ListCollect

7caa8836-211e-4f7a-8820-e843a9d7b1cf 19 4 5 decimal

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

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 :

D2 ... D3

0.38 -

D2 00 0.021 2.22 0.04 3.375 0.059 3.789 0.079 3.782 0.099 3.538 0.12 3.164 0.141 2.754 0.164 2.322 0.188 1.919 0.213 1.552 0.237 1.253 0.263 0.991 0.29 0.77 0.318 0.595 0.346 0.456 0.377 0.341 0.406 0.257 0.437 0.192 0.47 0.14 0.509 0.096 0.545 0.068 0.591 0.044 0.645 0.026 0.918 0.002 1.125 0 1.154 0272 mat :

D3 0 10.861 0.021 6.056 0.04 3.327 0.059 1.687 0.079 0.706 0.099 0.133 0.12 0.187 - 0.141 0.338 - 0.164 0.395 - 0.188 0.394 - 0.213 0.362 - 0.237 0.32 - 0.263 0.272 - 0.29 0.226 - 0.318 0.185 - 0.346 0.149 - 0.377 0.118 - 0.406 0.093 - 0.437 0.073 - 0.47 0.056 - 0.509 0.041 - 0.545 0.031 - 0.591 0.022 - 0.645 0.014 - 0.918 0.002 - 1.125 0 1.154 0272 mat :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

XY D2 :

Point solve equalities al_nleqsolve

D2 rows 27

1. selct the support points
2. collect for al_nleqsolve list 1514222715 mat : xy XY list ListCollect : 21 sys

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

support raw 2 1 sys

xy 00 0.079 3.782 0.29 0.77 0.545 0.068 1.154 052 mat

x xy 1 col : y xy 2 col : 21 sys

vector of guesses ... 
from robust2crucifying ! X0 0105 - 0.1 5 - 15 mat transpose :

t0 1 time :

AlgLib Solver for a system of nonlinear equations(Uni) sol k 1 α f rows range u k el α k el : for α Jac u f u Jacobian : StepMax 0 : ε 1012 -^: 12 mat u X0 StepMax ε α f α Jac al_nleqsolve : 41 line :

model to D2(x) x α Φ x α 1 el α 2 el x α 4 el / - exp * + α 3 el x α 5 el / - exp * + (* :

Implicit equalities = 0 α f x 1 el α Φ y 1 el - x 2 el α Φ y 2 el - x 3 el α Φ y 3 el - x 4 el α Φ y 4 el - x 5 el α Φ y 5 el - 51 mat :

α sol : 1.1077 142.40751 1.01751 - 0.07235 13.58616 - 51 mat

Notes . . . Smath 6179

1. solves a system of [n equalities = n parameters.

2. The order of equalities is immaterial.

3. Guess wisely the best support equalities !

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α f 0041016 -^* - 091015 -^* 51 mat

The support points X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 sys

1 time t0 - s 1

x c 10 x ≤ (x 1.25 ≤ (& cases :

Fit " a la carte" from al_nleqsolve

data x α Φ x c * support 3 1 sys

Support points xy 00 0.079 3.782 0.29 0.77 0.545 0.068 1.154 052 mat

XY D3 :

===== D3 data set =====

D3 rows 27

1. selct the support points
2. collect for al_nleqsolve list 1514222715 mat : xy XY list ListCollect : 21 sys

raw XY o 5 black plot : support xy . 15 blue plot : 21 line

support raw 2 1 sys

xy 0 10.861 0.079 0.706 0.29 0.226 - 0.545 0.031 - 1.154 052 mat

x xy 1 col : y xy 2 col : 21 sys

vector of guesses ... 
from robust2crucifying ! X0 01 0.1 0.075 0.1 15 mat transpose :

AlgLib Solver for a system of nonlinear equations(Uni) sol k 1 β f rows range u k el β k el : for β Jac u f u Jacobian : StepMax 0 : ε 1012 -^: 12 mat u X0 StepMax ε β f β Jac al_nleqsolve : 41 line :

model to D3(x) x β Φ β 1 el β 2 el x - β 3 el + β 5 el / exp x - β 3 el + (β 4 el β 5 el + β 4 el β 5 el * / * exp - (* - :

Implicit equalities = 0 β f x 1 el β Φ y 1 el - x 2 el β Φ y 2 el - x 3 el β Φ y 3 el - x 4 el β Φ y 4 el - x 5 el β Φ y 5 el - 51 mat :

β sol : 0.00064 1.00716 0.10644 0.06131 0.12738 51 mat

The support points X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 sys

x c 10 x ≤ (x 1.25 ≤ (& cases :

Fit " a la carte" from al_nleqsolve

data x β Φ x c * support 3 1 sys

===== Thurber data set =====

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 :

XY Thurber

XY 2.981 - 84.248 2.921 - 87.264 2.912 - 87.185 2.84 - 89.076 2.797 - 89.608 2.702 - 89.868 2.699 - 90.101 2.633 - 92.405 2.481 - 95.854 2.363 - 100.696 2.322 - 101.06 1.501 - 401.672 1.46 - 390.724 1.274 - 567.534 1.212 - 635.316 1.1 - 7330.54 1.046 - 759.087 0.915 - 894.206 0.714 - 990.785 0.566 - 1090 0.545 - 1080 0.4 - 1120 0.309 - 1180 0.109 - 1260 0.103 - 1270 0.01 1290 0.119 1330 0.377 1350 0.79 1420 0.963 1430 1.006 1420 1.115 1440 1.572 1460 1.841 1470 2.047 1450 2.2 1460362 mat :

1. selct the support points
2. collect for al_nleqsolve list 113243414 mat : xy XY list ListCollect : 21 sys

raw XY o 5 red plot : support xy . 16 black plot : 21 line

support raw 2 1 sys

xy 2.981 - 84.248 1.46 - 390.724 0.109 - 1260 1.841 147042 mat

x xy 1 col : y xy 2 col : 21 sys

vector of guesses ... 
from robust2crucifying ! X0 8014001014 mat transpose :

t0 1 time :

AlgLib Solver implicit equalities [Courtesy  Viacheslav] sol k 1 μ f rows range u k el μ k el : for μ Jac u f u Jacobian : StepMax 0 : ε 1012 -^: 12 mat u X0 StepMax ε μ f μ Jac al_nleqsolve : 41 line :

SGompertz . . .

is extremely reflexive, declared unfittable

in Smath [L-M, CG]. Possible attempt

OriginLab, Mathcad 11. As offered, and

fitted by al_nleqsolve, at this point, you

may want to round/refactor the coefficients.

The fillet region is a bit sparse !

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SGompertz Thurber model fnct x m Φ m 1 el m 2 el m 3 el x m 4 el - (* - exp - exp * + :

Implicit equalities = 0 μ f x 1 el μ Φ y 1 el - x 2 el μ Φ y 2 el - x 3 el μ Φ y 3 el - x 4 el μ Φ y 4 el - 41 mat :

μ sol : 84.25 1396.05 1.61 1.2 - 41 mat

Notes . . . Smath 6179

1. solves a system of [n equalities = n parameters].

2. The order of equalities is immaterial.

3. Guess wisely the best support equalities !

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1 time t0 - s 1

The support points X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 sys

μ f 0.000000000000 0.000000000002 - 0.000000000002 - 0.000000000001 41 mat

x c 14 - x ≤ (x 4 ≤ (& cases :

native al_nleqsolve from

113243414 mat

μ 84.25 1396 1.61 1.2 - 41 mat 87.5 1375 1.6 1.25 - 41 mat 901375 1.6 1.25 - 41 mat 801400 1.5 1.25 - 41 mat 901370 1.6 1.25 - 41 mat 15 mat :

observe fillet region j 2 :

data x μ 1 j el Φ x c * support 3 1 sys

Support points xy 2.981 - 84.248 1.46 - 390.724 0.109 - 1260 1.841 147042 mat