Genfit Utilities

1c3fd882-8777-40b8-83b0-d2ec73d473d7 8 4 5 decimal

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

TI 040018002200034000460005470063300724008160091100115001240013400132 mat :

TO 001 12.7726 2 78.4426 3 256.5482 4 673.6649 5 1148.3312 6 1455.0607 7 1599.1564 8 1637.7485 9 1610.9196 11 1450.7542 12 1341.1993 13 1240.1623 132 mat :

TE 03001 300.2944 2 300.9876 3 302.0817 4 303.7723 5 305.2664 6 306.1666 7 306.5675 8 306.6729 9 306.5997 11 306.1561 12 305.8406 13 305.5435 132 mat :

TI TO 2 1 sys TE 3 1 sys Genfit 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 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 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 :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

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 :

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 :

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 :

data 001 12.7726 2 78.4426 3 256.5482 4 673.6649 5 1148.3312 6 1455.0607 7 1599.1564 8 1637.7485 9 1610.9196 11 1450.7542 12 1341.1993 13 1240.1623 132 mat :

XY data 19 range 12 range el :

Model function x β f β 1 el 1 β 2 el β 3 el x * - exp + / β 4 el + :

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

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

16405112 - 41 mat

β β 1 el 16405112 - 41 mat : iter 5 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

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

β 1670.1633 5.2384 1.2147 15.1166 - 41 mat

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 380

FIT range, populate U 013 0.1 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

RMS difference SSD n / sqrt 6.5

data data 1 col data 2 col . 12 black plotG :

data FIT 2 1 sys

data 03001 300.2944 2 300.9876 3 302.0817 4 303.7723 5 305.2664 6 306.1666 7 306.5675 8 306.6729 9 306.5997 11 306.1561 12 305.8406 13 305.5435 132 mat :

XY data 19 range 12 range el :

Model function x β f β 1 el 1 β 2 el β 3 el x * - exp + / β 4 el + :

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

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

105130041 mat

β β 1 el 105130041 mat : iter 5 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

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

β 6.9539 3.6916 0.9875 299.8599 41 mat

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.01

FIT range, populate U 013 0.1 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

RMS difference SSD n / sqrt 0

data data 1 col data 2 col . 12 black plotG :

data FIT 2 1 sys Genfit 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 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 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 :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

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 :

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 :

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 :

data 040018002200034000460005470063300724008160091100115001240013400132 mat :

XY data :

Fréchet: extreme value-II x β f β 1 el β 2 el x β 5 el - (/ (β 3 el 1 +^* β 2 el x β 5 el - (/ (β 3 el^- exp * β 4 el + :

β 15230.09 43252.7 - 27354.7 - 400 43256.75 51 mat :

x β f 1 * data 2 1 sys

13990.5785 43252.7366 - 27354.7233 - 410.0794 43257.0208 51 mat

4 β f 6000.0002

FIT range, populate U 013 0.1 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

This TI data set can be fitted in two pieces. It might be possible to refit from special techniques borrowed from Mathcad

data data 1 col data 2 col . 12 black plotG :

data FIT 2 1 sys