SSD ... Pearson Correlation

032aaa29-0515-4cbb-959c-bd976fa5c412 8 4 5 decimal

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

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 f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

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

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 :

... GR-50-AA ... Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.73 1.4 19.32 2 13.66 4.2 102 mat :

Germanium Cryogenic Sensor Ge Ge 210 range 12 range el :

X Ge 1 col : Y Ge 2 col : 12 mat XY X Y augment : data Ge o 7 black plot : n Ge rows : x c 1 13.66 x ≤ (x 35000 ≤ (& cases : 51 sys

x φ 11 x 1.125^/ 1 x 2.25^/ 1 x 3.375^/ 1 x / 1 x 0.5^/ 1 x 0.25^/ 1 x 0.125^/ 18 mat transpose :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 3.843977 - 2401.820709 5401.63931 - 52172.808766 1901.25736 - 172.699658 82.887427 - 33.531555 81 mat

β b 4 round vectorize :

CWD C:\SmathFile CurrentDirectory :

β CWD βGe wfile 1

β 3.844 - 2401.8207 5401.6393 - 52172.8088 1901.2574 - 172.6997 82.8874 - 33.5316 81 mat

β CWD βGe rfile :

At this point, isolate manually or isolate via a for loop to enable fitting manipulation of the vector function φ(x). Rounding is necessary to relieve the overkilling floating point engine.

recast the fitting session for an easy export on scientific calculator x f β x φ * :

x f 27372662921358041 x 8 nthroot 19^* - (* 414437 x 8 nthroot 25^* - (* 54016393 - 2401820738440 x 8 nthroot 9^* - 1726997 x 8 nthroot 5^* + (x 8 nthroot 9^* + (x 8 nthroot 9^* + 335316 x 4 nthroot 13^* + 10000 x 8 nthroot 27^* /

Collect/Export

x Φ 27372662921358041 x 8 nthroot (19^* - (* 414437 x 8 nthroot (25^* - (* 10000 x 8 nthroot (27^* / 54016393 - 2401820738440 x 8 nthroot (9^* - 1726997 x 8 nthroot (5^* + (x 8 nthroot (9^* + (x 8 nthroot (9^* 10000 x 8 nthroot (27^* / 335316 x 4 nthroot (13^* 10000 x 8 nthroot (27^* / 31 sys :

x Ω x Φ 1 el x Φ 2 el + x Φ 3 el + :

Conformity from absolute residuals δ i 1 Ge rows range Δ i el Y i el X i el Ω - 3 round eval : for Ω °K Δ°K 13 mat X Y Δ augment stack 21 line :

SSD 0.00000

corr 1.0000

Quick linfit ... The 4th support point is unlikely exact 164 ...

data x Ω x c * 2 1 sys

https://www.lakeshore.com/Documents/LSTC_Germanium_l.pdf Lake Shore germanium resistance temperature sensors are recognized as “Secondary Standard Thermometers” and have been employed in the measurement of temperature from 0.05 K to 30 K for more than 40 years.

δ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0.001 73.75 0.5 0.001 - 33.55 1 0.001 24.73 1.4 0.001 - 19.32 20 13.66 4.2 0103 mat

What a great mistake linearly interpolating the elbow region, unless genereously decimated.

Cholesky to fit 'λ' PipeLine

SSD ... Pearson Correlation

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 f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

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

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 :

PipeLine 'λ'... λ 1642 5.9376 3 2.9688 5 1.4844 7 0.9896 11 0.5938 19 0.3299 100 0.06 300 0.0371 600 0.0315 102 mat :

X λ 1 col : Y λ 2 col : 12 mat XY X Y augment : data λ o 5 black plot : n λ rows : x c 11 x ≤ (x 600 ≤ (& cases : 51 sys

x φ 11 x 1.125^/ 1 x 2.25^/ 1 x / 1 x 0.75^/ 1 x 0.5^/ 1 x 0.25^/ 1 x 0.125^/ 18 mat transpose :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 695.849622 - 29095.252422 - 577.973568 50297.11362 35382.12013 - 19702.123315 10190.743227 - 4850.755644 81 mat

β b 2 round vectorize :

CWD C:\SmathFile CurrentDirectory :

β CWD λPipeLine wfile 1

β 695.85 - 29095.25 - 577.97 50297.11 35382.12 - 19702.12 10190.74 - 4850.76 81 mat

β CWD λPipeLine rfile :

At this point, isolate manually or isolate via a for loop to enable fitting manipulation of the vector function φ(x). Rounding is necessary to relieve the overkilling floating point engine.

recast the fitting session for an easy export on scientific calculator x f β x φ * :

x f 5779750297114 x 4 nthroot * 492553 x 4 nthroot * 884553 - (* + (x 8 nthroot * - 558190513917 x 8 nthroot 9^* + (* + 1019074 x 8 nthroot 7^* + (x 8 nthroot 9^* - 485076 x 8 nthroot 17^* + 100 x 4 nthroot 9^* /

Conformity from absolute residuals δ i 1 λ rows range Δ i el Y i el X i el f - 3 round eval : for Ω λ Δλ 13 mat X Y Δ augment stack 21 line :

SSD 0.00000

corr 0.9998

data x f x c * 2 1 sys

δ Ω λ Δλ 16402 5.9376 0.018 - 3 2.9688 0.045 5 1.4844 0.089 - 7 0.9896 0.02 11 0.5938 0.068 19 0.3299 0.061 - 100 0.06 0.016 300 0.0371 0.017 - 600 0.0315 0.003 113 mat