<p> plotG, Thiele </p>

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

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

ε 1012 -^:

n 3.5 :

n t f t n^t exp 1 - / :

x lin n t f t ε x int :

x c 10 x ≤ cases :

n x f x c * 1 1 sys

Reconciliate the canvas

Fnct x ε 3 π * (ε 0.05 + (range : i 1 x rows range Fnct i el n x i el f eval : for x Fnct augment 31 line :

LIN x ε 3 π * (ε 0.1 + (range : i 1 x rows range F i el x i el lin eval : for x F augment 31 line :

Adjust on canvas from discrete

Fnct LIN 2 1 sys

U 5 - 5 4.9 - range :

x F 11 x 2^+ / :

α 0.5 :

Σnl Cumulative NON-linear i 1 U rows range Cumul i el x F x U 1 el U i el α^abs int eval : for U Cumul augment 31 line :

Σnl 1 1 sys

1. user model parameter n 2.5 :

2. kernel integral n t f t n^t exp 1 - / :

ASSUME ... that the combination of [1, 2, 3, 4] successfully approximates a data set, the red line below. This is at the modeling stage. We need an exportable function to resume the project. The next part Thiele will do that.

3. user non-linear path x p 1 0.5 x + / :

4. non-linear integral x Nlin n t f t ε x p int :

Reconciliate the canvas

Fnct x ε 3 π * ε 0.05 + (range : i 1 x rows range u i el x i el : Fnct i el n u i el f : 21 line for u Fnct augment 31 line :

NONlin x ε 3 π * ε 0.1 + (range : i 1 x rows range u i el x i el : F i el u i el Nlin : 21 line for u F augment 31 line :

create a data set  =>
for Thiele, to resume
the model as an export XY ε ε Nlin 0.25 0.25 Nlin 0.5 0.5 Nlin 0.75 0.75 Nlin 11 Nlin 1.5 1.5 Nlin 22 Nlin 33 Nlin 44 Nlin 66 Nlin 102 mat :

XY 11012 -^* 1.0475 0.25 0.4963 0.5 0.2755 0.75 0.1703 1 0.1136 1.5 0.0589 2 0.035 3 0.0157 4 0.0086 6 0.0035 102 mat

XY XY 1 col XY 2 col . 10 black plotG :

support points from NON linear integral

Fnct NONlin XY 3 1 sys

Setup for Thiele suite, export

XY 11012 -^* 1.0475 0.25 0.4963 0.5 0.2755 0.75 0.1703 1 0.1136 1.5 0.0589 2 0.035 3 0.0157 4 0.0086 6 0.0035 102 mat :

vx XY 1 col : vy XY 2 col : 12 mat

evaluate/isolate for the 'K' Thiele vx vy 0 Thiele : 11012 -^* 1.0475 0.25 0.4536 - 0.5 1.2879 - 0.75 5.8979 1 0.2575 1.5 108.4294 - 2 0.0102 - 3 431.1187 - 4 0.0041 - 6 1343.1271 - 102 mat

vx vy 0 Thiele

K Thiele 2 col :

Thiele triangular table vx vy 1 Thiele

Thiele 'K' for Cf(x) vx vy 0 Thiele

x Cf K 1 el x vx 1 el - K 2 el x vx 2 el - K 3 el x vx 3 el - K 4 el x vx 4 el - K 5 el x vx 5 el - K 6 el x vx 6 el - K 7 el x vx 7 el - K 8 el x vx 8 el - K 9 el x vx 9 el - K 10 el / + / + / + / + / + / + / + / + / + :

L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx - (dx i * + : for U 41 line :

L ε :

H 8 :

N 99 :

U L H N xd :

XY vx vy . 10 black plotG :

Thiele continued fraction i 1 U rows range vx i el U i el : vy i el U i el Cf eval : 21 line for vx vy augment 31 line :

Fnct Thiele XY 3 1 sys