<p> Minimize Conjugate-Gradient </p>

976f1d24-e9cc-4aff-8c7b-e69782c8ad9b 70 3 12 decimal

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

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 :

init iter Minimize XY f φ β LS 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 : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop 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 :

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 :

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 :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat 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 / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

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

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

Otherwise Pearson independent of f(x,ParameterName) x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit.Y ii 1 n range Fit ii el X ii el β f : for Fit 21 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^* + / :

t0 1 time :

conjugate gradient x β φ x β f 8 φ :

X XY 1 col : Y XY 2 col : 12 mat data XY . 12 black plot : n XY rows : 31 line

3 appVersion 0.98.6179 ≡ Timing 17 sec ≡ 21 line

iter 13 :

init 0.5 - 20 1.5 - 0.05 0.01 00018 mat transpose :

algo solving for β β init iter Minimize :

assign/isolate .. 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 :

SSD 0.00197

1 time t0 - 32 s *

corr 1.00000000

β 0.00807 19.84766 3.08382 0.11462 0.00083 0.16745 0.00681 0.00003 81 mat

Fit.Y ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

δ Error

Y Fit.Y corr 1.00000000

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 :

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 :

Δelta X δ 3 col 2000 * augment : bar Δelta 0.075 BarSize : data XY . 12 black plot : 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

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

Pearson’s correlation coefficient x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit.Y ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

Y Fit.Y corr X Y corr X Fit.Y corr 31 mat 1 0.99673 0.99673 31 mat