Explode Lorentz data set

703fcf1e-56cc-4282-badc-20cbe158b9d9 50 4 5 decimal

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

FindIdx(V,key,col)

data 10 0.59 21 0.61 32 0.65 43 0.6 54862 0.55 7 0.3 0.6 - 8 0.4 0.62 - 9 0.4 0.6 10 0.38 6114 0.45 12 0.45 0.48 - 13 0.5 - 0.5 - 14 0.48 - 0.45 15 0.45 4166 0.38 17 0.6 0.4 18 0.62 - 0.4 19 0.6 - 0.3 20 0.55 2218422 0.6 323 0.65 224 0.61 125 0.59 0253 mat :

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

key 0.45 : col 3 : 12 mat

idxkey data key col FindIdx :

idxkey 11 0.45 12 mat

recover 'row'. data idxkey 11 el row 114 0.45 13 mat

school mark data 0000 Maya 40 Fred 30 Art 200062 mat :

search over 'string' key Maya : col 1 : 12 mat idxkey data key col FindIdx : 21 sys

idxkey data idxkey 11 el row 21 sys 3 Maya 12 mat Maya 4012 mat 21 sys

Brute force search successive Max(col,■)

Explode Lorentz data set

XY 0.1 6.905 0.3 10.567 0.5 18.504 0.7 39.878 0.8 64.004 0.9 101.6 1 126.706 1.1 101.822 1.2 64.451 1.3 40.556 1.5 19.673 1.7 12.293 1.9 9.293 3 15.124 3.2 21.711 3.4 34.35 3.6 60.908 3.7 84.199 3.8 116.214 3.9 150.8 4 167.442 4.1 150.756 4.2 116.126 4.3 84.065 4.4 60.726 4.6 34.065 4.8 21.306 5 14.572 5.5 7.542 6 5.847 6.5 10.223 6.7 22.186 6.8 42.04 6.9 101.908 7 201.789 7.1 101.681 7.2 41.582 7.3 21.492 7.5 9.026 7.7 6.026 8 3.014 8.5 1.711 9 1.175 9.5 0.883 10 0.699 452 mat :

U XY 115 range 2 el : V XY 125 range 2 el : Z XY 1 XY rows range 2 el : 31 mat

Observe ... If the matrix 'XY' has more cols, search respectively [U,V,Z]. Not yet click/click/done ! ! !

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

XY U Max 2 FindIdx XY V Max 2 FindIdx XY Z Max 2 FindIdx 31 mat 7 126.706 12 mat 21 167.442 12 mat 35 201.789 12 mat 31 mat

MaxLorentz 7 126.706 12 mat 21 167.442 12 mat 35 201.789 12 mat 31 mat ≡

FindIdx(V,key,col)... applied to project

Unknown Projet Smath Forum

P.2ном 11 :

cosφ 0.88 :

f.c 50 :

I.1ном 21.4 :

λ.k 3.5 :

p.n 1 :

n.ном 2905 :

i.п 7.5 :

η 0.894 :

n.max 4000 :

ω.ном π 30 / n.ном * : М.ном 1000 P.2ном * ω.ном / : 21 sys 304.21 36.16 21 sys

M.к λ.k М.ном * : n.0 60 f.c * p.n / : 21 sys 126.56 300021 sys

ω.0 π 30 / n.0 * : I.пуск I.1ном i.п * : s.н n.0 n.ном - n.0 / : s.к s.н λ.k λ.k 2^1 - sqrt + (* : ω.к ω.0 1 s.к - (* : 51 sys 314.16 160.5 0.03 0.22 245.97 51 sys

s 0.01 1 0.011 range :

s M 2 M.к * s s.к / s.к s / + / :

s ω ω.0 1 s - (* :

s 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019 101 mat

s ω 311.018 310.704 310.389 310.075 309.761 309.447 309.133 308.819 308.504 308.19 101 mat

s M vectorize 11.637 12.795 13.951 15.106 16.259 17.409 18.558 19.704 20.848 21.989 101 mat

y s M vectorize :

x s ω :

data y x augment :

data rows 991

store/isolate data data eval :

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

All values project

data data rows row 52.4659 012 mat

data 1 col Max 126.5569

data 1 row 11.637 311.0177 12 mat

sanity √ data 207 row data 208 row data 209 row 31 sys 126.5555 246.3009 12 mat 126.5569 245.9867 12 mat 126.5557 245.6725 12 mat 31 sys

# # # FindIdx

key data 1 col Max : col 1 : 12 mat

idxkey data 1 col key col FindIdx :

row of Max(X) idxkey 208 126.5569 12 mat

XY data idxkey 11 el row : 126.6 24612 mat

Length ... Width H.L 16 : H.W 10 : 12 mat

XY XY eval :

Arrow in there

SP.x SP.y L.v α Arrow 00 L.v 0 L.v H.L - H.W 2 / L.v H.L - H.W 2 / - L.v 052 mat α rot * (SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y 52 mat + :

α rot α cos α sin α sin - α cos 22 mat :

pilot from command line arrow 0311 126.6 0 ° * Arrow :

j 600 :

xy data j 1 el data j 2 el augment :

data value(s) 'J' explorer xy xy eval :

xy 80.04 122.84 12 mat

data arrow XY 1 1 el 400 XY 1 1 el 0 2 2 mat XY 1 1 el XY 1 2 el + 50 black 1 5 mat 4 1 sys data arrow XY xy 4 1 sys

126.6 24612 mat

data Σ Finite differences Cumul Integration Y 0 : 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 71 line :

Σ

Σ data Σ :

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X 1 deriv * augment 101 line :

D data Deriv :

Scalar piecewise interpolation ...

sub_1 data 1208 range 12 range el : 11 mat sub_2 data 209 data rows range 12 range el : ux sub_1 1 col : uy sub_1 2 col : 12 mat vx sub_2 1 col : vy sub_2 2 col : 12 mat x f ux uy x ainterp : x Φ vx vy x ainterp : x λ1 1 11.64 x ≤ (x 126.6 ≤ (& cases : x λ2 1 x 126.6 ≤ (x 52.5 ≥ (& cases : 81 sys

sub_1 sub_2 2 1 sys

x f x λ1 * x 11.64 126.6 int 33482

x Φ x λ2 * x 52.5 126.6 int #

u 96 : u f 12 mat v 72 : v Φ 12 mat 21 mat 96 282.84 12 mat 72 95.74 12 mat 21 mat

Bivalent interpolation wrt [u, v] ... ►

x f x λ1 * x Φ x λ2 * arrow u u f + 20 black 1 5 mat v v Φ + 20 black 1 5 mat 5 1 sys

126.6 24612 mat

Scalar derivative(s) is NOT directly possible f(x) & Φ(x) are not Smath symbolic. In lieu, transit via infinitesimal analysis.

h 0.01 :

x f x f x λ1 * : x h f D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / : 21 sys

x f x Φ x λ2 * : x h f D2 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / : 21 sys

Infinitesimal derivatives ... wrt piecewise project values .

x h f D1 x h f D2 11.64 2 11.64 2 - 2 2 mat 52.5 10 52.5 5 - 2 2 mat 126.6 0 + 200 black 1 5 mat 5 1 sys

contour data :

XY 126.6 24612 mat :

τ 1 contour rows range :

t NX contour 1 col t el : t NY contour 2 col t el : 12 mat

t 1 ≡ path t NX t NY 1 2 mat : path path t NX t NY 1 2 mat stack : if XY 1 1 el XY 1 2 el + 40 red 1 5 mat 2 1 sys

jmG: 20230218