Genfit Algo

9c0b6b0b-7670-4732-82b1-fe900fde81bb 19 6 9 decimal

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

Genfit Algo

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 : x β f x β f : x β φ x β φ transpose : 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 + : 151 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 :

Data Set

XY 0 5.916105 1021 -^* 0.002299 8.874158 1020 -^* 0.004598 7.099326 1019 -^* 0.006897 4.022952 1018 -^* 0.009195 1.810328 1017 -^* 0.011494 6.879247 1017 -^* 0.013793 2.293082 1016 -^* 0.016092 6.879247 1016 -^* 0.018391 1.891793 1015 -^* 0.02069 4.834582 1015 -^* 0.022989 1.1603 1014 -^* 0.025287 2.637045 1014 -^* 0.027586 5.713597 1014 -^* 0.029885 1.18667 1013 -^* 0.032184 2.37334 1013 -^* 0.034483 4.588458 1013 -^* 0.036782 8.488964 1013 -^* 0.03908 1.528014 1012 -^* 0.041379 2.801358 1012 -^* 0.043678 4.83871 1012 -^* 0.045977 8.234295 1012 -^* 0.048276 1.375212 1011 -^* 0.050575 2.249576 1011 -^* 0.052874 3.616299 1011 -^* 0.055172 5.721562 1011 -^* 0.057471 8.921901 1011 -^* 0.05977 1.372666 1010 -^* 0.062069 2.08489 1010 -^* 0.064368 3.127334 1010 -^* 0.066667 4.636672 1010 -^* 0.068966 6.800509 1010 -^* 0.071264 9.872665 1010 -^* 0.073563 1.4191 109 -^* 0.075862 2.021222 109 -^* 0.078161 2.85348 109 -^* 0.08046 3.994822 109 -^* 0.082759 5.548387 109 -^* 0.085057 7.647793 109 -^* 0.087356 0 0.089655 0 0.091954 0 0.094253 0 0.096552 0 0.098851 0 0.101149 0 0.103448 0 0.105747 0 0.108046 0 0.110345 0 0.112644 0 0.114943 0 0.117241 0 0.11954 0 0.121839 0.000001 0.124138 0.000001 0.126437 0.000001 0.128736 0.000001 0.131034 0.000001 0.133333 0.000002 0.135632 0.000002 0.137931 0.000003 0.14023 0.000003 0.142529 0.000004 0.144828 0.000005 0.147126 0.000006 0.149425 0.000007 0.151724 0.000009 0.154023 0.000011 0.156322 0.000013 0.158621 0.000015 0.16092 0.000018 0.163218 0.000022 0.165517 0.000026 0.167816 0.000031 0.170115 0.000037 0.172414 0.000044 0.174713 0.000052 0.177011 0.000061 0.17931 0.000072 0.181609 0.000084 0.183908 0.000099 0.186207 0.000116 0.188506 0.000135 0.190805 0.000157 0.193103 0.000182 0.195402 0.000211 0.197701 0.000244 0.2 0.000282 0.202299 0.000325 0.204598 0.000374 0.206897 0.00043 0.209195 0.000493 0.211494 0.000565 0.213793 0.000645 0.216092 0.000736 0.218391 0.000839 0.22069 0.000954 0.222989 0.001083 0.225287 0.001227 0.227586 0.001389 0.229885 0.00157 0.232184 0.001771 0.234483 0.001996 0.236782 0.002245 0.23908 0.002522 0.241379 0.002829 0.243678 0.003169 0.245977 0.003545 0.248276 0.003959 0.250575 0.004416 0.252874 0.004919 0.255172 0.005471 0.257471 0.006077 0.25977 0.006742 0.262069 0.00747 0.264368 0.008265 0.266667 0.009132 0.268966 0.010079 0.271264 0.011108 0.273563 0.012228 0.275862 0.013444 0.278161 0.014763 0.28046 0.016191 0.282759 0.017735 0.285057 0.019403 0.287356 0.021203 0.289655 0.023143 0.291954 0.02523 0.294253 0.027473 0.296552 0.029882 0.298851 0.032463 0.301149 0.035228 0.303448 0.038185 0.305747 0.041344 0.308046 0.044713 0.310345 0.048304 0.312644 0.052126 0.314943 0.056189 0.317241 0.060502 0.31954 0.065077 0.321839 0.069922 0.324138 0.075047 0.326437 0.080464 0.328736 0.08618 0.331034 0.092206 0.333333 0.09855 0.335632 0.105223 0.337931 0.112231 0.34023 0.119583 0.342529 0.127288 0.344828 0.135352 0.347126 0.143782 0.349425 0.152584 0.351724 0.161764 0.354023 0.171325 0.356322 0.181273 0.358621 0.19161 0.36092 0.202339 0.363218 0.21346 0.365517 0.224975 0.367816 0.236881 0.370115 0.249179 0.372414 0.261864 0.374713 0.274933 0.377011 0.288381 0.37931 0.302201 0.381609 0.316384 0.383908 0.330923 0.386207 0.345807 0.388506 0.361024 0.390805 0.376561 0.393103 0.392403 0.395402 0.408536 0.397701 0.424941 0.4 0.4416 0.402299 0.458494 0.404598 0.475601 0.406897 0.4929 0.409195 0.510365 0.411494 0.527973 0.413793 0.545698 0.416092 0.563512 0.418391 0.581386 0.42069 0.599293 0.422989 0.617202 0.425287 0.635081 0.427586 0.652899 0.429885 0.670624 0.432184 0.688223 0.434483 0.705662 0.436782 0.722907 0.43908 0.739925 0.441379 0.75668 0.443678 0.773139 0.445977 0.789268 0.448276 0.805031 0.450575 0.820395 0.452874 0.835328 0.455172 0.849795 0.457471 0.863764 0.45977 0.877204 0.462069 0.890084 0.464368 0.902375 0.466667 0.914048 0.468966 0.925074 0.471264 0.93543 0.473563 0.945088 0.475862 0.954027 0.478161 0.962225 0.48046 0.969662 0.482759 0.976319 0.485057 0.982181 0.487356 0.987232 0.489655 0.991461 0.491954 0.994857 0.494253 0.997411 0.496552 0.999118 0.498851 0.999972 0.501149 0.999972 0.503448 0.999118 0.505747 0.997411 0.508046 0.994857 0.510345 0.991461 0.512644 0.987232 0.514943 0.982181 0.517241 0.976319 0.51954 0.969662 0.521839 0.962225 0.524138 0.954027 0.526437 0.945088 0.528736 0.93543 0.531034 0.925074 0.533333 0.914048 0.535632 0.902375 0.537931 0.890084 0.54023 0.877204 0.542529 0.863764 0.544828 0.849795 0.547126 0.835328 0.549425 0.820395 0.551724 0.805031 0.554023 0.789268 0.556322 0.773139 0.558621 0.75668 0.56092 0.739925 0.563218 0.722907 0.565517 0.705662 0.567816 0.688223 0.570115 0.670624 0.572414 0.652899 0.574713 0.635081 0.577011 0.617202 0.57931 0.599293 0.581609 0.581386 0.583908 0.563512 0.586207 0.545698 0.588506 0.527973 0.590805 0.510365 0.593103 0.4929 0.595402 0.475601 0.597701 0.458494 0.6 0.4416 0.602299 0.424941 0.604598 0.408536 0.606897 0.392403 0.609195 0.376561 0.611494 0.361024 0.613793 0.345807 0.616092 0.330923 0.618391 0.316384 0.62069 0.302201 0.622989 0.288381 0.625287 0.274933 0.627586 0.261864 0.629885 0.249179 0.632184 0.236881 0.634483 0.224975 0.636782 0.21346 0.63908 0.202339 0.641379 0.19161 0.643678 0.181273 0.645977 0.171325 0.648276 0.161764 0.650575 0.152584 0.652874 0.143782 0.655172 0.135352 0.657471 0.127288 0.65977 0.119583 0.662069 0.112231 0.664368 0.105223 0.666667 0.09855 0.668966 0.092206 0.671264 0.08618 0.673563 0.080464 0.675862 0.075047 0.678161 0.069922 0.68046 0.065077 0.682759 0.060502 0.685057 0.056189 0.687356 0.052126 0.689655 0.048304 0.691954 0.044713 0.694253 0.041344 0.696552 0.038185 0.698851 0.035228 0.701149 0.032463 0.703448 0.029882 0.705747 0.027473 0.708046 0.02523 0.710345 0.023143 0.712644 0.021203 0.714943 0.019403 0.717241 0.017735 0.71954 0.016191 0.721839 0.014763 0.724138 0.013444 0.726437 0.012228 0.728736 0.011108 0.731034 0.010079 0.733333 0.009132 0.735632 0.008265 0.737931 0.00747 0.74023 0.006742 0.742529 0.006077 0.744828 0.005471 0.747126 0.004919 0.749425 0.004416 0.751724 0.003959 0.754023 0.003545 0.756322 0.003169 0.758621 0.002829 0.76092 0.002522 0.763218 0.002245 0.765517 0.001996 0.767816 0.001771 0.770115 0.00157 0.772414 0.001389 0.774713 0.001227 0.777011 0.001083 0.77931 0.000954 0.781609 0.000839 0.783908 0.000736 0.786207 0.000645 0.788506 0.000565 0.790805 0.000493 0.793103 0.00043 0.795402 0.000374 0.797701 0.000325 0.8 0.000282 0.802299 0.000244 0.804598 0.000211 0.806897 0.000182 0.809195 0.000157 0.811494 0.000135 0.813793 0.000116 0.816092 0.000099 0.818391 0.000084 0.82069 0.000072 0.822989 0.000061 0.825287 0.000052 0.827586 0.000044 0.829885 0.000037 0.832184 0.000031 0.834483 0.000026 0.836782 0.000022 0.83908 0.000018 0.841379 0.000015 0.843678 0.000013 0.845977 0.000011 0.848276 0.000009 0.850575 0.000007 0.852874 0.000006 0.855172 0.000005 0.857471 0.000004 0.85977 0.000003 0.862069 0.000003 0.864368 0.000002 0.866667 0.000002 0.868966 0.000001 0.871264 0.000001 0.873563 0.000001 0.875862 0.000001 0.878161 0.000001 0.88046 0 0.882759 0 0.885057 0 0.887356 0 0.889655 0 0.891954 0 0.894253 0 0.896552 0 0.898851 0 0.901149 0 0.903448 0 0.905747 0 0.908046 0 0.910345 0 0.912644 0 0.914943 7.647793 109 -^* 0.917241 5.548387 109 -^* 0.91954 3.994822 109 -^* 0.921839 2.85348 109 -^* 0.924138 2.021222 109 -^* 0.926437 1.4191 109 -^* 0.928736 9.872665 1010 -^* 0.931034 6.800509 1010 -^* 0.933333 4.636672 1010 -^* 0.935632 3.127334 1010 -^* 0.937931 2.08489 1010 -^* 0.94023 1.372666 1010 -^* 0.942529 8.921901 1011 -^* 0.944828 5.721562 1011 -^* 0.947126 3.616299 1011 -^* 0.949425 2.249576 1011 -^* 0.951724 1.375212 1011 -^* 0.954023 8.234295 1012 -^* 0.956322 4.83871 1012 -^* 0.958621 2.801358 1012 -^* 0.96092 1.528014 1012 -^* 0.963218 8.488964 1013 -^* 0.965517 4.588458 1013 -^* 0.967816 2.37334 1013 -^* 0.970115 1.18667 1013 -^* 0.972414 5.713597 1014 -^* 0.974713 2.637045 1014 -^* 0.977011 1.1603 1014 -^* 0.97931 4.834582 1015 -^* 0.981609 1.891793 1015 -^* 0.983908 6.879247 1016 -^* 0.986207 2.293082 1016 -^* 0.988506 6.879247 1017 -^* 0.990805 1.810328 1017 -^* 0.993103 4.022952 1018 -^* 0.995402 7.099326 1019 -^* 0.997701 8.874158 1020 -^* 1 5.916105 1021 -^* 4362 mat :

data n Decimate collects every 'n' points range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

XY XY 10 Decimate :

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

data X Y . 12 black plotG :

x β f β 2 el β 1 el 2 π * sqrt * / 12 / x 0.5 - β 1 el / (2^* - exp * :

Model function

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

x β φ x β f 2 φ :

<= ConjugateGradient Vector Fnct

β 0.0776 0.1953 21 mat :

0.1 0.195 21 mat

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

re-inject to iterate manually

FIT range, populate U 01 0.01 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

β 0.07785 0.19565 21 mat

data FIT 2 1 sys

The scaling β2 is the last value of the cumulative integration, to be optimized as it is not exact. Decimation has a sanity effect, creating asymmetric pairs of data.

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data XY :

data Σ 492 el 0.195