<p> Minimize Conjugate-Gradient </p>

854ce97b-3e43-4888-90ba-13ed8ac89864 12 15 12 decimal

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

Project Note:

The 3 points data set comes from an horrible empirical approximation related

to the depth of insertion of the moulinet [ a rough volumetric flow measuring

device in large pipe sizes not covered by ISO-5167 Orifice Plate].

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f init TOL GivenFind f init TOL FindRoot :

TOL 0.000001 :

X 1513563531 mat :

Y 0.121229 0.119489 0.118596 31 mat :

init K 0.1 ≡ H 1 ≡ L 10 ≡ 31 mat :

<= very 1rst initials 0.1 11031 mat

f H K L X 1 el + / + Y 1 el ≡ H K L X 2 el + / + Y 2 el ≡ H K L X 3 el + / + Y 3 el ≡ 31 mat :

K, H, L in "init" order.
Keep increasing L up to best.
Finish refining manually or 
alternately Genfit [slow convergence]. K H L 31 mat f init TOL GivenFind : 0.1182 0.2615 72.0925 31 mat

XY X Y augment :

x Rational K H L x + / + :

constrain u 0 x ≤ :

x Rational u * XY X 1 el Y 1 el o 7 red X 2 el Y 2 el o 7 red X 3 el Y 3 el o 7 red 3 5 mat 3 1 sys

x Rational x 0635 int 75.7

sanity check wrt support points X Rational Y - vectorize 0.000000046 - 0.000000011 - 0.000000024 31 mat

Alternately ... here is the Genfit

<p> Minimize Conjugate-Gradient </p>

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 :

XY 15 0.121229 135 0.119489 635 0.118596 32 mat :

Model function x β f β 1 el β 2 el β 3 el x + / + :

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

Conjugate Gradient vector function x β φ x β f 3 φ :

range/populate L 0 : H 15 : N 399 : 13 mat U L H N xd : 21 line

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

init 01013 mat transpose :

iter 9 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 11029 -^*

corr 1.0000

Relative residuals δ 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 07001 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

β 0.1182 0.2615 72.0945 31 mat

Moulinet depth of insertion [Instrument flow measurement]

XY FIT data 3 1 sys

δ 1531014 -^* 13531015 -^* - 63541015 -^* - 32 mat