<p> Scale(M,Low,High) </p>

6e425924-ef39-40bf-a187-06bd09111c4e 38 3 5 auto

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

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

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

x plot x a 2 x - : x b 4 x - : x c x : x d x 2^4 - sqrt : 41 sys :

N 1000 :

xRnd N 1100 Random.N : yRnd N 1100 Random.N : zRnd N 1100 Random.N : 31 line

X xRnd 1 2.5 Scale : Y yRnd 02 Scale : Z zRnd 016 Scale : 31 line

x plot

Monte Carlo Integration

input integrand x y f x y + (2^:

The region of interest falls entirely within the rectangle defined by ... 1 ≤ x ≤2.5 and 0 ≤ y ≤2

Bolean factor Bol 2.5 1 - (20 - (* 160 - (* : 48

kount(x,y,z): the scalar Bolean counting function Monte Carlo integration x y z kount x a y < (x b y > (x c y > (* * z x y f < (* x d y < x 2 ≥ 1 cases * :

Monte Carlo double integration I 2.5 1 - (20 - (* 160 - (* 1 N / (* X n el Y n el Z n el kount n 1 N sum * : 11.664

I_1 x y f y 2 x - x int x 12 int : ----- I_2 x y f y x d 4 x - int x 2 2.5 int : 13 mat

I_1 I_2 I_1 I_2 + 31 mat 7.333 4.667 1231 mat

'N' random in critical region N 1000 :

size/define critical region.
Plot first before filling xmin 1 : xmax 2.5 : ymin 0 : ymax 2 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

x plot x a 2 x - : x b 4 x - : x c x : x d x 2^4 - sqrt : 41 sys :

A function that tests an arbitrary point 
for its membership in the critical region. x y Test x a y < (x b y > (* x c y > (* x d y < x 2 ≥ 1 cases * :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

a b c spec . 6 #808080 13 mat : fill Pts a b c spec pts : 21 line

x plot fill 2 1 sys