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 thicker trace,

discretize lot more than the canvas size . . .

]]> 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]

XY 0 :

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

init 1111111118 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

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 :

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

corr 1.00000

Relative residuals zoomΔr i 1 XY rows range Δ i el 1 Y i el X i el β f / - eval : for X 50000 Δ * augment 21 line :

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

relative zoomΔr 0.125 BarSize :

relative FIT Data 3 1 sys Δr 0.125 BarSize

Linfit rational [other style]

XY 0 :

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 0 0.75 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 Genfit Minimize Utilities [disabled] Those utilities saved in "Genfit Minimize Include"

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 :

all 9 components utilities recovered Genfit Minimize Include.sm include 9

Each new project starts here from new data set and model function

XY 104092030430260401925017052 mat :

Model function x β f β 1 el β 2 el x * exp * :

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

<= ConjugateGradient Vector Fnct x β φ x β f 2 φ :

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

init 500 0.05 - 12 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

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

SSD 512

β 504.902 0.023 - 21 mat

corr 0.9839

FIT range, populate U 060 0.1 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

Lifetime of the decay τ 1 β 2 el / abs : 43.4

data FIT 2 1 sys

Relative residuals

Residuals 0.5 BarSize 1 1 sys

Langmir model function x β f β 1 el x β 3 el^* 1 β 2 el x β 3 el^* + / (β 4 el^:

A most difficult data set to fit. For that one, Mathcad is no better, all sorts of coefficients will result ... LM no better either [ERR 0.32]

data n ‖ data n col :

XY 0.5 0.1 20 3.341 50 6.429 100 9.366 200 12.184 300 13.645 500 15.393 1000 17.767 14001992 mat :

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

<= ConjugateGradient Vector Fnct x β φ x β f 4 φ :

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

init 7574 0.4 45014 mat transpose :

iter 13 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 0.101

corr 1.003

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

FIT range, populate U 0150010 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

β 646.775 646.312 0.411 4607.136 41 mat

data FIT 2 1 sys

Relative residuals

Residuals 0.1 BarSize 1 1 sys