<p> plotG Hatch </p>

acf1eaa2-6724-4edc-924a-5d9a139e75de 16 6 9 decimal

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

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 :

Pseudo-Toricelli expérimentale ==============================

b 0.538998 0.731717 1.384734 0.701107 1.075599 51 mat :

Soit: des données expérimentales représentant une "Toricelli" de forme inconnue. On propse le modèle f(x,b), déboutant de réalisme dans notre example.

x b f b 1 el x b 2 el - (* b 3 el x b 2 el - (b 4 el^+ / b 5 el + :

XY 0.5 1 1.5 1.262469 2.5 1.406973 3.5 1.511077 4.5 1.593828 5.5 1.663146 6.5 1.723145 7.5 1.77626 8.5 1.824057 9.5 1.86761 10.5 1.907688 11.5 1.944863 12.5 1.979573 13.5 2.012159 14.5 2.042896 15.5 2.072005 16.5 2.09967 17.5 2.126045 18.5 2.151257 19.5 2.175418 202 mat :

X XY 1 col : Y XY 2 col : ΔTor X Y o 8 black plotG : 31 line

Δ i 2 X rows range delta i el Y i el X i el b f - : for X delta augment 21 line :

Range/populate the discrete fit FIT U 0.5 25 0.55 range : i 1 U rows range FIT i el U i el b f eval : for U FIT augment 31 line :

5 Decimales Δ 0.5 0 1.5 0 2.5 0.00002 - 3.5 0.00004 4.5 0.00003 5.5 0 6.5 0.00002 - 7.5 0.00003 - 8.5 0.00003 - 9.5 0.00002 - 10.5 0.00001 - 11.5 0 12.5 0.00002 13.5 0.00003 14.5 0.00003 15.5 0.00003 16.5 0.00002 17.5 0.00001 18.5 0.00002 - 19.5 0.00005 - 202 mat

Pseudo Toricelli NF ... from source.

ΔTor FIT 2 1 sys

Explain "Shadow in the Context"

This expression is from Mathematica 4.0. Simply confusing the project wrt some user symbols vs Mathematica packages. That rings a bell in Smath, considering all plugins ... etc.

In the above example, the Genfit Minimise works well with only those initial parameters and only one pass. The shadow is simply between the hyper-reactivity of the parameters and Genfit Minimise. That's not all, observe: in f(x,b), 'b' is 6 significant figures and we get Δ=[0.5 0], that differs so much from the full numerical 15 figures in Genfit. In my own words "shadow in the numerical context".

0.02477 0.02477 i * + abs 0.03503

initial 0.53 0.726 1.35 0.7 151 mat

Δ 15 fig. from Genfit Δ 0.5 0.02477 0.02477 i * + 1.5 0 2.5 0.00002 - 3.5 0.00004 4.5 0.00003 5.5 062 mat :

Shadow in the session

What could that be ? Remember TI-58 and TI-59 had a command 'NOP' [No Op => No operation]. Some suites in the PN [Polish Notation] stack could not reach the end of the project unless the NOP would be included in the PN stack. Invisibly, similar "Shadow in the session" happened in Mathcad 8 Pro, Mathcad 2001i, Mathcad 11. If a region got "Corrupted", the work was scrapped, had to be reconstructed from blank, no copy/paste. In less critical non productive coding, it was necessary and sufficient to close the PC to recover the work sheet. .................................................................... Similar "Shadow in the session" happens in Smath 5346. If you attempt plotting ln(t) ... 'x not defined', no damage done. In other instances you may have called incompatible plot arguments, damage is done and remains in the session ... no matter how you have rescued or though you have rescued the plot, the final rescue needs the PC shut down and restart.

<p> plotG Hatch </p>

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

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f1 g1 x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f1 x.1 x.1 g1 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g1 x dx 2 / + x dx 2 / + f1 x dx + x dx + f1 x dx + x dx + g1 42 mat stack : for h 41 line :

X 1 1.5 2 2.5 41 mat :

Y 1.3 3.1 5.2 0.8 41 mat :

... suite of Spline Quadratic.sm

data X Y . 14 black plotG :

D 1 el 0 : i 24 range D i el 2 Y i el Y i 1 - el - X i el X i 1 - el - / (* D i 1 - el - : for 21 line

data 1 1.3 . 14 black 1.5 3.1 . 14 black 2 5.2 . 14 black 2.5 0.8 . 14 black 45 mat

D 0 7.2 1.2 18.8 - 41 mat

j x Q i j : D i el 2 / x X i 1 - el - (2^X i el X i 1 - el - (/ * D i 1 - el 2 / x X i el - (2^X i el X i 1 - el - (/ * - Y i el + D i el 2 / X i el X i 1 - el - (* - 21 line :

2 x Q 3 x Q 4 x Q data 4 1 sys

"if/else" exception style.
It throws the "exception report"
generated by the complete style x f x X 2 el < 2 x Q x X 3 el < 3 x Q 4 x Q if if :

Plot "data" otherwise.

x f 2 x Q 3 x Q 4 x Q 1 1.3 . 14 black 1.5 3.1 . 14 black 2 5.2 . 14 black 2.5 0.8 . 14 black 4 5 mat 5 1 sys

Shadow in "data" plot argument

x f 2 x Q 3 x Q 4 x Q data 5 1 sys

Shadow in the arguments context

x f x X 1 el X 4 el int #

x sqrt x 010 int 21.081822

x f x 12 int #

Transit the scalar f(x) u F x f :

z Σ u F u X 1 el x int :

Does not support the compactum

re-transit
plot canvas x Σ z Σ :

Shadow in the plot session

Shadow in the "data" plot argument

x f x Σ 2 x Q 3 x Q 4 x Q 1 1.3 o 7 black 1.5 3.1 o 7 black 2 5.2 o 7 black 2.5 0.8 o 7 black 4 5 mat 6 1 sys

Interpolate Σ(x) 1 Σ 1.5 Σ 1.75 Σ 2.5 Σ 41 mat 0 1.55 3.394 1.2 41 mat

At the time this plot was created, "data not defined" excluded the f(x) plot argument. After shutting down the PC, the corrupted plot region got cleared, now allowing to plot f(x).

x D x X 2 el < 2 x Q x diff x X 3 el < 3 x Q x diff 4 x Q x diff if if :

scalar derivative of the spline. f x h deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

h 0.000001 :

x f x h deriv 1 1.3 . 14 red 1.5 2.5 . 14 red 2 5.2 . 14 red 2.5 0.8 . 14 red 4 5 mat 2 1 sys x f x diff x D 1 1.3 . 14 red 1.5 2.5 . 14 red 2 5.2 . 14 red 2.5 0.8 . 14 red 4 5 mat 2 1 sys