<p> plotG(vx,vy,a,b,c) </p>

45fb2099-1315-40b2-aba4-81965f70f9a9 3 6 9 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

k 6.798095 1.004688 0.889606 0.903627 0.140563 51 mat :

z 0.35 0.1 0.1 0.1 0.35 51 mat :

t0 1 time :

Φ f z n el k n el 1 - (* k n el 1 - (Φ * 1 + / (n 1 z length sum :

x Low 1.864 - : δ 1.1636 : 21 line

δ f 7356.057234

0 x ≤ x 1.5 ≤ & x f rejected if δ 200 δ 200 - 2 2 mat x Low 3 1 sys

0 x ≤ (x 1.5 ≤ (& x f rejected if δ 200 δ 200 - 22 mat x Low 31 sys

Given f(x) => solve for 'x'

f L H N Inverse dx H L - N / : i 1 N 1 + 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 1.1636 solve eval : for ω sol augment 41 line :

Sol f 1.7 1.8 - 35 Inverse :

Sol 1.7 0.001 1.6 0.009 1.5 0.019 1.4 0.03 1.3 0.042 1.2 0.055 1.1 0.07 1 0.088 0.9 0.107 0.8 0.13 0.7 0.155 0.6 0.185 0.5 0.22 0.4 0.261 0.3 0.307 0.2 0.36 0.1 0.419 0 0.482 0.1 - 0.545 0.2 - 0.606 0.3 - 0.662 0.4 - 0.711 0.5 - 0.754 0.6 - 0.792 0.7 - 0.824 0.8 - 0.851 0.9 - 0.875 1 - 0.895 1.1 - 0.914 1.2 - 0.929 1.3 - 0.944 1.4 - 0.956 1.5 - 0.967 1.6 - 0.978 1.7 - 0.987 1.8 - 0.995 362 mat

Working range of f(Φ)

0 x ≤ ( x 1 ≤ ( & x f rejected if 1.1636 2 1.1636 2 - 2 2 mat 2 1 sys

vx Sol 1 col : vy Sol 2 col : sol vx vy . 9 black plotG : 31 line

Global solution => think modelling

sol 1.8 - 2 1.8 - 0.5 - 2 2 mat 1.7 0.5 1.7 0.5 - 2 2 mat 3 1 sys

Sanity of "Sol" wrt support points Φ f 1.7 ≡ Φ 0 0.1 solve Φ f 1 ≡ Φ 0 0.1 solve Φ f 0 ≡ Φ 0.4 0.6 solve Φ f 1 - ≡ Φ 0.8 1 solve Φ f 1.8 - ≡ Φ 0.95 1 solve 51 mat 0.001 0.088 0.482 0.895 0.995 51 mat

User on-line "solve/collect" Φo OnLine 1.8 - Φo ≤ 1.7 ≤ Φ Φ f Φo ≡ Φ 0 1.1636 solve eval : i 1 z length range x i el z i el k i el 1 - (Φ * 1 + / : y i el k i el x i el * : 21 line for header Φo Φsol x.....y 13 mat : header Φo Φ x y augment 13 mat stack 51 line :

Φo 1.25 - :

1 time t0 - 6.6 sec *

Φo OnLine Φo Φsol x.....y 1.25 - 0.9367 0.0544 0.37 0.0996 0.1 0.1115 0.0992 0.1099 0.0993 1.7955 0.2524 52 mat 23 mat