕←>2 2⍴1J2 3J4 4J3 2J1 1 2 3 4 4 3 2 1 2 2 2 ⍴⎕←>[1] 2 2⍴1J2 3J4 4J3 2J1 1 3 4 2 2 4 3 1 2 2 2 ⍴⎕←>2 2⍴1i2j3k4 5i6j7k8 8i7j6k5 4i3j2k1 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 2 2 4 ⍴⎕←>2 2⍴1i2j3k4l5ij6jk7kl8 9i10j11k12l13ij14jk15kl16 16i15j14k13l12ij11jk10kl9 8i7j6k5l4ij3jk2kl1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 2 8
Identities
R ←→ < > R for all R (see Condense for the definition of monadic Left Caret)
R ←→ <[X] >[X] R for all R
R ←→ > < R for all R with (¯1↑⍴ R)∊1 2 4 8
1/R ←→ > < R for all R with (¯1↑⍴1/R)∊1 2 4 8
R ←→ >[X] <[X] R for all nonscalar R with (⍴R)[X]∊1 2 4 8
Acknowledgements
This symbol and its name were suggested by David A. Rabenhorst.