fd479d66-8f70-4bd7-8896-aff10fcf2eaa 5 4 5 decimal

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

x f 2 - 7 x 2^* - 2 x 3^* - x 4^+ :

Golden-Ratio search [min/max]

TOL 1012 -^:

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 71 line :

t0 1 time :

X f 1.5 - 1 - y1 y2 ≤ TOL Extrema 1 el f 0.5 - 0.5 y1 y2 ≥ TOL Extrema 1 el f 2.5 3 y1 y2 ≤ TOL Extrema 1 el 31 mat :

1 time t0 - 0.4 s *

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

x f X 1 el X 1 el f + 20 red X 2 el X 2 el f + 20 red X 3 el X 3 el f + 20 red 3 5 mat 2 1 sys

X 1.265564 - 2.816018 108 -^* - 2.765564 31 mat

X X f vectorize augment 1.2656 - 6.5923 - 2.816 108 -^* - 2 - 2.7656 39.3452 - 32 mat

vector polyroots c 2 - 07 - 2 - 151 mat :

iter f 1.5 - 1 - y1 y2 ≤ TOL Extrema 2 el f 0.5 - 0.5 y1 y2 ≥ TOL Extrema 2 el f 2.5 3 y1 y2 ≤ TOL Extrema 2 el 31 mat :

iter 56585731 mat

r c polyroots : 0.0352 0.5185 i * + 0.0352 0.5185 i * - 1.9225 - 3.8522 41 mat

r r eval :

x Φ x r j el - (j 1 r rows product :

x Φ

Solving for a vectorised function

t0 1 time :

x f x 2 π * / 2 π * x / tanh * sqrt :

Design a discrete function inverser  in the L, H span , N points f L H N Inverse dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range sol j el x f ω j el - 0 ≡ x 0.02 20 solve : for ω sol augment 51 line :

Sol f 0.06 0.99 100 Inverse :

1 time t0 - 17 s *

Magnify the function to see

50 x f * Sol 2 1 sys

The native function

x f

Delimitate and fill citical domain

'N' random in critical region N 1000 :

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 :

size/define critical region.
Plot first before filling xmin 2 : xmax 6 : ymin 15 : ymax 22 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

x critical 303 x * - 10 - 10 x * + 20 x - 31 sys : fill 21 sys

A function that tests an arbitrary point 
for its membership in the critical region. x y Test 3 x * 1 y * + 30 ≤ (10 x * y - 10 ≥ (* x 1 y * + 20 ≥ (* :

centroid 3.6 17.7 + 100 black 15 mat :

m 4.04 17.88 . 15 blue 2.905 19.05 . 15 red 3.865 16.135 . 15 green 35 mat :

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 . 5 #808080 13 mat : fill Pts a b c spec pts : 21 line

x critical fill centroid m 4 1 sys

X Y 3.08 20.77 2.73 17.27 51542 mat