Function Utilities

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Function Utilities

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 :

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 :

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 :

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].

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 :

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 :

Model rational fraction x β f β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + 1 β 5 el x * + β 6 el x 2^* + / :

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

x β φ x β f 6 φ :

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

β 0.2378 - 19.7388 0.7286 0.068 - 0.0473 0.0039 - 61 mat :

0.5 5 0.25 - 0.1 0.05 061 mat

Genfit coeff's of fit β XY f φ β Minimize :

β 0.1922 - 19.726 0.7207 0.0652 - 0.0471 0.0038 - 61 mat

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

FIT range, populate U 8.1 - 19.5 8 - range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

δ 8.0957 - 210.002 - 0.33 - 7.7963 - 195.802 - 0.3 7.4807 - 182.962 - 0.3 3.7187 - 78.476 - 0.54 - 1.9063 - 38.862 - 0.13 - 00 0.19 1.3739 26.87 0.3 5.2677 100 0.18 6.4886 122.37 0.07 8.3743 156.634 0.09 - 12.5517 231.9681 0.23 - 14.7427 271.442 0.13 - 17.4928 321.108 0.05 17.8462 327.502 0.05 19.456 356.66 0.15 - 153 mat

data X Y . 12 black plotG :

data FIT 2 1 sys

0.5 5 0.25 - 0.1 0.05 061 mat 0.192231 - 19.726001 0.720699 0.065183 - 0.047112 0.003758 - 61 mat 12 mat

Δelta X δ 3 col augment : stem Δelta Error : 21 line

0 stem 2 1 sys

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 4 manual iterates. No more calibration is needed except "offset" the 0°C.

BarSize Unicolor QuickPlot or any color X_Y

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 :

MyBar Δelta 0.075 BarSize :

Mutual deviation between data set and rational fit.

0 MyBar 2 1 sys