NBS 125

b008d2d0-2eaf-418d-b09f-dea2c6528dfe 29 15 12 decimal

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

NBS 125

T 6.25629 - 268.935 - 6.22919 - 259.340 - 6.19773 - 252.870 - 6.17138 - 248.595 - 6.15358 - 246.048 - 5.87302 - 218.789 - 5.75328 - 210.002 - 5.53559 - 195.802 - 5.31472 - 182.962 - 2.74070 - 78.476 - 1.43494 - 38.862 - 00 1.0679 26.87 4.2773 100 5.3414 122.37 7.0364 156.634 11.0133 231.9681 13.2188 271.442 16.0953 321.108 16.4733 327.502 18.2179 356.66 212 mat :

J 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 22.9259 419.58 24.3123 444.674 30.1095 548.23 34.9108 630.74 36.6933 660.37 55.669 961.93 61.716 1064.43 62.880 1084.5 232 mat :

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 :

data list ListCollect collects index list select list : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

XY J :

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

num order
denom order p.n 8 : p.d 7 : 21 sys

...k is total order of rational fit k 1 p.n + p.d + : 16

"Normalized" rational fraction have
leading "1" in denom.  Reputed stable
numerically. Most if not all computer
approximations are  "Normalized".
Generally, Num_order is Denom_order+1.
Some fit were found not "Normalized. x β f β 1 el β j 1 + el x j^* j 1 p.n sum + 1 β j 1 + p.n + el x j^* j 1 p.d sum + / maple :

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 :

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^* + β 6 el x 5^* + β 7 el x 6^* + β 8 el x 7^* + β 9 el x 8^* + 1 β 10 el x * + β 11 el x 2^* + β 12 el x 3^* + β 13 el x 4^* + β 14 el x 5^* + β 15 el x 6^* + β 16 el x 7^* + /

support points ≡ k support 1346789101112141618202122116 mat :

x β Clear 1

can't truncate 'β' wrt x^8
otherwise: scale down variate 'x'. 638^248155780267521

β Discrete Cholesky solver slight recast from Alyles ct 1 : j support Xs ct el XY j 1 el : Ys ct el XY j 2 el : 12 mat ct ct 1 + : 21 line for Ms k Ones : i 1 p.n range Ms Ms Xs i^vectorize augment : for i 1 p.d range Ms Ms Xs i^Ys * vectorize - augment : for Ms 1 -^Ys * 81 line :

b β :

β ct 1 : j 1 b rows range u ct el b j el 15 round : ct ct 1 + : 21 line for u 31 line :

CWD C:\SmathFile CurrentDirectory :

β CWD βTypeJ wfile 1

β CWD βTypeJ rfile :

β β :

β rows 16

faster than
f(x,β) ... x f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + β 6 el x 5^* + β 7 el x 6^* + β 8 el x 7^* + β 9 el x 8^* + 1 β 10 el x * + β 11 el x 2^* + β 12 el x 3^* + β 13 el x 4^* + β 14 el x 5^* + β 15 el x 6^* + β 16 el x 7^* + / :

Absolute residuals [mutual conformity] δ i 1 XY rows range Δ i el Y i el X i el f - 2 round eval : for X Y Δ augment 21 line :

Conformity 'J' NBS-125 ... δ 8.0957 - 210.002 - 0 7.7963 - 195.802 - 0.04 7.4807 - 182.962 - 0 3.7187 - 78.476 - 0 1.9063 - 38.862 - 0000 1.3739 26.87 0 5.2677 1000 6.4886 122.37 0 8.3743 156.634 0 12.5517 231.9681 0 14.7427 271.442 0 17.4928 321.108 0 17.8462 327.502 0 19.456 356.66 0 22.9259 419.58 0 24.3123 444.674 0 30.1095 548.23 0 34.9108 630.74 0.02 36.6933 660.37 0 55.669 961.93 0 61.716 1064.43 0 62.88 1084.5 0.62 - 233 mat

FIT u 8.0957 - 65 8.05 - range : i 1 u rows range FIT i el u i el f eval : for u FIT augment 31 line :

8.0957 - 65 8.085 - range

12946832 / 0.19

1. selcted  support pts
2. collect for plot list support : xy XY list ListCollect : 21 sys

data XY . 12 black plot : support xy + 20 blue plot : x c 1 8.0957 - x ≤ (x 65 ≤ (& cases : 31 line

Rational fraction to Type 'J' T/C, NBS Monograph 125 Certified free of glitch @ XTR resolution ± 0.2 °C

data x f x c * support 3 1 sys

Support pts 'J' NBS-125 xy 8.0957 - 210.002 - 7.4807 - 182.962 - 3.7187 - 78.476 - 00 1.3739 26.87 5.2677 100 6.4886 122.37 8.3743 156.634 12.5517 231.9681 14.7427 271.442 17.8462 327.502 22.9259 419.58 30.1095 548.23 36.6933 660.37 55.669 961.93 61.716 1064.43 162 mat

__ Type 'J' Thermocouple __

-210.002 . . . 1084.5 °C

]]> 'c' normalised coefficients

'c' ...recovered from Mathcad c 19.8518394369938 3.39708430077966 0.052276519294839 8.91649190043396 103 -^* - 9.92828185332406 105 -^* 8.38053206800752 106 -^* 3.1464248690302 107 -^* - 4.25243756863902 109 -^* 2.07174891774966 1011 -^* - 0.183112912617708 3.87083881009766 103 -^* 5.08713285834413 104 -^* - 2.26745307368593 106 -^* 6.6275111583499 107 -^* 2.21691344604783 108 -^* - 2.87497042511128 1010 -^* 1.36525976453514 1012 -^* - 171 mat :

'β' ... recovered from Smath b 0.00000000262727 - 19.8520614070612 1.44449548339689 - 0.182140077987682 - 0.023436694906595 0.000180113626196 0.000033011046229 - 0.000000843291563 0.000000005497645 - 0.060761237973477 - 0.010863420285349 - 0.001177409875546 0.000023924502883 0.00000244239685 - 0.000000058587167 0.000000000381957 - 161 mat

recover 
reduced x J1084 x c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + c 5 el x 4^* + c 6 el x 5^* + c 7 el x 6^* + c 8 el x 7^* + c 9 el x 8^* + 1 c 10 el x * + c 11 el x 2^* + c 12 el x 3^* + c 13 el x 4^* + c 14 el x 5^* + c 15 el x 6^* + c 16 el x 7^* + c 17 el x 8^* + / * :

X J 1 col : Y J 2 col : 12 mat XY X Y augment : J XY . 12 black plot : 31 line

J1084 mV 8.25 - 638 - range : i 1 mV rows range t i el mV i el J1084 eval : for mV t augment 31 line :

Type 'J' ultimate fit to NBS 125

J J1084 2 1 sys

ΔJ1084 X Y Y X J1084 - (vectorize augment :

ΔJ1084 8.096 - 210.002 - 0.000 7.796 - 195.802 - 0.000 7.481 - 182.962 - 0.000 3.719 - 78.476 - 0.000 1.906 - 38.862 - 0.000 0.000 0.000 0.000 1.374 26.870 0.000 5.268 100.000 0.000 6.489 122.370 0.000 8.374 156.634 0.000 12.552 231.968 0.000 14.743 271.442 0.001 17.493 321.108 0.000 17.846 327.502 0.000 19.456 356.660 0.000 22.926 419.580 0.000 24.312 444.674 0.000 30.110 548.230 0.000 34.911 630.740 0.000 36.693 660.370 0.000 55.669 961.930 0.000 61.716 1064.430 0.000 62.880 1084.500 0.000 233 mat

Calibrate the 'J' mV/I converter

XmV 100 - :

XmV °C ≡

mV 1 :

mV J1084 XmV - 0 ≡ mV 6 - 4 - solve mV 4.6322 -

4.6322 - J1084 100 -

Low range : -100°C => -4.6322mV

XmV 200 :

XmV °C ≡

mV 1 :

mV J1084 XmV - mV 812 solve mV 10.7765

10.7765 J1084 200

High range : 200°C => 10.7765mV

β 11 mat 0.00000000262727 - 19.8520614070612 1.44449548339689 - 0.182140077987682 - 0.023436694906595 0.000180113626196 0.000033011046229 - 0.000000843291563 0.000000005497645 - 0.060761237973477 - 0.010863420285349 - 0.001177409875546 0.000023924502883 0.00000244239685 - 0.000000058587167 0.000000000381957 - 161 mat 11 mat

c 11 mat 19.8518394369938 3.39708430077966 0.052276519294839 0.008916491900434 - 0.000099282818533 0.000008380532068 0.000000314642487 - 0.000000004252438 0.000000000020717 - 0.183112912617708 0.003870838810098 0.000508713285834 - 0.000002267453074 0.000000662751116 0.000000022169134 - 0.000000000287497 1.36525976453514 1012 -^* - 171 mat 11 mat