Unforgettable Numbers
Professor Kip Murray asked on the J Forum for the “unforgettable” times seen on a 24-hour digital clock. The problem is that every number has something notable about it, so that each number is “unforgettable” and consequently it’s hard to remember any single one of them. 0000 all zeros 0001 first counting number 0002 first […]
Changes of Heart
Karen Shaw started the ball rolling (hearts afluttering?) by asking Jay Foad to come up with a one-liner for St. Valentine’s Day; he then solicited contributions from the language development group. Nick Nickolov responded with the following, with no explanation other than that there is room for improvement: ⎕io←0 ⋄ (⊢,⌽)’ X'[{(.5×n*2)>+/(⍺-.6×⍵)⍵*2}/¨0↓n-⍳(2×n),n←20] XXXXX XXXXX XXXXXXXXXX […]
The Diamond Kata
Acknowledgments Morten Kromberg is the other co-author of this text but the blogging software prevents his being listed as such. We are indebted to Jay Foad, Nick Nikolov, John Scholes, and Fiona Smith for comments on successive drafts of the MS. The Problem The diamond kata is a programming exercise used in the agile development, […]
Cholesky Decomposition
Morten was visiting Dyalog clients and forwarded a request: Can we have the Cholesky decomposition? If A is a Hermitian, positive-definite matrix, its Cholesky decomposition [0] is a lower-triangular matrix L such that A ≡ L +.× +⍉L. The matrix L is a sort of “square root” of the matrix A. For example: ⎕io←0 ⋄ […]
Quicksort in APL
Quicksort is a classic sorting algorithm invented by C.A.R. Hoare in 1961 [0, 1]. It has been known for some time that quicksort has a terse rendition in APL [2]. To get right to it, here is the code: Q←{1≥≢⍵:⍵ ⋄ S←{⍺⌿⍨⍺ ⍺⍺ ⍵} ⋄ ⍵((∇<S)⍪=S⍪(∇>S))⍵⌷⍨?≢⍵} The “pivot” ⍵⌷⍨?≢⍵ is randomly chosen. ((∇<S)⍪=S⍪(∇>S)) is a […]
Ken Iverson's Favourite APL Expression?
What was Ken Iverson’s favourite APL expression? I don’t know that he had one and if he had I don’t know what it was, but if I have to guess … From Sixteen APL Amuse-Bouches: The expression (0,x)+(x,0) or its commute, which generates the next set of binomial coefficients, is present in the document that […]
A Speed-Up Story
The first e-mail of the work week came from Nicolas Delcros. He wondered whether anything clever can be done with ∘.≡ on enclosed character strings. I immediately thought of using “magic functions“, an implementation technique whereby interpreter facilities are coded as dfns. I thought of magic functions because the APL expressions involved in this case […]
