TOC of "GenfitAlgoInclude.sm"

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Search in the same directory, 11 algorithms in the referenced WS "GefitAlgoInclude"

data char size clr plot XY f φ β Minimize x β f n φ data Error L H N xd data dt BarSize corr SSD x y corr Fit # 111 sys

GenfitAlgoInclude.sm include 11

4 appVersion 0.98.6179.21440 ≡

XY 0 1.787 5 1.519 10 1.307 20 1.002 30 0.798 40 0.653 50 0.547 60 0.467 70 0.404 80 0.355 90 0.315 100 0.282 122 mat :

<= ExpDecay model function
viscosity water [cP/°C] x β f β 1 el β 2 el β 3 el x + / + exp :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

<= Gradient Vector Function x β φ x β f 3 φ :

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

init 3 - 50010013 mat transpose :

iter 7 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

FIT U 0100 0.1 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 31 line :

SSD 3105 -^*

corr 1.0006

°C μ °C β f :

cP 1 :

assign/isolate β β : 3.47 - 488.56 120.643 31 mat

°C 25 :

°C μ cP 0.89

data XY o 5 black plot : Title 240 Viscosity Water cP 12 blue 15 mat : 21 line

collect 8 - °C μ °C °C μ °C 0.25 - 32 mat FIT data Title 41 sys :

Remark . . . As set, the plotting canvas is

332 pixels, thus and whereas Smath plots scalar

calculated values on pixels, for the matrix FIT,

for thicker trace, discretize lot more than the

canvas size . . . try [0,0.1..100]

]]> collect

°C °C μ 12 mat cP 25 0.891 12 mat

Minimize Conjugate-Gradient .... that stuff is what "GenfitAlgoInclude" contains

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 :

Linfit rational [advanced example]

This data set is the reduced smoothed "Corn Thermies". Though XY looks rational, it is not at all, thus reverse reduction fails aroubd point 8/9. OBSERVE the fixed 'u'.

u 2.62 :

x β f β 1 el β 2 el x u + (1 -^* + β 3 el x u + (2 -^* + β 4 el x u + (3 -^* + β 5 el x u + (4 -^* + β 6 el x u + (5 -^* + β 7 el x u + (6 -^* + β 8 el x u + (7 -^* + :

XY 0 2113.3 1 1055.8 2 703.1 3 526.3 4 419.9 5 348.7 6 297.8 7 259.8 8 230.6 9 207.4 10 188.6 11 172.9 12 159.5 131481413815 129.2 16 121.4 17 114.6 18 108.4 19103202 mat :

range/populate L 0 : H 24 : N 500 : 13 mat U L H N xd : 21 line

x β φ x β f 8 φ :

X XY 1 col : Y XY 2 col : Data XY . 12 black plot : n XY rows : 41 line

28.1674 - 3576.6254 28508.2554 - 3.4628 105^* 1.9663 106^* - 6.4049 106^* 1.0872 107^* - 7.7453 106^* 81 mat

Iter_5 11 mat

init 1111111118 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 0.23

β 28.1 - 3574.1 28448.8 - 3.5 105^* 2106^* - 6.4 106^* 1.1 107^* - 7.7 106^* 81 mat

Relative residuals Δr i 1 XY rows range Δ i el 1 Y i el X i el β f / - eval : for X Δ augment 21 line :

corr 1.00000

FIT i 1 U rows range FIT i el U i el β f eval : for U FIT augment 21 line :

Data FIT 2 1 sys Δr 0.125 BarSize

Linfit rational [other style]

XY XY Clear :

XY 0 0.3311 0.0263 2.3873 0.0526 3.0086 0.0789 3.0952 0.1053 3.083 0.1316 3.054 0.1579 3.025 0.1842 2.9995 0.2105 2.9778 0.2368 2.9594 0.2632 2.9436 0.2895 2.9301 0.3158 2.9185 0.3421 2.9083 0.3684 2.8993 0.3947 2.8914 0.4211 2.8843 0.4474 2.878 0.4737 2.8723 0.5 2.8671 202 mat :

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

x β f β 1 el 1200 x * 150 x * + (* + (* 10000 β 2 el x 2^* + / :

x β φ x β f 2 φ :

init 300100000012 mat transpose :

iter 7 :

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 1107 -^*

corr 1.0001

bar δ Error (:

FIT U 005 0.01 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

bar

β 33131107^* 21 mat

data FIT 2 1 sys