Régression parabolique non triviale

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leon1789
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Re: régression parabolique non triviale

par leon1789 » 07 Juil 2023, 21:56

PS. C'est marrant, un clown (déjà mentionné durant ces pages) dont les remarques pseudo-mathématiques le rapprochent d'un simple perroquet, ne comprenant absolument rien au présent sujet, se permet comme à son habitude de critiquer des échanges sur ce forum , alors qu'il ne sait pas lire la moindre explication mathématique. Il connaîtrait même Sylvain, et le qualifie de personne "pas vraiment sympathique". C'est dire sa piètre mentalité .

Clairement incapable de tracer la moindre parabole, il se croit "meilleur que meilleur" (sic). Un vendeur d'intelligence qui n'en a pas un échantillon sur lui, disait Coluche.
Et comme on peut s'en douter, il n'a aucune idée de ce qu'est la "recherche", il n'a pas la moindre réflexion qui ne soit pas absurde à l'évidence. Quand on est d'une telle incompétence en analyse et en géométrie (*), on évite de le montrer en étalant ses bêtises... enfin, les gens normaux évitent...

(*) cf une histoire récente d'un vecteur qui n'existe pas, ou plutôt nul par permutation, etc. des démonstrations ridiculement bidons mais à mourir de rire. Bien pire que ChatGPT. Heureusement que les étudiants font nettement mieux... remarque, eux ont étudié un peu de maths, et ne prétendent pas avoir les maths infuses.



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leon1789
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Re: régression parabolique non triviale

par leon1789 » 08 Juil 2023, 07:06

Pour une branche seulement
Code: Tout sélectionner
[206.8,298.6]
[206.9,298.6]
[207,298.6]
[207.1,298.6]
[207.2,298.6]
[207.3,298.6]
[207.4,298.6]
[207.5,298.6]
[207.6,298.6]
[207.7,298.6]
[207.8,298.6]
[207.9,298.6]
[208,298.6]
[208.1,298.6]
[208.2,298.6]
[208.3,298.6]
[208.4,298.6]
[208.5,298.6]
[208.6,298.6]
[208.7,298.6]
[208.8,298.6]
[208.9,298.6]
[209,298.6]
[209.1,298.6]
[209.2,298.6]
[209.3,298.6]
[209.4,298.6]
[209.5,298.6]
[209.6,298.6]
[209.7,298.6]
[209.8,298.6]
[209.9,298.6]
[210,298.6]
[204.3,298.7]
[204.4,298.7]
[204.5,298.7]
[204.6,298.7]
[204.7,298.7]
[204.8,298.7]
[204.9,298.7]
[205,298.7]
[212.9,298.7]
[213,298.7]
[213.1,298.7]
[213.2,298.7]
[213.3,298.7]
[213.4,298.7]
[213.5,298.7]
[213.6,298.7]
[203.2,298.8]

sommet en (200,300)
Image

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leon1789
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Re: régression parabolique non triviale

par leon1789 » 08 Juil 2023, 08:54

leon1789 a écrit:En fait, a²+b²=1 n'est pas la bonne contrainte pour minimiser. Comme ni a ni b ne peuvent être nuls, j'ai pris ab=1 , et là, les formules sont plus simples et les résultats absolument corrects sur tous les exemples donnés par Sylvain.


Ben314 a écrit:Tu as une idée de pourquoi ça marche mieux ?
Sachant que, le cas , signifie qu'on considère que la distance de à la parabole est alors que le cas signifie que la distance est .

Dans un cas comme dans l'autre, je vois pas bien à quoi ça correspond géométriquement . . .


Une explication :
pour la parabole et un point du plan, on pose la "distance" :


Cette distance est compatible avec les homothéties (centrées en (0,0) ) : si on fait agir une homothétie de rapport h>0 sur le plan, alors les distances habituelles associées à une norme (dont la distance euclidienne) sont multipliées par h. Et c'est exactement ce qui ce passe avec cette distance :
via l'homothétie, l'image du point est et
l'image de la parabole est avec .
Alors
la distance est multipliée par h.


Sauf erreur de ma part, il n'y a pas cette compatibilité avec .



P.S Je précise pour notre clown dlz qui se complet dans son incompétence qu'on essaie de trouver une rotation et une homothétie appliquée à la parabole y=x² depuis le début de cette recherche.
Modifié en dernier par leon1789 le 08 Juil 2023, 10:29, modifié 1 fois.

sylvain231
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Re: régression parabolique non triviale

par sylvain231 » 08 Juil 2023, 10:28

vous avez vu le spam ?
Léon ta fonction à minimiser :
f := ( E40*E02 )^(1/2) - E21 :
n'est pas fonction de t ?! à moins que tu fasses une rotation sur les points avant le calcul des E est-ce le cas ?

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leon1789
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Re: régression parabolique non triviale

par leon1789 » 08 Juil 2023, 10:30

sylvain231 a écrit:vous avez vu le spam ?

oui.

sylvain231 a écrit:Léon ta fonction à minimiser :
f := ( E40*E02 )^(1/2) - E21 :
n'est pas fonction de t ?! à moins que tu fasses une rotation sur les points avant le calcul des E est-ce le cas ?

si si bien sûr, elle est fonction de t : oui, on fait rotation sur les points avant le calcul des E, c'est écrit bien Xt et Yt... comme avec les méthodes précédentes :)

Et attention, on minimise pour t variant dans ] -Pi ; Pi ]
(avant, pour des raisons de symétrie, on étudiait sur ]0 ; Pi] )

sylvain231
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Re: régression parabolique non triviale

par sylvain231 » 08 Juil 2023, 10:39

c'est bon entre temps je l'ai vu et codé, ça marche, bravo !

sylvain231
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Re: régression parabolique non triviale

par sylvain231 » 08 Juil 2023, 10:42

C’est la meilleure méthode proposée elle a marché sur tous mes exemples cet après-midi je testerai sur plus d’exemples

sylvain231
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Re: régression parabolique non triviale

par sylvain231 » 08 Juil 2023, 11:28

ah pour une parabole avec un a très petit (ici a=0.0001) ça me met une parabole étroite au lieu de plate, voici mes points :

Code: Tout sélectionner
points.size()=1007
[497.631, 255.157]
[503.359, 254.141]
[497.888, 253.509]
[493.589, 258.192]
[496.202, 253.424]
[495.619, 258.24]
[493.263, 256.382]
[492.04, 259.569]
[499.334, 256.74]
[497.993, 257.858]
[496.278, 258.098]
[490.201, 254.982]
[490.39, 260.723]
[488.745, 260.684]
[487.858, 260.99]
[492.606, 253.344]
[495.023, 258.722]
[485.967, 254.538]
[487.623, 262.591]
[490.908, 257.983]
[489.73, 260.827]
[489.848, 257.103]
[485.578, 256.701]
[483.454, 253.479]
[487.241, 257.117]
[488.737, 253.857]
[488.743, 261.499]
[482.733, 259.321]
[485.325, 261.037]
[489.169, 254.09]
[488.604, 260.495]
[482.177, 258.011]
[479.972, 257.468]
[484.961, 260.626]
[485.407, 258.468]
[485.073, 257.976]
[479.396, 259.544]
[475.753, 261.981]
[476.447, 261.182]
[481.505, 261.713]
[476.435, 257.573]
[474.928, 257.203]
[474.836, 256.305]
[475.103, 257.248]
[480.948, 260.885]
[471.88, 263.858]
[479.434, 254.424]
[474.246, 260.146]
[474.795, 261.384]
[472.412, 260.74]
[475.178, 256.146]
[474.859, 259.407]
[474.862, 256.752]
[469.612, 262.208]
[468.494, 261.808]
[472.239, 264.546]
[470.447, 264.177]
[473.816, 262.223]
[465.686, 256.034]
[467.863, 260.653]
[469.159, 262.53]
[471.448, 255.104]
[467.2, 256.161]
[472.352, 261.99]
[463.624, 255.364]
[468.32, 256.043]
[464.774, 260.147]
[463.431, 262.606]
[463.542, 261.522]
[464.25, 263.58]
[467.347, 261.592]
[459.016, 259.354]
[462.642, 259.838]
[457.897, 258.304]
[464.12, 264.225]
[457.009, 262.025]
[457.282, 258.723]
[465.516, 261.615]
[460.602, 264.702]
[461.331, 256.572]
[458.457, 259.011]
[461.855, 263.855]
[455.45, 258.094]
[456.225, 257.226]
[457.215, 266.391]
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[457.223, 259.364]
[453.666, 262.644]
[454.327, 259.248]
[449.301, 260.263]
[453.028, 264.459]
[453.129, 266.501]
[453.59, 266.751]
[452.022, 266.993]
[454.098, 257.682]
[452.525, 266.694]
[448.595, 257.837]
[452.26, 263.615]
[446.588, 262.454]
[449.231, 261.533]
[454.176, 266.596]
[444.016, 264.101]
[443.667, 263.491]
[451.032, 260.279]
[447.414, 264.161]
[447.37, 262.236]
[442.262, 259.315]
[443.769, 265.607]
[446.795, 266.361]
[448.584, 265.211]
[449.257, 258.104]
[444.866, 262.892]
[443.572, 264.19]
[438.898, 262.16]
[446.387, 264.191]
[444.072, 262.558]
[446.883, 265.381]
[442.308, 265.649]
[438.755, 267.014]
[442.479, 262.157]
[445.45, 267.54]
[442.284, 259.702]
[438.35, 264.076]
[443.795, 263.91]
[437.071, 264.587]
[435.785, 260.858]
[437.325, 268.283]
[437.88, 263.816]
[435.089, 264.822]
[436.971, 266.641]
[433.49, 264.572]
[435.938, 266.237]
[432.95, 267.94]
[434.897, 261.292]
[434.796, 269.459]
[433.642, 263.813]
[435.988, 261.832]
[432.175, 261.207]
[428.466, 269.174]
[428.962, 260.459]
[426.487, 262.805]
[432.739, 262.259]
[427.945, 265.562]
[429.594, 267.605]
[429.507, 263.225]
[430.774, 263.455]
[426.822, 262.091]
[432.026, 264.403]
[429.734, 267.384]
[422.577, 261.998]
[430.522, 267.878]
[422.759, 269.198]
[420.887, 267.167]
[423.908, 265.17]
[421.661, 268.841]
[421.244, 266.044]
[419.768, 270.037]
[425.89, 267.571]
[417.398, 263.353]
[420.135, 266.919]
[422.724, 262.057]
[424.606, 270.291]
[424.15, 262.176]
[424.053, 263.169]
[420.189, 270.16]
[415.028, 266.116]
[422.302, 262.151]
[415.02, 268.785]
[412.588, 271.636]
[418.992, 261.944]
[412.517, 270.564]
[413.105, 267.783]
[411.752, 264.952]
[412.671, 263.245]
[410.462, 271.85]
[413.886, 262.529]
[411.246, 270.217]
[411.043, 262.826]
[409.904, 262.916]
[406.337, 264.32]
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[412.387, 263.535]
[412.508, 269.3]
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[394.716, 269.01]
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[393.708, 264.439]
[400.075, 273.023]
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[395.563, 271.106]
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[383.394, 271.033]
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[381.219, 267.192]
[377.284, 275.629]
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[380.979, 273.302]
[379.109, 273.636]
[375.309, 271.063]
[369.978, 272.89]
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[370.98, 272.977]
[368.337, 275.851]
[376.807, 273.881]
[370.499, 272.878]
[373.986, 277.551]
[375.807, 275.499]
[366.809, 268.896]
[374.533, 270.19]
[367.372, 268.373]
[366.609, 276.392]
[368.374, 270.408]
[366.388, 272.002]
[363.723, 272.188]
[370.796, 270.9]
[367.637, 274.463]
[364.494, 278.072]
[360.725, 274.245]
[362.874, 269.645]
[366.19, 275.185]
[360.764, 276.279]
[359.723, 271.036]
[365.011, 269.848]
[366.72, 273.6]
[357.22, 271.33]
[356.781, 275.39]
[356.444, 269.71]
[364.52, 270.798]
[361.149, 277.38]
[361.7, 275.042]
[360.282, 275.564]
[361.373, 269.745]
[354.978, 277.93]
[360.781, 278.35]
[360.982, 273.327]
[353.306, 276.883]
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[357.134, 271.046]
[353.238, 279.102]
[349.437, 279.964]
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[351.121, 271.763]
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[349.887, 278.485]
[345.898, 280.595]
[348.57, 281.283]
[348.628, 276.215]
[341.936, 271.899]
[340.722, 276.266]
[348.777, 279.718]
[345.241, 276.223]
[347.568, 272.469]
[343.144, 276.647]
[344.331, 276.383]
[343.102, 279.756]
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[345.128, 272.684]
[336.269, 273.902]
[340.585, 274.137]
[336.304, 280.821]
[337.709, 273.345]
[341.032, 279.655]
[336.392, 276.457]
[337.134, 279.795]
[341.322, 281.041]
[335.057, 273.222]
[332.774, 282.665]
[333.273, 281.072]
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[331.536, 281.483]
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[330.149, 281.413]
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[333.246, 279.03]
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[332.185, 274.177]
[328.617, 282.203]
[327.832, 280.471]
[330.955, 278.49]
[329.614, 274.942]
[325.607, 275.164]
[325.97, 281.388]
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[326.723, 281.08]
[328.741, 283.383]
[331.548, 280.948]
[330.293, 276.055]
[322.828, 280.864]
[328.086, 283.969]
[326.083, 275.049]
[320.112, 281.085]
[324.293, 283.956]
[322.663, 280.635]
[322.726, 277.292]
[321.979, 275.578]
[319.291, 282.423]
[321.225, 283.248]
[317.928, 278.033]
[323.562, 276.614]
[323.388, 280.562]
[321.169, 282.048]
[317.454, 284.883]
[315.308, 276.196]
[322.719, 283.093]
[317.523, 284.341]
[315.273, 283.003]
[316.193, 278.469]
[317.266, 282.453]
[317.891, 278.341]
[317.266, 277.246]
[315.444, 279.247]
[316.496, 285.617]
[315.659, 277.562]
[315.262, 280.137]
[315.975, 277.686]
[309.732, 277.452]
[308.966, 279.582]
[316.611, 277.758]
[314.048, 281.151]
[309.274, 277.752]
[315.182, 277.144]
[313.307, 279.785]
[307.25, 286.623]
[309.27, 285.239]
[304.688, 285.468]
[302.512, 285.964]
[302.539, 280.845]
[301.794, 278.941]
[303.422, 279.842]
[303.756, 284.019]
[304.329, 278.525]
[302.52, 282.51]
[302.2, 283.533]
[304.546, 278.015]
[305.169, 287.229]
[306.534, 284.012]
[297.323, 285.701]
[298.562, 281.121]
[296.651, 283.33]
[299.899, 284.953]
[295.614, 287.294]
[302.793, 281.862]
[300.152, 287.036]
[298.793, 286.802]
[292.531, 284.24]
[295.013, 288.051]
[297.468, 281.56]
[300.217, 285.608]
[296.916, 284.034]
[295.84, 282.903]
[294.692, 282.679]
[291.201, 283.703]
[296.375, 287.509]
[294.132, 286.789]
[289.641, 285.81]
[288.676, 281.235]
[290.841, 287.125]
[287.236, 281.521]
[293.556, 282.446]
[286.365, 280.708]
[285.717, 281.799]
[293.038, 286.04]
[290.117, 280.83]
[292.463, 285.766]
[289.929, 282.065]
[285.481, 288.654]
[289.735, 283.368]
[289.268, 288.305]
[284.285, 288.639]
[288.277, 288.679]
[282.977, 288.604]
[281.305, 285.169]
[279.251, 284.565]
[282.598, 287.541]
[287.74, 283.338]
[278.215, 290.376]
[280.925, 281.596]
[283.871, 282.661]
[277.575, 286.993]
[280.193, 287.788]
[282.894, 290.042]
[284.05, 288.83]
[283.225, 289.175]
[275.635, 283.187]
[276.67, 290.052]
[277.953, 288.969]
[280.131, 286.733]
[273.151, 282.22]
[276.001, 288.101]
[274.428, 290.932]
[274.887, 283.078]
[273.487, 290.949]
[275.077, 283.486]
[277.222, 287.027]
[276.774, 282.91]
[273.33, 290.018]
[270.059, 289.691]
[268.483, 291.14]
[269.809, 285.497]
[272.903, 285.243]
[270.715, 286.049]
[268.695, 285.16]
[265.523, 288.479]
[266.155, 287.734]
[268.544, 283.56]
[268.833, 287.326]
[266.877, 288.085]
[268.31, 293.228]
[267.795, 292.998]
[268.811, 284.545]
[263.518, 293.096]
[266.547, 292.943]
[262.94, 287.917]
[262.3, 289.066]
[262.07, 286.228]
[262.521, 291.954]
[265.282, 291.741]
[260.711, 292.756]
[258.088, 289.377]
[265.18, 291.516]
[264.119, 287.919]
[255.933, 293.502]
[256.444, 288.39]
[259.645, 285.093]
[260.555, 292.616]
[262.139, 292.482]
[253.872, 290.828]
[262.205, 287.177]
[256.389, 291.203]
[256.552, 290.939]
[252.915, 289.815]
[260.528, 291.995]
[255.735, 293.542]
[256.026, 295.282]
[248.901, 290.7]
[251.742, 286.745]
[249.533, 286.519]
[249.203, 294.253]
[250.24, 289.024]
[254.109, 291.89]
[248.073, 292.217]
[254.669, 294.263]
[245.957, 287.527]
[253.244, 287.973]
[246.054, 295.128]
[243.919, 294.703]
[245.274, 296.551]
[247.941, 296.696]
[241.23, 288.274]
[246.899, 294.179]
[246.403, 292.614]
[247.694, 296.181]
[247.699, 297.21]
[242.744, 296.997]
[245.724, 295.613]
[243.189, 289.552]
[241.647, 297.269]
[242.147, 288.76]
[234.9, 288.645]
[235.923, 296.463]
[241.423, 296.959]
[238.467, 290.184]
[241.445, 293.258]
[232.839, 298.235]
[240.443, 291.133]
[234.002, 296.013]
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[231.769, 293.971]
[236.707, 298.747]
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[234.19, 293.119]
[231.321, 298.354]
[232.669, 296.386]
[235.427, 297.607]
[229.772, 298.567]
[226.886, 291.23]
[229.35, 291.921]
[226.034, 294.551]
[229.494, 293.682]
[226.188, 292.505]
[228.892, 294.775]
[223.063, 292.024]
[231.773, 293.839]
[223.54, 292.553]
[230.367, 291.473]
[222.405, 291.918]
[219.922, 294.888]
[221.907, 292.057]
[221.883, 300.283]
[220.547, 299.37]
[218.08, 298.288]
[225.272, 294.926]
[223.904, 292.647]
[220.027, 291.561]
[222.695, 295.582]
[223.872, 292.296]
[215.866, 299.314]
[217.52, 294.015]
[218.701, 300.741]
[217.831, 301.288]
[219.99, 299.216]
[215.778, 299.833]
[220.036, 293.037]
[212.529, 297.327]
[216.087, 301.476]
[212.583, 301.865]
[215.319, 301.993]
[214.173, 301.272]
[219.102, 300.183]
[214.073, 299.934]
[215.057, 294.462]
[208.238, 301.337]
[210.314, 300.901]
[212.679, 297.312]
[215.934, 298.285]
[207.164, 301.076]
[207.752, 297.985]
[208.949, 294.848]
[205.626, 293.968]
[213.656, 299.751]
[212.023, 300.962]
[203.773, 299.793]
[206.552, 299.158]
[206.894, 298.219]
[204.111, 297.552]
[207.105, 300.379]
[206.411, 299.217]
[202.668, 294.951]
[204.691, 296.237]
[203.909, 301.503]
[199.448, 303.709]
[203.695, 299.149]
[200.588, 295.488]
[202.491, 299.489]
[198.274, 301.105]
[198.811, 301.879]
[202.555, 295.047]
[196.095, 300.012]
[202.726, 300.641]
[195.172, 299.741]
[198.24, 299.34]
[199.084, 304.415]
[194.418, 304.741]
[195.68, 303.638]
[192.946, 296.897]
[199.259, 300.476]
[198.884, 299.933]
[192.024, 302.206]
[194.165, 305.693]
[194.129, 304.55]
[190.511, 304.009]
[197.408, 305.77]
[196.606, 300.919]
[192.403, 297.924]
[190.075, 305.991]
[190.204, 298.308]
[194.653, 304.582]
[193.791, 299.121]
[187.775, 300.926]
[193.312, 297.946]
[185.044, 303.109]
[189.226, 303.046]
[186.874, 300.468]
[191.52, 300.469]
[189.091, 303.011]
[188.621, 299.853]
[181.578, 300.184]
[188.134, 298.448]
[185.982, 305.121]
[186.938, 298.187]
[181.87, 306.011]
[178.296, 301.448]
[182.197, 303.683]
[186.677, 300.631]
[177.14, 299.456]
[182.184, 298.737]
[176.559, 302.819]
[181.026, 300.269]
[183.69, 299.819]
[174.349, 301.567]
[174.989, 301.387]
[173.672, 308.078]
[181.059, 299.695]
[172.432, 304.573]
[173.623, 300.169]
[173.329, 304.277]
[172.756, 306.935]
[170.544, 299.886]
[174.848, 303.889]
[170.274, 301.331]
[173.386, 305.904]
[171.196, 305.923]
[167.904, 300.604]
[173.793, 307.23]
[173.743, 307.117]
[170.006, 307.648]
[174.686, 302.406]
[175.032, 301.634]
[165.937, 303.499]
[169.157, 301.87]
[164.87, 307.274]
[165.166, 306.69]
[164.101, 304.368]
[164.749, 308.805]
[171.245, 309.363]
[164.972, 306.335]
[168.802, 309.187]
[168.782, 303.554]
[162.567, 308.253]
[165.898, 309.499]
[166.572, 309.18]
[161.422, 304.483]
[161.828, 305.342]
[159.357, 310.569]
[163.143, 308.136]
[160.257, 308.448]
[165.433, 304.882]
[156.511, 307.592]
[158.899, 304.331]
[163.44, 308.653]
[161.073, 308.283]
[157.694, 309.468]
[153.651, 311.176]
[155.016, 303.989]
[159.891, 304.481]
[158.206, 310.207]
[159.29, 308.651]
[153.875, 304.439]
[150.289, 309.92]
[159.701, 306.308]
[155.396, 309.84]
[157.809, 303.922]
[153.238, 307.121]
[148.596, 307.55]
[153.928, 310.61]
[154.351, 305.81]
[154.108, 305.144]
[149.882, 307.025]
[145.76, 310.494]
[154.381, 306.286]
[148.117, 305.594]
[144.704, 312.349]
[148.487, 310.777]
[153.101, 307.327]
[147.169, 307.869]
[149.116, 307.697]
[142.776, 312.026]
[151.342, 313.707]
[146.57, 309.771]
[150.176, 305.477]
[142.626, 307.567]
[147.78, 305.172]
[140.138, 310.5]
[144.054, 308.443]
[142.465, 306.778]
[141.653, 307.18]
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[138.653, 308.095]
[140.69, 309.515]
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[136.295, 311.6]
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[135.485, 309.135]
[133.95, 310.411]
[135.52, 310.097]
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[140.094, 309.764]
[132.964, 313.802]
[138.651, 315.607]
[132.028, 307.958]
[137.923, 316.232]
[132.697, 316.495]
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[135.84, 312.906]
[131.686, 312.732]
[133.729, 310.274]
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[132.858, 309.724]
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[126.751, 310.522]
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[126.723, 314.526]
[133.67, 308.866]
[125.543, 313.661]
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[129.806, 313.082]
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[130.518, 315.855]
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[120.004, 316.93]
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[108.342, 318.677]
[108.425, 315.046]
[103.234, 319.434]
[107.767, 316.333]
[105.994, 322.344]
[103.985, 316.058]
[100.362, 318.537]
[106.374, 319.959]
[100.966, 314.317]
[100.493, 317.866]
[103.675, 321.839]
[103.405, 318.112]
[101.87, 317.731]
[95.7213, 319.449]
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[94.5791, 315.459]
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[95.1441, 317.505]
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[95.8019, 315.004]
[96.3825, 324.311]
[93.5689, 321.98]
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[92.1801, 316.063]
[90.5609, 318.951]
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[91.8848, 315.074]
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[92.0748, 322.995]
[93.1653, 319.625]
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[95.1987, 322.452]
[89.2674, 318.771]
[90.287, 324.359]
[87.3501, 316.766]
[92.1371, 317.772]
[91.5138, 317.777]
[90.726, 326.006]
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[82.9778, 318.825]
[87.6078, 323.006]
[83.7911, 326.468]
[89.469, 316.642]
[79.9777, 325.603]
[86.6066, 321.784]
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[80.7296, 318.53]
[78.4589, 326.166]
[80.1921, 322.819]
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[80.566, 324.654]
[84.0559, 320.954]
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[83.0123, 319.896]
[76.0634, 327.357]
[76.457, 324.941]
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[82.2491, 319.641]
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[80.6788, 326.866]
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[69.035, 328.776]
[73.3279, 328.642]
[74.9784, 324.779]
[74.7955, 325.075]
[74.7892, 322.139]
[72.3504, 322.464]
[69.1757, 326.249]
[67.1284, 321.441]
[68.752, 322.24]
[71.27, 324.489]
[69.7961, 327.564]
[63.5517, 329.439]
[66.9211, 327.054]
[65.7198, 320.753]
[66.7986, 330.489]
[66.725, 320.836]
[60.2983, 330.088]
[65.4793, 321.058]
[63.2558, 322.606]
[59.3537, 328.471]
[59.8698, 326.392]
[63.3305, 324.363]
[65.0005, 327.815]
[62.0322, 328.016]
[66.1001, 327.292]
[63.9863, 325.565]
[56.4902, 327.06]
[55.2736, 323.026]
[55.7418, 328.456]
[59.5161, 331.124]
[61.66, 331.51]
[54.6964, 324.807]
[54.3657, 331.142]
[58.5399, 326.014]
[52.4007, 325.188]
[52.6866, 332.568]
[50.86, 324.004]
[54.1347, 330.531]
[53.013, 329.628]
[55.9176, 325.131]
[50.9013, 332.761]
[52.3734, 326.456]
[52.782, 330.984]
[56.0956, 332.737]
[52.6781, 333.131]
[47.4943, 330.713]
[50.4305, 326.658]
[46.4356, 330.796]
[53.0555, 328.652]
[48.2696, 326.925]
[52.5066, 332.563]
[44.3684, 331.067]
[46.9164, 324.859]
[51.3402, 327.499]
[50.0637, 333.048]
[41.5138, 330.175]
[44.5182, 326.418]
[45.5948, 334.592]
[49.6919, 328.22]
[43.5187, 325.401]
[44.5594, 331.235]
[41.1786, 333.006]
[46.2948, 325.572]
[37.7866, 329.591]
[37.8528, 327.161]
[41.3296, 329.282]
[39.0421, 328.528]
[35.6931, 332.517]
[42.2639, 334.275]
[44.5553, 333.232]
[39.0439, 327.077]
[40.0619, 331.302]
[33.8337, 333.217]
[37.0367, 330.14]
[41.4796, 331.251]
[39.1901, 327.864]
[34.4439, 327.27]
[37.6305, 335.006]
[31.772, 328.658]
[36.3871, 327.611]
[38.0825, 331.861]
[34.7624, 328.097]
[31.4108, 329.186]
[32.8153, 327.987]
[36.6738, 337.281]
[36.1999, 330.561]
[35.8161, 334.107]
[26.6251, 335.843]
[32.9929, 333.729]
[29.5477, 337.744]
[34.1616, 328.459]
[27.6138, 337.94]
[26.0397, 331.907]
[30.6383, 332.403]
[29.23, 336.518]
[22.552, 336.31]
[27.6321, 335.998]
[29.6213, 331.018]
[28.9953, 334.652]
[23.3733, 338.283]
[20.8113, 337.699]
[23.412, 329.411]
[19.8333, 333.944]
[19.6974, 332.62]
[19.1734, 332.337]
[24.2804, 335.029]
[24.4558, 338.107]
[23.515, 334.03]
[22.0066, 336.497]
[23.2495, 335.563]
[16.9115, 333.81]
[17.151, 332.476]
[20.8336, 338.795]
[19.182, 338.462]
[21.3213, 334.209]
[16.8254, 332.664]
[19.4921, 335.269]
[10.1489, 336.088]
[17.2006, 340.933]
[18.0415, 339.828]
[11.0189, 338.745]
[11.8319, 339.823]
[8.35535, 336.611]
[11.7628, 336.783]
[6.40407, 333.319]
[8.48504, 333.369]
[7.78602, 332.663]
[5.7849, 333.366]
[6.08961, 337.256]
[10.21, 333.42]
[8.05242, 336.467]
[3.70095, 342.045]
[4.65064, 336.056]
[11.6535, 341.707]
[6.86233, 340.934]
[7.97643, 337.075]
[6.42342, 341.378]
[4.13271, 341.827]
[1.0484, 333.816]
[1.34656, 342.23]
[-1.79737, 341.261]
[0.722635, 337.827]
[-2.26806, 340.932]
[2.12197, 341.487]
[0.504238, 342.843]
[-0.755544, 334.796]
sommet = [200, 300]





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leon1789
Membre Transcendant
Messages: 5486
Enregistré le: 27 Nov 2007, 15:25

Re: régression parabolique non triviale

par leon1789 » 08 Juil 2023, 12:08

ok, t := 0.176 "ancien" a := 0.000099
mais ton exemple est quasiment une droite... :)


Image
Mais ok, tout n'est pas totalement clair encore.
Oui, avec un grand (ie. ancien "a" proche de 0), alors pour tout pas trop grand, le point est estimé (à tort) proche de la parabole . C'est pourquoi on observe une ligne de points derrière le sommet sur l'exemple mal traité.

sylvain231
Membre Relatif
Messages: 307
Enregistré le: 07 Avr 2020, 12:20

Re: régression parabolique non triviale

par sylvain231 » 13 Juil 2023, 15:58

Bonjour Léon,
tu cherches encore ou tu as laissé tomber ?
Merci
Bonne soirée

 

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