Genfit Utilities

5bb00ff9-01cb-43d9-8fcf-8bce622f4772 13 3 5 decimal

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

The familiar Pt100 graph

! two poly segments order 10 and 13 from 12 support points !

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Part: 1

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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 :

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 :

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 :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 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 :

Pt100 XFR x β f β 1 el β 2 el 1 β 4 el β 3 el β 4 el - (/ x 259.3467 + (- β 4 el β 2 el * / exp * + β 3 el β 3 el β 4 el - (/ x 259.3467 + (- β 3 el β 2 el * / exp * - (* + :

eit90 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.56891730 660.323 3.37600860 961.78 4.28642053 122 mat :

<= ConjugateGradient Vector Fnct x β φ x β f 4 φ :

X eit90 1 col : Y eit90 2 col : XY X Y augment : n XY rows : data XY o 5 black plot : 51 line

010100141 mat

β β 1 el 010100114 mat transpose : iter 9 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

β 0.001193801 - 12.53643279 228.598706609 1.683320629 41 mat

L 259.3467 - : H 961.78 : N 1221 : 13 mat U L H N xd : 21 line

FIT range, populate i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

Δwr i 1 XY rows range u i el X i el β f eval : for Y u - augment 21 line :

Pt100 ... mutual conformity to eit90 'wr'... will produce °C ± 0.005

data FIT 2 1 sys

Wr conformity
     wrt eit90 Δwr 0.002 0.001 - 0.005 - 0.002 0.003 0.001 0.000 0.002 - 0.003 - 0.001 - 0.003 0.001 - 121 mat

data FIT 2 1 sys

Part: 2

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The extrapolated Pt100 calculator

- 273.15 . . . 1200 °C

]]> Pt100 [-273.15 ... 1200 °C]

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 :

Smath al_nleqsolve λ 4.582374490 0.689736236 - 4.153686384 - 50.944725014 - 41 mat :

Mathcad  Minerr LM μ 1015.59658242 0.05304418 1.32997985 - 2.19590058 - 41 mat :

Mathcad Minerr LM ζ 795.75522816 0.05179366 0.39683701 1.58191684 - 41 mat :

231.928 419.524 660.323 961.78 41 mat

... exact eit90 inverse in the subCryo  [-259.3467...-189.3442] x λ subCryo λ 1 el x λ 3 el - (λ 2 el x *^(* 1 x ln + x λ 3 el - (- exp + λ 4 el + (* :

... exact eit90 inverse mid range[-189.3442  ... 156.5985 x μ Φ μ 1 el x μ 3 el - (μ 2 el x *^(* 1 x 2 + ln + x μ 3 el - (- exp + μ 4 el + (* :

1.89279768 μ Φ 231.928 - 0.02

...exact eit90 inverse upper range [231.928 ... 961.78] x ζ Extrapol ζ 1 el x ζ 3 el - (ζ 2 el x *^(* 1 x ln + x ζ 3 el - (- exp + ζ 4 el + (* :

Ω °C Ω λ subCryo 0.00006230541 Ω ≤ (Ω 0.21585975 ≤ (& Ω μ Φ 0.21585975 Ω ≤ (Ω 1.60980185 ≤ (& Ω ζ Extrapol 1.60980185 Ω ≤ (Ω 4.62715523 ≤ (& 4.62715523 ζ Extrapol cases :

abs 0.00006230541 :

°C 1 :

Ω 1 :

Extrapolated eit90

eit90 273.15 - abs 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.5689173 660.323 3.3760086 961.78 4.28642053 1064.43 4.57255961 1084.5 4.62715523 152 mat :

Deviation °C(Ω) @ eit90  fixed
Exceptional recovery depending
upon the accuracy of measured Ω Δ°C X eit90 2 col : Y eit90 1 col : n eit90 rows : i 1 eit90 rows range u i el X i el °C eval : for Y Y u - augment 51 line :

Δ°C 273.1500 - 0.0000 259.3467 - 0.0000 248.5939 - 0.0000 218.7916 - 0.0000 189.3442 - 0.0000 38.8344 - 0.0000 0.0100 0.0000 29.7646 0.0000 156.5985 0.0000 231.9280 0.0000 419.5270 0.0000 660.3230 0.0000 961.7800 0.0000 1064.4300 0.0000 1084.5000 0.0000 152 mat

ε 0.02 < 11 sys

X 1.89279768 :

balistic region
..mid segment.. 156.5985 231.9280 21 sys

X μ Φ 231.928 - 0.02

on-line user 1.23456789 °C °C 59.36

data eit90 2 col eit90 1 col augment : x sub 1 0.00006230541 x ≤ (x 0.21585975 ≤ (& cases : x mid 1 0.21585975 x ≤ (x 1.60980185 ≤ (& cases : x up 1 1.60980185 x ≤ (x 5 ≤ (& cases : fixed data o 7 black plot : 51 sys

x λ subCryo x sub * x μ Φ x mid * x ζ Extrapol x up * fixed 4 1 sys

273.15 - 259.3467 - 248.5939 - 218.7916 - 189.3442 - 38.8344 - 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 1064.43 1084.5 151 mat_TP Hydrogen TP Neon TP Oxygen TP Argon TP Mercury TP Water MP Gallium FP Indium FP Tin FP Zinc FP Aluminum FP Silver FP Gold FP Copper 151 mat 12 mat

x λ subCryo x sub * fixed abs 273.15 - + 40 red 1 5 mat 3 1 sys

Part: 3

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The upper Pt100 calculator

- 189.3442 . . . 961.78 °C

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midup global segment ± 0.005 °C
          [-189.3442 ... 961.78
strictly  limited  [-189.3442 °C] x midup c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + 1 c 5 el x * + c 6 el x 2^* + c 7 el x 3^* + / :

c 192024.583280267 70687043.6045327 - 78330309.3311223 7833856.73646206 - 290262.847540217 41930.7867554404 - 841.720014672866 71 mat :

1.60980185 midup 156.5985 - °C 0.0062

eit90 eit90 513 range 21 range el :

eit90 0.21585975 189.3442 - 0.84414211 38.8344 - 1 0.01 1.11813889 29.7646 1.60980185 156.5985 1.89279768 231.928 2.5689173 419.527 3.3760086 660.323 4.28642053 961.78 92 mat :

Δ°C X eit90 1 col : Y eit90 2 col : n eit90 rows : i 1 eit90 rows range u i el X i el midup eval : for Y Y u - augment 51 line :

Δ°C 189.344 - 0 38.834 - 0.004 - 0.01 0.004 29.765 0.003 156.598 0.006 - 231.928 0.003 419.527 0 660.323 0 961.78 092 mat

IMHO . . .

Some savant(s) decided the triple point of water was warmer that

it used to be for decades. At this point in maths, 0.01 is unknown

just approximate. The question is: how do you measure exactly [1]

from unknown ? In short, no matter savant arguments, Pt100 is

bound in the range ± 0.01 °C, not accounting XTR .

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__ Reconciliate Pt100 Calculator __

-273.15 . . . 961.78 °C

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Part: 4

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Ω Pt100 Ω λ subCryo 0.00006230541 Ω ≤ (Ω 0.21585975 ≤ (& Ω midup 0.21585975 Ω ≤ (Ω 4.28642053 ≤ (& * cases :

read °C on-line 1.60980185 Pt100 °C 156.6

Calibrate the XTR [-100 ... 200 °C] Low High 21 mat Ω Pt100 100 - (- 0 ≡ Ω 0.2 1 solve Ω Pt100 200 - 0 ≡ Ω 12 solve 21 mat :

Low High 21 mat Ω 0.59453073 1.77365682 21 mat

100 - 20021 mat

Ucertainty on Pt100

x Γ x Gamma :

vy incertitude n vy length : u vy StdDev n sqrt / n 1 - 2 / Γ n 1 - sqrt * n 2 / Γ 2 sqrt * / * : 21 line :

vy Δ°C 2 col :

Uncertainty vy incertitude 0.0012

Personalizing the Pt100

from Lat tests

1. the 4 subcryo support points

2. the 8 mid-up support points

3. run for the parameters

4. plug in the calculator . . . done

5. the 4 optional upper support points

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ANCESTRY of design 1. XFR Pt100 [2003 jmG] 2. inverse calculator .. [January 2019 jmG]

jmGiraud: 20190126 Smath 6179

http://bibli.ec-lyon.fr/exl-doc/patrimoine/11944V01/11944V01.pdf On ne pourra jamais déclarer les Wr du thermomètre théorique à résistance de platine; d'une part inférant à l'incertitude des mesures, d'autre part concluant le canevas résolvant. En d'autres mots: les Wr ne pourront que refléter la coïncidence résolvante. Dans les faits, le thermomètre théorique à résistance de platine n'existe pas par privation de la nature de se reproduire elle-même exactement et infiniment au grès de la transformation de l'homme. La nature ne donne le platine que sous forme de pépite ou par extraction. Le Créateur a donné la température [état et sensation physique] mais pas le thermomètre.

. . . in short: fixed points are physically generated at best, resistance measured at best .

In operation, it's the inverse, i.e: resistance is measured for a conclusive °C.

This is the all key of this document: calculate °C from measured resistance.

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