Plot Utilities

388fdf3e-093e-4094-83ae-c01c5156efb7 34 4 5 true true 0 decimal

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Plot Utilities

vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

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 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

ListCollect

data list ListCollect collects index list select list : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Levenberg Marquardt's second algorithm

x y β Tol βs LMSA Eps Tol : eta1 Eps sqrt : eta2 eta1 : h eta1 : stop 0 : 15 mat m Clear 1 : m x rows : n β rows : 12 mat β fx i 1 m range ff i el x i el ft y i el eval - : for ff 21 line : β derfh i 1 m range j 1 n range β j el β j el h + : jjh1 β fx i el : β j el β j el 2 h * - : jjh2 β fx i el : jjh0 i j el jjh1 jjh2 - 2 h * / : β j el β j el h + : 61 line for 11 line for jjh0 21 line : A n n Zeros : g n Zeros : J m n Zeros : 13 mat Fn 1 Zeros : dL 1 Zeros : dF 1 Zeros : F 1 Zeros : 14 mat f β fx : J β derfh : 12 mat A J transpose J * : g J transpose f * : ng g normi : 13 mat F f transpose f * 2 / : mu eta1 A Diag max * : nu 2 : 13 mat stop ¬ ng eta2 ≤ stop 1 : p A mu n identity * + invert g - (* : break try np β normi : nx eta2 β normi + : np eta2 nx * ≤ stop 2 : stop ¬ xnew β p + : fn xnew fx : Jn xnew derfh : Fn fn transpose fn * 2 / : dL p transpose mu p * g - (* 2 / : dF F Fn - : dL 1 el 0 > (dF 1 el 0 > (& β xnew : F Fn : J Jn : f fn : A J transpose J * : g J transpose f * : ng g normi : mu mu 13 / 12 dF 1 el dL 1 el / * 1 - (3^- Max * : nu 2 : 91 line mu mu nu * : nu 2 nu * : 21 line if 71 line 11 line if if 41 line if 11 line while βs β : 121 line :

x ft β 1 el x * 1 x β 5 el - β 3 el / exp + ln (β 2 el^(* β 4 el + :

al_nleqsolve suffers ln0, can't rescue ε 1012 -^:

XY 3 ε 4 0.1653 - 5 0.1313 6 0.219 7 0.8097 8 1.2045 9 1.302 10 2.1009 11 2.6004 12 3.7002 13 4.3001 112 mat :

1. selct the support points
2. collect for al_nleqsolve
3. collect variates [X, Y] list 24681115 mat : xy XY list ListCollect : X XY 1 col : Y XY 2 col : 12 mat 31 sys

data XY o 5 black plot : support xy . 14 blue plot : 21 line

data support 2 1 sys

The support points x XY 1 col : y XY 2 col : 12 mat

xy 4 0.1653 - 6 0.219 8 1.2045 10 2.1009 13 4.3001 52 mat

Model borrowed from Tesla project

β 0.01 11 0.1 - 115 mat transpose :

Tol 106 -^:

Jean Solution 0.00717 0.80738 0.06782 0.16339 - 4.87525 51 mat

SS 6179 OK 5 data β x y β Tol βs LMSA : 0.0082 1.5167 1.0008 0.1946 - 1.1136 51 mat

t0 1 time :

1 time t0 - s 0

x β ft β 1 el x * 1 x β 5 el - β 3 el / exp + ln (β 2 el^(* β 4 el + :

Absolute residuals Residuals i 1 XY rows range Δ i el Y i el X i el β ft - eval : for X Δ augment 21 line :

FIT U 015 0.01 range : i 1 U rows range vy i el U i el β ft eval : for U vy augment 31 line :

data FIT 0.1653 + support 3 1 sys

Residuals 0.1 BarSize

ConjugateGradient diverges, hyperdifficult initialized ...

NO more exploration needed . . .

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data FIT 0.1653 + support 31 sys