Linear Interpolation
⎕io=0 assumed throughout; works in 1-origin with the obvious modifications. Introduction On Wednesday, a question arrived via Dyalog Support from an intern in Africa: If M is the matrix on the left, use linear interpolation to compute the result on the right. 1 20 1 20 4 80 2 40 6 82 3 60 4 […]
Stencil Lives
⎕io←0 throughout. ⎕io delenda est. Stencil A stencil operator ⌺ is available with Dyalog version 16.0. In brief, stencil is a dyadic operator f⌺s which applies f to (possibly overlapping) rectangles. The size of the rectangle and its movement are controlled by s. For example, enclosing 3-by-3 rectangles with default movements of 1: ⊢ a←4 […]
Stencil Maneuvers
Introduction The e-mail arrived in the early afternoon from Morten, in Finland attending the FinnAPL Forest Seminar. How do I speed this up and impress the Finns? 0 cmpx ‘e←⊃∨/0.2 edges¨r g b’ 6.4E¯1 edges {⍺←0.7 ⋄ 1 1↓¯1 ¯1↓⍺<(|EdgeDetect apply ⍵)÷1⌈(+⌿÷≢),⍵} apply {stencil←⍺ ⋄ {+/,⍵×stencil}⌺(⍴stencil)⊢⍵} EdgeDetect ¯1 ¯1 ¯1 ¯1 8 ¯1 ¯1 ¯1 […]
Calculation v Look-Up
(⎕io←0 and timings are done in Dyalog version 15.0.) Table Look-Up Some functions can be computed faster by table look-up than a more traditional and more conventional calculation. For example: b←?1e6⍴2 cmpx ‘*b’ ‘(*0 1)[b]’ *b → 1.32E¯2 | 0% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕ (*0 1)[b] → 1.23E¯3 | -91% ⎕⎕⎕ Some observations about this benchmark: (a) The […]
Beauty and the Beast
Finally, the last accessory I ordered for my Raspberry Pi Zero (that’s the little red thing behind my keyboard) has arrived – an Acer 43″ ET430K monitor. The Zero won’t quite drive this monitor at its maximum resolution of 3840×2160 pixels, but as you can see, you get enough real estate to do real graphics […]
Charting Reaction Times on the Raspberry Pi
Earlier this week I collected some reaction timer data on my Pi using the BBC micro:bit as an input device. I only produced an “ASCII art” chart at the time: times←ReactionTimer.Play times 251 305 294 415 338 298 294 251 378 ReactionTimer.AsciiChart times 425| 400| * 375| * 350+ 325| * 300| […]
micro:bit Reaction Timer in APL on the Pi and BBC micro:bit
I have a bit of a cold today, so I decided that instead of hopping in an icy car and driving to the office in order to spend the day drinking coffee and answering e-mail, I should stay at home, turn up the radiators, make lots of tea (with honey!) and have some fun writing […]
50847534
⎕io←0 throughout. I was re-reading A Mathematician’s Apology before recommending it to Suki Tekverk, our summer intern, and came across a statement that the number of primes less than 1e9 is 50847478 (§14, page 23). The function pco from the dfns workspace does computations on primes; ¯1 pco n is the number of primes less […]
A Memo Operator
Abstract Some functions are simply stated and easily understood as multiply-recursive functions. For example, the Fibonacci numbers are {1≥⍵:⍵ ⋄ (∇ ⍵-2)+∇ ⍵-1}. A drawback of multiple recursion is abysmal performance even for moderate-sized arguments, consequently motivating resorts to circumlocutions. The memo operator addresses the performance problem and restores multiple recursion to the toolkit of […]
I-Beam Mnemonics
I-Beam (⌶) is an operator that takes as its operand a numeric code and derives a function which isn’t really considered to be part of the APL language – for example: something which could be experimental, which might provide access to parts of the interpreter that should only be accessed with care, or may set […]
