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

7d65ac36-f112-423e-a96b-38e7a6c68a96 21 6 9 decimal

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

The Matlab Rkadapt Minerr

A 2 : B 3 : α 2.25 : β 1.25 : γ 1.25 : 51 line

t 07142128354249566370111 mat transpose :

C 0 1.065 1.2 0.9793 0.9 0.7289 0.7236 0.4674 0.6031 0.6149 0.3369 111 mat transpose :

D 0 0.0058 0.2203 0.4019 0.3638 0.456 0.5014 0.715 0.4723 0.7219 0.7294 111 mat transpose :

t Y f e Y 3 el^A Y 1 el - α Y 2 el * - (* B Y 1 el - β Y 2 el * - (* e Y 4 el^Y 1 el * - γ e Y 5 el^Y 1 el (2^* Y 2 el e Y 6 el^* - (* - 1.125 e Y 5 el^* Y 1 el (2^* 0.75 e Y 6 el^* Y 2 el * - 000061 mat :

a b c d Z 00 a b c d 16 mat transpose 07010 t Y f Rkadapt :

S a b c d Z :

a 2.85 - : b 4 - : c 4.25 - : d 9 - : 14 mat

collect t C augment t D augment t S 2 col augment t S 3 col augment 41 sys :

init t S 2 col S 3 col augment :

blue/red => Brute experimental data green/magenta => guesstimate Rkadapt initial

collect

init 0007 1.056 0.063 14 1.145 0.207 21 1.033 0.342 28 0.888 0.445 35 0.755 0.521 42 0.647 0.575 49 0.562 0.616 56 0.495 0.647 63 0.442 0.671 70 0.4 0.69 113 mat

Zsol 00 a' b' c' d' 16 mat transpose 070300 t Y f Rkadapt :

Optimised coefficients from Mathcad Minerr a' 2.766 - : b' 3.7 - : c' 4.318 - : d' 8.155 - : 14 mat

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

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 :

Optim optim a' b' c' d' Z : Rkadapt from optimised borrowed a,b,c,d ≡ t optim 2 col optim 3 col augment 21 line :

collect t C o 5 black plotG t D o 5 black plotG Zsol 1 col Zsol 2 col augment Zsol 1 col Zsol 3 col augment t Optim 2 col + 14 red plotG t Optim 3 col + 14 blue plotG 61 sys :

XY init Optim init Optim 22 mat :

black 'o' => Brute experimental data [Matlab] green/magenta => optimised Rkadapt Minerr [Mathcad]

collect

XY init Optim 0007 1.056 0.063 14 1.145 0.207 21 1.033 0.342 28 0.888 0.445 35 0.755 0.521 42 0.647 0.575 49 0.562 0.616 56 0.495 0.647 63 0.442 0.671 70 0.4 0.69 113 mat 0007 1.082 0.064 14 1.15 0.201 21 1.031 0.327 28 0.89 0.423 35 0.765 0.494 42 0.665 0.547 49 0.585 0.587 56 0.523 0.618 63 0.472 0.643 70 0.432 0.664 113 mat 22 mat

That's all what Mathcad Minerr does: It takes the guess (a,b,c,d) ...

a 2.85 - : b 4 - : c 4.25 - : d 9 - : 14 mat

... the Given/Minerr block returns the optimised (a',b',c',d')

a' 2.766 - : b' 3.7 - : c' 4.318 - : d' 8.155 - : 14 mat

The original proposal came from the Mathsoft "Advisor" Collaboratory. Viktor Korobov & Tom Gutmann optimised the "Advisor" to this short form. Several application projects resulted [Jean Giraud]: _ Berkley Madonna [2007/02/13] _ Gadjson Lake _ The Hagues Black Plague _ Multiple Pharmacokinetics Projects

The Smath challenge ...

... code/design the Minerr block The Minerr block minimises by iterations the SSE

α β # SSE y i el x i el α β # F - (2^(i 0 y rows sum ≡

where yi are the wild ordinates. F(el(x,i),α,β,#) are the model ordinates wrt guess (α,β,_)

α β # 31 mat α β # Minerr ≡