Plot Utilities

388fdf3e-093e-4094-83ae-c01c5156efb7 44 15 12 decimal

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

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 :

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 . . . Carlos 20200122

x y β Tol βs LMSA Eps Tol : eta1 Eps sqrt : eta2 eta1 : h eta1 : stop 0 : 15 mat m Clear 1 : β fx i 1 m range ff i el x i el β ft y i el eval - : for ff 21 line : β m n h derfh i 1 m range j 1 n range β j el β j el h + : jjh1 x i el β ft y i el - : β j el β j el 2 h * - : jjh2 x i el β ft y i el - : jjh0 i j el jjh1 jjh2 - 2 h * / Re : β j el β j el h + : 61 line for 11 line for jjh0 21 line : m x rows : n β rows : 12 mat 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 m n h 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 ¬ cont cont 1 + : 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 : i 11 range stop ¬ xnew β p + : fn xnew fx : Jn β m n h derfh : brake 11 line try 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 for if 41 line if 21 line while βs β : 121 line :

m Clear 1 :

x 1234567891011111 mat :

y 0.4897 1.3079 2.84 3.0364 1.7709 0.5491 0.4606 0.3345 0.2073 0.0012 0.0024 111 mat :

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

UV x y augment :

XY x y augment : data XY . 10 black plot : 21 line

234571016 mat

1. selct the support points
2. collect for al_nleqsolve list 12345678919 mat : new UV list ListCollect : 21 sys

raw UV o 5 black plot : support new . 14 blue plot : 21 line

x1 new 1 col : y1 new 2 col : 21 sys

x1 12345678991 mat

y1 0.4897 1.3079 2.84 3.0364 1.7709 0.5491 0.4606 0.3345 0.2073 91 mat

Very native SS 6179 rejects too low Tol

β 857 3.75 - 14 mat transpose :

Tolerance Tol 0.0001 :

t0 1 time :

SS 6179 OK 9 data β x1 y1 β Tol βs LMSA : 8.3283 13.7093 18.0237 14.6328 - 41 mat

1 time t0 - min 1.5

recover @ 'tol' β β 4 round vectorize :

x β f β 1 el β 3 el x β 4 el - / (β 2 el 1 +^* β 3 el x β 4 el - / (β 2 el^- exp * :

x α F α 1 el α 3 el x α 4 el - / (α 2 el 1 +^* α 3 el x α 4 el - / (α 2 el^- exp * :

Fréchet & many more 
are reflexive ... β 8.3283 13.7093 18.0237 14.6328 - 41 mat

conjugated
gradient α 8.5418 40.7318 52.0514 48.7382 - 41 mat :

x c 10 x ≤ (x 12 ≤ (& cases :

x α F x c * x β f x c * data 3 1 sys

857 3.75 - 14 mat transpose

new 1 0.4897 2 1.3079 3 2.84 4 3.0364 5 1.7709 6 0.5491 7 0.4606 8 0.3345 9 0.2073 92 mat

0.0001