Utilities => Scale, Barsize, Histogram

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M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

N histogram value table count k 1 : j k table rows range table j el value ≡ index k el j : k k 1 + : 21 line index k el 0 : if for index rows 31 line : i 1 N max range x i el i : count i el i N count : 21 line for x count augment 31 line :

Part 1: Generate normal random

n 100 :

m 4 n * :

t0 1 time :

v 1 n range :

h n 1 matrix :

size 0.1 :

Random normal [rnd] i 1 m range r n random : h r 1 + el h r 1 + el 1 + : 21 line for

½noise size h 0.5 h Max * - (* :

data v h augment :

Rnd v ½noise augment :

h Max 10

1 time t0 - 0.2 s *

μ h Mean : σ h StdDev : 21 mat 4 1.8749 21 mat

Export user normal random noise

Rnd 0.001 BarSize

Read first => 'h'

This document will generate normal random noise of length 'n'.

For your needs: export ½noise. The setup n = 100, m = 4*n is

just to make Histogram work and confirm noise is normal.

Module 'h' is equivalent to the "Central Limit Theorem".

If "H" turns red, it indicates some values were not accounted

count(value,table) ... F9 to recalculate but "½noise" => OK.

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N h sort :

H N histogram :

h N Max Ceil N Min Floor - H rows / : λ n h * : 21 mat 0.9 9021 mat

Central Limit Theorem: confirmed

H 0.125 BarSize λ x μ σ pdf.Normal * 2 1 sys

H 17218323419516615768291102102 mat

Part 2: Randomize a function

data spec pts i 1 data rows range pt i el a b c spec : for Unest 'p' v pt 1 el : j 2 pt rows range v v pt j el stack : for data v augment 51 line :

This part is stand alone: copy/paste in blank sheet. To regenerate new set of randomized function, click in any active gray region => press F9. "level" = max level of random excursion...± level.

Random(n)=> Uniform ...  -1 < rnd < 1 n level rnd level n Random * level 2 / - 11 line :

# f L H N level randomize x 0 : dx H L - N / : i 1 N 1 + (range x i el L dx i * dx - (+ : for i 1 x rows range y i el x i el f : for x y x rows level rnd + augment x y augment 21 mat 51 line :

level 0.25 :

XY 1 el noisy ≡ XY 2 el clean ≡ 21 mat

XY x sin 04 π * 100 level randomize :

a b c spec . 8 black 13 mat : noise XY 1 el a b c spec pts : 21 line

2 periods of noisy sine ... noise is "uniform" in this example

noise XY 2 el 2 1 sys

Part 3: Signum Random

Utilities

M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Part 3: Signum Random This algorithm is sourced from the Mathsoft Collaboratory. The programmed version reproduces the original from author Mircea Andreacut [Roumanie]. No specific application(s) is given.

n 100 : k 4 : size 0.1 : 31 line

t n Φ 1 t n - sign + 2 / :

V n place n  decimals in V i 1 V rows range r i el V i el n round : for r 31 line :

k 4, 8, 16 ... ≡

t0 1 time :

X N k n * : u 1 el 1 Random 1 el : v 1 el 1 Random 1 el : i 1 N range u i 1 + el 4 u i el * 1 u i el - (* : v i 1 + el 4 v i el * 1 v i el - (* : b i el u i el v i el Φ : 31 line for m 1 N 1 - k / 1 - (range w m el b m k * j + el 2 j^* (j 0 k sum eval : for w size - size Scale 61 line :

Y N k n * : u 1 el 1 Random 1 el : v 1 el 1 Random 1 el : i 1 N range u i 1 + el 4 u i el * 1 u i el - (* : v i 1 + el 4 v i el * 1 v i el - (* : b i el u i el v i el Φ : 31 line for m 1 N 1 - k / 1 - (range w m el b m k * j + el 2 j^* (j 0 k sum eval : for w size - size Scale 61 line :

X Y augment

v 1 n 2 - (range : dt 0.001 : 21 line

signum v X Y + 2 / vectorize augment :

Part 4: Thermal Random

Signum random=> NOT bounded like uniform, reasonable outliers

signum dt BarSize

var 0.5 : N 128 : n 1 N range : 13 mat

C 2 - (var * N Random n el ln * vectorize sqrt vectorize 11 Random * (1 el cos * : μ C Mean : xy n C μ - augment : 31 line

1 time t0 - 14 s *

Thermal => piecewise normal random ... an exceptional multi-use random generator. Observe: compared to "uniform", generates reasonable outliers !

xy 0.001 BarSize