<p> Genfit Utilities </p>

b364b872-d263-49a5-81e6-c0832a233d08 7 4 5 decimal

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

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 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line 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 :

XY 8.0957 - 210.002 - 7.7963 - 195.802 - 7.4807 - 182.962 - 3.7187 - 78.476 - 1.9063 - 38.862 - 00 1.3739 26.87 5.2677 100 6.4886 122.37 8.3743 156.634 12.5517 231.9681 14.7427 271.442 17.4928 321.108 17.8462 327.502 19.456 356.66 152 mat :

Genfit NRF to Normalized Rational Fraction

This 4/3 rational is difficult to initialise. Start by low 'iter' up to some fit appear. It is slow converging up to exceptional fit. Same result as Mathcad GenfitMatrix. Normalized RF are numerically stable, unlikely to produce glitches.

Padé rational fraction
..... NORMALIZED .....
leading 1 in denom. x β f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + 1 β 6 el x * + β 7 el x 2^* + β 8 el x 3^* + / :

t0 1 time :

conjugate gradient x β φ x β f 8 φ :

3 appVersion 0.98.6179 ≡ Timing 17 sec ≡ 21 mat

X XY 1 col : Y XY 2 col : n XY rows : 13 mat

0.5 - 20 1.5 - 0.05 0.01 00018 mat

β β 1 el 0.5 - 20 1.5 - 0.05 0.01 00018 mat transpose : iter 13 : 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 :

1 time t0 - 17 s *

Absolute  residuals δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

β 0.0081 19.8477 3.0838 0.1146 0.0008 0.1675 0.0068 2.948 105 -^* 81 mat

δ Error

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.002

Absolute residuals ... mutual deviations δ i 1 XY rows range Δ i el Y i el X i el β f - 3 round eval : for X Y Δ augment 21 line :

FIT U 8.1 - 19.5 8 - range : i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

δ 8.0957 - 210.002 - 0.003 - 7.7963 - 195.802 - 0.012 7.4807 - 182.962 - 0.01 - 3.7187 - 78.476 - 0.012 1.9063 - 38.862 - 0.01 - 00 0.008 - 1.3739 26.87 0.001 5.2677 100 0.013 6.4886 122.37 0.008 8.3743 156.634 0.006 - 12.5517 231.9681 0.019 - 14.7427 271.442 0.002 - 17.4928 321.108 0.016 17.8462 327.502 0.015 19.456 356.66 0.018 - 153 mat

Δelta X δ 3 col 2000 * augment : datum X 0 Y * . 12 black plotG : bar Δelta 0.075 BarSize : data X Y . 12 black plotG : 41 line

x c 1 8.0957 - x ≤ (x 19.456 ≤ (& cases :

Note:

NRF [NormalizedRationalFraction] have excellent

virtue of interpolation were no model can be found.

NIST has abused of their use instead of models !

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Explain the Project . . .

This rational fraction approximates type 'J' thermocouple, i.e: it will personalize Type 'J' to

equivalent accuracy than Pt 100 RTD ... T/C are lot more robust than RTD. This personalization

is costly as you need Lab ITS-90. 'Δ' is the mutual conformity wrt NBS Monograph 125.

Since NBS Monograph 125, the Triple Point of Water has been fixed 0.01 °C.

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Type 'J' Thermocouple fit to NBS Monograph 125

bar FIT data 3 1 sys

1rst derivative

x β f x diff x c *

More statistical insight

χ X Mean : μ Y Mean : n XY rows : 31 line

χ μ n 31 mat 4.97308 80.56334 1531 mat

Pearson’s correlation coefficient corr X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / : 0.999999998

correlation between [X,Y data]

correlation between [X,fitted model]

X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / 21 mat 0.996732679 0.996732681 21 mat