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

e03b38dc-01ba-4601-8db5-2c4b5ae75f3c 13 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 1001 Random 1 el * Floor : R v rotate transpose 31 mat 012345678910111 mat 85891001234567111 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 0255 Scale :

iMage U 1010 zoom :

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

The scheduler is governed by the "rotated" M construction

iMage iVBORw0KGgoAAAANSUhEUgAAABQAAABuCAIAAACoUqT9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADHSURBVFhH7dgxVUVBEAXBbwMb6MAGOrCBjmcDHdjgkFQ2p8fAbsV90wnmtftZiYoqiIoqiIoqiIoqiIoqiIoqiIoqiIoqiIoqvN5Wv6s7HlThyPH76m91x4MqHDn+WLmDRRVERRVERRVERRVERRVERRVERRVERRVERRVE5XPlDoY7HlThyPHXyh0MdzyowpHj75U7GO54UIUjx8/KHQx3PKjCkWNfi+AOhjseVOHIsa9FcAfDHQ+qcOTY1yK4g+GOB1U4b/w8/yE5xj0Xa6q2AAAAAElFTkSuQmCC rotRnd

rnd 081921030415263748596107112 mat

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

iVBORw0KGgoAAAANSUhEUgAAABQAAABuCAIAAACoUqT9AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADHSURBVFhH7dgxEcNQDATRT8M0jCM0jCM0jMM0jCM0/qTZTrNHQHr1XqtC641WRiWIDJUgMlSCyFAJIkMliAyVIDJUgshQCSJDJYjMLzqiGRdUouV4R2c044JKtBxnn4jIUAkiQyWIDJUgMlSCyFAJIkMliAyVIDJUgshQicUtE1c044JKtBxzy8Q3mnFBJVqOuWXijmZcUImWY26ZeKIZF1Si5ZhbJvh4iBkXVKLlmFsm+HiIGRdUouWYWyb4eIgZF1Si33jvPyE5xj3xfTTMAAAAAElFTkSuQmCC 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 5694196682551442453106146108662521436140214388119827215631071246209223191241103664184192112416335208139106451342262415012035421447198177108963118625381905611812113572168250811155031295817617018539469689188148226219941427517817994166271782244180254154205 mat

Smath rainbow 21 sys