84fa8076-c4ab-4342-b9c0-af41b34fda24 61 15 12 decimal

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

Introduction to Smath random uniform

In the definition Random(n), 'n' defines the length 'n' of the vector, i.e: a range vector. The LHS argument is not coded for for "range" [n:=1.."end"] Its counterpart is the local definition.

Unform ...  -1 < rnd < 1 n rnd μ n 11 line : 2 μ Random * 1 - 21 line :

'N' decimals ...Uniform ... -1 < rnd < 1 n N Nrnd i 1 n range r i el n rnd i el N round : for r 21 line :

102 Nrnd 0.69 0.2 - 0.19 0.59 - 0.18 - 0.22 - 0.98 - 0.05 0.25 0.26 101 mat

10 rnd 0.418908 - 0.335923 - 0.150544 0.964344 0.609775 - 0.812614 - 0.307824 0.402129 0.95013 - 0.055345 - 101 mat

n R X n rnd : Y n rnd : 21 line X Y augment 21 line :

Filling the UnitSquare

2000 R 0 2 1 sys

absolute from data set V 5 rnd : i 1 V rows range abs i el V i el abs : for 21 line

abs 0.58 0.804 0.288 0.5 0.277 51 mat

ii 15 range :

10 rnd ii el abs vectorize 0.735 0.595 0.469 0.297 0.696 51 mat

n 3 :

n XY X n rnd : Y n rnd : 21 line X Y augment 21 line :

n XY 0.372 0.765 0.262 - 0.091 0.426 - 0.66 32 mat

Smath Random(n) is very reactive in the Ws. It may need special construction. In this example, update (n) ... X extracted from XY(n) don't update equally.

X n XY 1 col : Y n XY 2 col : 21 line

X transpose 0.779 0.191 - 0.518 13 mat

Optimiz Numeric, decimals 1 rnd 4 / 1 rnd 4 / 1 el 21 mat 0.032057 - 11 mat 0.13947 21 mat

The raw result is nested by Smath code. Unest by indexing. Expect "reactivity". No problem, we will use either result. --------<---Both reactive --->--------

n rnd n random :

n 10 :

Indexed .... random(n) Smath buit-in
Visit : Stem style n myrnd j 1 n range rn j el j rnd j / 0.5 - : idx j el j : 21 line for idx rn augment 21 line :

n myrnd 1 0.5 - 2 0.5 - 3 0.167 4 0.25 - 5 0.1 - 6 0.167 7 0.5 - 8 0.125 - 9 0.056 10 0.2 102 mat

Single vector  -1 < rnd < 1 
runs on programmme n myrnd j 1 n range rn j el j rnd j / 0.5 - : 11 line for rn 21 line :

n myrnd 0.5 - 0 0.167 0.5 - 0.1 0.5 - 0.214 0.125 - 0.389 0.3 - 101 mat

Some project need  |absolute| n myrnd j 1 n range rn j el j rnd j / 0.5 - abs : 11 line for rn 21 line :

n myrnd 0.5 0.5 0.167 0.25 0.5 0 0.214 0.25 0.167 0.5 101 mat

Collect two randomised vectors n myrnd j 1 n range x j el j rnd j / 0.5 - : y j el j rnd j / 0.5 - : 21 line for x y augment 21 line :

n myrnd 0.5 - 0.5 - 0.5 - 0 0.167 - 0.167 0.5 - 0.25 0.3 - 0.1 0.5 - 0.167 - 0.357 0.071 0.375 - 0.125 0.278 0.278 - 0.5 - 0.3 102 mat

Size filling the square/rectangle

Unform ...  -1 < rnd < 1 n size rnd μ n 11 line : 2 size * μ Random * size - 21 line :

n size Size X n size rnd : Y n size rnd : 21 line X Y augment 21 line :

Filling any size square

1000 1.23456789 Size 0 2 1 sys

n size λ Rectangle X n size rnd : Y λ n size rnd (* : 21 line X Y augment 21 line :

Filling any size rectangle. Apply 'λ' on repective direction.

1000 1 0.5 Rectangle 0 2 1 sys

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m Random

m n Random

Bestandteil des Plugins

Part of plugin

Statistical Tools

Gleichverteilte Zufallszahlen zwischen 0 und 1. Je nach Zahl und Wert der Argumente werden Einzelwerte, Vektoren oder Matrizen erzeugt.

Uniformly distributed random numbers between 0 and 1. Depending on number and value of the arguments, scalar values, vectors or matrices are generated.

0 Random 0.3882

5 Random 0.5174 0.6172 0.3621 0.0639 0.8256 51 mat

53 Random 0.0439 0.7553 0.1019 0.6721 0.6006 0.1842 0.9575 0.441 0.0685 0.1374 0.6669 0.5408 0.5679 0.911 0.2736 53 mat

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Rnd 10002 Random :

n rnd n random :

n 1000 :

Quadrant square is unique for Random(n,2) ... 'n' density.

0.5 Rnd * 0.5 Rnd * - 2 1 sys

Collect two randomised vectors n myrnd j 1 n range x j el j rnd j / 0.5 - : y j el j rnd j / 0.5 - : 21 line for x y augment 21 line :

n myrnd

n rnd n random :

n 100 :

Single vector  -1 < rnd < 1 
runs on programmme n myrnd j 1 n range rn j el j rnd j / 0.5 - : 11 line for rn 21 line :

data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

M n myrnd transpose n myrnd transpose n myrnd transpose 31 mat :

this interlacing should enable to plot the Higgs Boson. Can't offer the data set > 13000 !

zoom 10 :

R M UnestV :

M 3100 Random :

i 13 range j 1 R cols range New i 2 j * el R i j el : for for

i 13 range j 1 M cols range N i 2 j * el M i j el : for for

New transpose zoom * N transpose zoom *