<p> Scale(M,low,high) ... UnestH(data)... zoom(Ω,a,b) </p>

e03b38dc-01ba-4601-8db5-2c4b5ae75f3c 16 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

The infinite vector scheduler

Implicit 'zoom fractional' Up/Down Ω a b zoom a b ≡ (a b | (1 ≠ (& (=> ≡ => implicit conditions ≡ i 1 Ω rows a * (range j 1 Ω cols b * (range Nu i j el Ω i a / Ceil j b / Ceil el : a 1 ≥ Nu i j el Ω i a / Floor j b / Floor el : cases for for Nu 41 line :

data UnestH v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

M Low High Scale High Low - (M M Min - M Max M Min - 1012 -^+ / (* Low + :

Range 'n' ∞ - n ≤ (n ∞ ≤ (&

User scale xs 1 : ys 1 : 12 mat

v 012345678910111 mat transpose :

n v rotate N v length : p n N mod : p p p 0 ≥ p N + p 0 < ignored cases : Ω v : p 0 ≡ i 1 p range Ω i N + p - el v i el : for i p 1 + (N range Ω i p - el v i el : for 21 line cases Ω 51 line :

n 4 :

<= Pilot the rotation

v transpose n v rotate transpose 21 mat 012345678910111 mat 456789100123111 mat 21 mat

Vrot n v rotate :

XY xs v * ys Vrot * augment :

rot xs v * ys Vrot * . 10 black plotG :

C n n + 200 black 15 mat :

n v rotate x 1 + el observe the plot effect ≡

Reversible rotation of vector. You can shrink/expand either direction via [xs, ys]. Illustrative plot wrt 'n'.

x n v rotate x 1 + el rot C 4 1 sys

The "rotated" XY 041526374859610708192103112 mat

Typical Matrix Scheduler M v transpose n v rotate transpose 8 v rotate transpose 2 v rotate transpose 7 v rotate transpose 51 mat transpose : 012345678910111 mat 456789100123111 mat 891001234567111 mat 234567891001111 mat 789100123456111 mat 15 mat

n 4

U M UnestH : Schedule day Pet Jos Art Leslie 15 mat : Assign Schedule U stack : 31 line

in this example, we rotate Peter_'n'  [week 1] Assign day Pet Jos Art Leslie 048271593826104937051048160592716103827049381510492605103716125 mat

A possible application:

Assume you are looking at aspecific star, you need several

parameters [Azimut, Horizon, Focus ...]. If the vector 'v' is

wrt parameters, easy to address and automate the system.

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'R' is subscripted to explode  100*Random(1) v transpose R 101 Random 1 el * Floor : R v rotate transpose 31 mat 012345678910111 mat 7789100123456111 mat 31 mat

random from F9 calculate WS ... rnd v R v rotate augment : random rnd 0255 Scale : rotRnd random 1010 zoom : 31 sys

U U 2550 Scale :

iMage U 1010 zoom :

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

The scheduler is governed by the "rotated" M construction

iMage iVBORw0KGgoAAAANSUhEUgAAABQAAABuCAIAAACoUqT9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADHSURBVFhH7ddBUUVBDEXBbwMb6MAGOrDxdGADHdig2PRu6sRAptfnrlN5zb5HoqIKoqIKoqIKoqIKoqIKoqIKoqIKoqIKoqIKr7fRz+iOD6qwcvw++h3d8UEVVo4/Rn+jOz6owsrx58ilLaogKqogKqogKqogKqogKqogKqogKqogKqogKl8jlzbc8UEVVo6fkUsb7vigCivHfsrg0oY7PqjCyrGfMri04Y4PqrBy7KcMLm2444MqrBz7KYNLG+74oAr7xs/zD5Zdxj0tyYZEAAAAAElFTkSuQmCC rotRnd

rnd 071829310405162738495106112 mat

random from F9 calculate WS ... rnd R v rotate v augment : random rnd 0255 Scale : rotRnd random 1010 zoom : 31 sys

iVBORw0KGgoAAAANSUhEUgAAABQAAABuCAIAAACoUqT9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADHSURBVFhH7dcxEcNQDATRT8M0jCM0jCM0jMM0jCM0/qTZTrNHQHr1Xq3ReqKVUQkiQyWIDJUgMlSCyFAJIkMliAyVIDJUgshQCSLzRkc044JKtBz/ojOacUElWo539IlmXFCJluPsiogMlSAyVILIUAkiQyWIDJUgMlSCyFAJIkMliAyVWFxL8Y1mXFCJlmOupbijGRdUouWYayn4R8WMCyrRcsy1FPyjYsYFlWg55loK/lEx44JKtBxzLQX/qJhxQSX6jff+A5Zdxj2qgNevAAAAAElFTkSuQmCC rotRnd

Stand alone section ... export =======================

Implicit 'zoom fractional' Up/Down Ω a b zoom a b ≡ (a b | (1 ≠ (& (=> ≡ => implicit conditions ≡ i 1 Ω rows a * (range j 1 Ω cols b * (range Nu i j el Ω i a / Ceil j b / Ceil el : a 1 ≥ Nu i j el Ω i a / Floor j b / Floor el : cases for for Nu 41 line :

rows

cols

M 2050255 Random.N : iMage M 1010 zoom : 21 sys

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 iMage

M 168211501772923085771441422997541521061611718518918219136163217212762071745719214019343659775921211281191482341945325198197127432162001641042014914124221672153134159862061441591186885180631461463441198110222114134791319624723289231722128813249230240245147243164205 mat