<p> Genfit Utilities </p>

976f1d24-e9cc-4aff-8c7b-e69782c8ad9b 37 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 :

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^* + / :

conjugate gradient x β φ x β f 8 φ :

0.5 - 20 1.5 - 0.05 0.01 00081 mat

X XY 1 col : Y XY 2 col : n XY rows : 31 line

The rule to initialise is the rule of "lottery", i.e: the rule of shape. Observe the initial shape through data.

β β 1 el 0.5 - 20 1.5 - 0.05 0.01 00081 mat : 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 :

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 :

bar δ Error (:

bar

Absolute residuals ... 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 :

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

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

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 :

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

Type 'J' Thermocouple fit to NBS Monograph 125

data FIT 2 1 sys

Mutual deviation between data set and rational fit.

0 bar datum 3 1 sys

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

χ μ n 31 mat 4.97308 80.56334 1531 mat

More statistical insight

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 0.996733 0.996733 21 mat

Project NOTE: This rational fraction approximates type 'J' thermocouple. The mutual conformity between NBS Monograph 125 and this rational fraction is within the probable 'J' error [± 1°C] from current suppliers. This "β rational fit" is obtained in 13 auto-iterates. No more calibration is needed except "offset" the 0°C.