Minimize Conjugate-Gradient

89bbe068-4a9b-4197-9c65-aba3598b6e85 22 4 5 decimal

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

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 :

Collected data for fitting session

XY 0.0048 0.1486 0.024 2.087 0.0384 3.2092 0.0528 4.3405 0.072 5.9079 0.0864 6.9334 0.1008 7.9525 0.1152 8.9573 0.1344 10.3092 0.1512 11.5249 0.1656 12.6212 0.1848 13.9393 0.204 15.2584 0.2184 16.3402 0.2352 17.5355 0.2496 18.531 0.2712 19.9545 0.2904 21.2875 0.3072 22.4996 0.324 23.5858 0.3432 25.1146 0.3624 26.3951 0.3792 27.4926 0.3984 28.751 0.4152 29.8585 0.4296 30.9342 0.4464 32.184 0.4656 33.4054 0.4824 34.559 0.5016 35.7135 0.5232 37.1843 0.5424 38.5224 0.5616 39.8321 0.5808 40.9397 0.5976 41.9262 0.6168 43.139 0.6384 44.5527 0.6576 45.7654 0.6816 46.9972 0.6984 48.096 0.72 49.2923 0.7392 50.2898 0.7584 51.3518 0.7776 52.3406 0.7944 53.2948 0.816 54.5127 0.8352 55.4919 0.8568 56.5669 0.8784 57.6507 0.9 58.7205 0.924 59.8017 0.9432 60.7766 0.9672 61.7594 0.9888 62.7259 1.0104 63.6836 1.032 64.6396 1.056 65.5913 1.08 66.5616 1.1016 67.4872 1.1256 68.4315 1.152 69.3449 1.176 70.2421 1.2 71.0967 1.224 71.9249 1.2504 72.7605 1.2744 73.5582 1.2984 74.3658 1.3248 75.1534 1.3488 75.9022 1.3752 76.6308 1.3992 77.3295 1.4232 78.032 1.452 78.7269 1.476 79.4232 1.5024 80.0897 1.5312 80.7257 1.5576 81.3455 1.584 81.9484 1.608 82.5341 1.6392 83.1173 1.6656 83.6877 1.692 84.237 1.7208 84.7897 1.7472 85.3123 1.776 85.8156 1.8024 86.279 1.8336 86.7614 1.8624 87.2275 1.8888 87.6757 1.92 88.1325 1.9488 88.538 1.9752 88.9558 2.0064 89.3426 2.0352 89.7179 2.0664 90.0923 2.0952 90.4462 2.1264 90.779 2.1576 91.0979 2.1864 91.4123 2.22 91.7002 2.2488 91.9537 2.28 92.2315 2.3136 92.4977 2.3472 92.7617 2.3784 93.006 2.412 93.2058 2.4456 93.3994 2.4792 93.5692 2.5128 93.7372 2.5464 93.8991 2.5824 94.0539 2.6184 94.1834 2.652 94.3021 2.688 94.3838 2.7264 94.4363 2.76 94.4578 2.8008 94.4881 1172 mat :

data n Decimate collect every 'n' pairs 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 :

X XY 1 col : Y XY 2 col : 12 mat

"binding Ligand" is largely used in Pharmacokinetics. Recognized as a good fit to systems of 2 underlying DE. Atmosperic properties [0 ... 20km] is typical of 2 DE. The fit is not arguable on corr 1.000009. The data set does NOT look raw from experimental. Most likely, it has been freaked from collection.

x λ 1 0.5 - x ≤ (x 4 ≤ (& cases :

Ligand system M 183.75 : m 0 : 21 sys

xy XY 10 Decimate : sparse xy . 14 black plot : 21 sys

XY rows 117

1. Shifted binding Ligand Sigmoidal...

Experimetal initials.
Convenient iterative CG.
Just a bit weird ! 0.0006 3.586 0.8125 46.3 41 mat

Model function x β f m M m - (110 β 1 el log10 x β 2 el - (- (β 3 el *^+ / + β 4 el - :

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

init 0.0006 3.586 0.8125 46.3 14 mat transpose :

iter 7 :

XY 1 row XY 10 row XY 50 row XY XY rows row 41 mat 0.0048 0.1486 12 mat 0.1512 11.5249 12 mat 0.9 58.7205 12 mat 2.8008 94.4881 12 mat 41 mat

algo solving for β β init iter Minimize :

assign/isolate .. β β :

Pearson correlation corr 1.000009

β 0.000178 3.818773 0.68919 86.389722 41 mat ≡

β 0.000178 3.818773 0.68919 86.389722 41 mat

0.0048 β f 1 β f 2 β f 2.8008 β f 41 mat 0.7839 63.201 89.1603 94.983 41 mat

plot XY x β f x λ * sparse 31 sys :

δ j 2 XY rows range Δ j el 1 Y j el X j el β f / - eval : for X Δ augment 21 line :

M iter corr 183.75 7 1.000009 23 mat

Proposed fit to the unknown data set XY

plot

Relative residuals on reduced range ...

δ Error

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 :

2. Recast project, suite export ...

M 183.75 :

Ligand x β f M 110 β 1 el log10 x β 2 el - (- (β 3 el *^+ / β 4 el - :

0 β f 2.5 β f 5 β f 31 mat 0.435 93.559 97.287 31 mat

β 0.000178 3.818773 0.68919 86.389722 41 mat :

vx 05100 xd :

vy vx β f :

export vx vy 4 round vectorize augment :

u 3 :

U u β f :

track 532232 u U 32 mat :

export track 2 1 sys

NOT sanity checked x β f x 05 int 400

u U 12 mat 3 95.62 12 mat