Fitting polynôme à deux variables par the physist - page 1

Bonjour,

Je dispose des données suivantes (y, d, T) te je souhaite trouver un modèle (polynôme) mathématique y=f(d,T) pour fitter ces data.

Rq: Voici un modèle sur lequel je travaillais (sous python),

def y(X, a1, a2, a3, a4, a5, a6, a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44):

T, d =X

g0 = a1 + a2/d + a3/d**2 + a4/d**3 + a5/d**4 + a6/d**5

g1 = a11*T**(-1) +a12*T**(-1)/d +a13*T**(-1)/d**(2) +a14*T**(-1)/d**(3)

g2 = a21*T**(-2) +a22*T**(-2)/d +a23*T**(-2)/d**(2) +a24*T**(-2)/d**(3)

g3 = a31*T**(-3) +a32*T**(-3)/d +a33*T**(-3)/d**(2) +a34*T**(-3)/d**(3)

g4 = a41*T**(-4) +a42*T**(-4)/d +a43*T**(-4)/d**(2) +a44*T**(-4)/d**(3)

return g0 + g1 + g2 + g3 + g4

C'est plutôt ok dans l'espace (y, d) mais pas trop dans l'espace (y, T)

Merci de votre précieuse aide!!

Voici les données:

T, d, y

1.5, 0.005, 6.351541921250011

1.5, 0.01, 3.679755726250005

1.5, 0.02, 2.345516219375003

1.5, 0.03, 1.8954071543750017

1.5, 0.04, 1.7098251931250013

1.5, 0.4, 1.078458044375

1.5, 0.45, 1.069405534375

1.5, 0.5, 1.0623397275000002

1.5, 0.65, 1.0502433668749998

1.5, 0.7, 1.049157990625

1.5, 0.75, 1.04903245125

1.5, 0.8, 1.049837563125

1.5, 0.85, 1.0513933406250002

1.5, 0.9, 1.0539067481250002

1.5, 0.95, 1.0572572906250002

1.6, 0.005, 6.445032418750009

1.6, 0.01, 3.7247316156250045

1.6, 0.02, 2.3577017062500025

1.6, 0.03, 1.9121623450000018

1.6, 0.04, 1.6863705825000013

1.6, 0.05, 1.5503948100000011

1.6, 0.06, 1.4631177987500008

1.6, 0.07, 1.4126009575000007

1.6, 0.08, 1.3649939900000005

1.6, 0.1, 1.2961869581250005

1.6, 0.15, 1.2008694875000003

1.6, 0.2, 1.1523014312500004

1.6, 0.25, 1.1226564531250003

1.6, 0.3, 1.1032209625000002

1.6, 0.35, 1.0889277512500002

1.6, 0.4, 1.0776994968750002

1.6, 0.45, 1.069156563125

1.6, 0.5, 1.0622608175

1.6, 0.55, 1.057206124375

1.6, 0.65, 1.0518096350000001

1.6, 0.7, 1.0507223206249998

1.6, 0.75, 1.0506033918750002

1.6, 0.8, 1.05136237

1.6, 0.85, 1.0528515818750002

1.6, 0.9, 1.055185629375

1.6, 0.95, 1.058414321875

1.7, 0.005, 6.492766285000009

1.7, 0.01, 3.758106689375004

1.7, 0.02, 2.386983729375002

1.7, 0.03, 1.9245021268750016

1.7, 0.04, 1.6954211456250015

1.7, 0.05, 1.557137534375001

1.7, 0.06, 1.4659704493750008

1.7, 0.07, 1.4007398081250009

1.7, 0.08, 1.3529350368750006

1.7, 0.1, 1.2875036750000008

1.7, 0.15, 1.1976133862500005

1.7, 0.2, 1.1504827031250002

1.7, 0.25, 1.12167269625

1.7, 0.3, 1.1022904868750003

1.7, 0.35, 1.0878816293750002

1.7, 0.4, 1.0774104543750003

1.7, 0.45, 1.0691026512500001

1.7, 0.5, 1.062884313125

1.7, 0.52, 1.0608710606250003

1.7, 0.55, 1.058345080625

1.7, 0.65, 1.0531854656250002

1.7, 0.7, 1.052199821875

1.7, 0.75, 1.051943620625

1.7, 0.8, 1.052620544375

1.7, 0.85, 1.0541000768750002

1.7, 0.9, 1.05631487

1.7, 0.95, 1.05929043375

1.8, 0.005, 6.6032359450000095

1.8, 0.01, 3.7976427093750047

1.8, 0.02, 2.394871319375002

1.8, 0.03, 1.9339593700000015

1.8, 0.04, 1.7044863400000012

1.8, 0.05, 1.564160570000001

1.8, 0.06, 1.471654300625001

1.8, 0.07, 1.4055483262500008

1.8, 0.08, 1.3551611193750006

1.8, 0.1, 1.2866902225000008

1.8, 0.15, 1.1947808175000003

1.8, 0.2, 1.1487626400000002

1.8, 0.25, 1.1209453112500003

1.8, 0.3, 1.101530404375

1.8, 0.35, 1.0877397181250004

1.8, 0.4, 1.0775358275000002

1.8, 0.45, 1.0696785181250001

1.8, 0.5, 1.06387984875

1.8, 0.55, 1.0593716574999998

1.8, 0.65, 1.0543139968750002

1.8, 0.7, 1.0532613087500002

1.8, 0.75, 1.053163918125

1.8, 0.8, 1.0538122268749999

1.8, 0.85, 1.0550931425

1.8, 0.9, 1.05722411125

1.9, 0.005, 6.656480071250009

1.9, 0.01, 3.832839105000004

1.9, 0.02, 2.419435661875002

1.9, 0.03, 1.9446313550000016

1.9, 0.04, 1.7108280781250012

1.9, 0.05, 1.5697103306250009

1.9, 0.06, 1.4765907075000007

1.9, 0.07, 1.4089572318750005

1.9, 0.08, 1.3588533962500007

1.9, 0.1, 1.2886989668750006

1.9, 0.15, 1.1952353350000005

1.9, 0.2, 1.1488010762500003

1.9, 0.25, 1.1207031531250002

1.9, 0.3, 1.1016840056250001

1.9, 0.35, 1.0880953900000003

1.9, 0.4, 1.078200608125

1.9, 0.45, 1.070492690625

1.9, 0.5, 1.064741309375

1.9, 0.55, 1.060532074375

1.9, 0.65, 1.0555098706250001

1.9, 0.7, 1.0543690518750002

1.9, 0.75, 1.054136331875

1.9, 0.8, 1.054667506875

1.9, 0.85, 1.0559537618750001

1.9, 0.9, 1.058167804375

1.9, 0.95, 1.06084372625

2.0, 0.005, 6.6950006562500075

2.0, 0.01, 3.8373007200000036

2.0, 0.02, 2.430107680625002

2.0, 0.03, 1.9567370375000013

2.0, 0.04, 1.7150070468750012

2.0, 0.05, 1.576639463125001

2.0, 0.1, 1.2911291056250005

2.0, 0.2, 1.149635881875

2.0, 0.3, 1.1023993493750002

2.0, 0.4, 1.0788663956250002

2.0, 0.5, 1.065718833125

2.0, 0.6, 1.058550673125

2.0, 0.65, 1.05642703

2.0, 0.7, 1.05528647375

2.0, 0.75, 1.055066970625

2.0, 0.8, 1.0555202775

2.0, 0.85, 1.0567080406250002

2.0, 0.9, 1.0586962343750002

3.0, 0.005, 7.049750107500005

3.0, 0.01, 4.016296978125003

3.0, 0.02, 2.5170094187500016

3.0, 0.03, 2.012995694375001

3.0, 0.04, 1.7612487693750007

3.0, 0.05, 1.6108346393750006

3.0, 0.1, 1.3090674962500002

3.0, 0.2, 1.158725885625

3.0, 0.3, 1.1093815837500003

3.0, 0.4, 1.0853732150000002

3.0, 0.5, 1.0721743831250001

3.0, 0.6, 1.0646515275000001

3.0, 0.65, 1.06238323625

3.0, 0.7, 1.061092145625

3.0, 0.75, 1.06033652125

3.0, 0.8, 1.0602190412499999

3.0, 0.85, 1.060658163125

3.0, 0.9, 1.06159375625

4.0, 0.005, 7.2074144737500045

4.0, 0.01, 4.106390920625002

4.0, 0.02, 2.560247993750001

4.0, 0.03, 2.040396855000001

4.0, 0.04, 1.7822926581250007

4.0, 0.05, 1.6280526356250005

4.0, 0.1, 1.3176889037500001

4.0, 0.2, 1.1637171843750003

4.0, 0.3, 1.1130651281250001

4.0, 0.4, 1.088656450625

4.0, 0.5, 1.0751258587499999

4.0, 0.6, 1.067265088125

4.0, 0.65, 1.064874729375

4.0, 0.7, 1.0632104525

4.0, 0.75, 1.0621684875000001

4.0, 0.8, 1.06157615

4.0, 0.85, 1.0615347525

4.0, 0.9, 1.061794515625

Fitting polynôme à deux variables

Fitting polynôme à deux variables

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