- #1
evgenx
- 14
- 0
Analytical form of an "Interpolated" function
Hallo,
I have a question on the use of "Interpolation" function in Mathematica.
I am wondering whether it is possible to extract an analytical expression
for a function built using the "Interpolation" option. Say, I have the following
function of two variable f(x,y) represented on a grid:
Ra=Interpolation[{
{{ 2.777897, 0.000000}, -0.202683},
{{ 2.777897, 0.043633}, -0.203579},
{{ 2.777897, 0.087266}, -0.200988},
{{ 2.777897, 0.130900}, -0.192908},
{{ 2.777897, 0.174533}, -0.176695},
{{ 2.777897, 0.218166}, -0.155857},
{{ 2.777897, 0.261799}, -0.129889},
{{ 2.815692, 0.000000}, -0.202618},
{{ 2.815692, 0.043633}, -0.203585},
{{ 2.815692, 0.087266}, -0.201401},
{{ 2.815692, 0.130900}, -0.194172},
{{ 2.815692, 0.174533}, -0.179481},
{{ 2.815692, 0.218166}, -0.163498},
{{ 2.815692, 0.261799}, -0.140403},
{{ 2.853486, 0.000000}, -0.201962},
{{ 2.853486, 0.043633}, -0.203003},
{{ 2.853486, 0.087266}, -0.201219},
{{ 2.853486, 0.130900}, -0.194830},
{{ 2.853486, 0.174533}, -0.181844},
{{ 2.853486, 0.218166}, -0.170511},
{{ 2.853486, 0.261799}, -0.150171},
{{ 2.891281, 0.000000}, -0.200745},
{{ 2.891281, 0.043633}, -0.201863},
{{ 2.891281, 0.087266}, -0.200472},
{{ 2.891281, 0.130900}, -0.194926},
{{ 2.891281, 0.174533}, -0.184095},
{{ 2.891281, 0.218166}, -0.176901},
{{ 2.891281, 0.261799}, -0.159191},
{{ 2.929075, 0.000000}, -0.198999},
{{ 2.929075, 0.043633}, -0.200197},
{{ 2.929075, 0.087266}, -0.199196},
{{ 2.929075, 0.130900}, -0.194513},
{{ 2.929075, 0.174533}, -0.186552},
{{ 2.929075, 0.218166}, -0.182673},
{{ 2.929075, 0.261799}, -0.167464},
{{ 2.966870, 0.000000}, -0.196757},
{{ 2.966870, 0.043633}, -0.198037},
{{ 2.966870, 0.087266}, -0.197426},
{{ 2.966870, 0.130900}, -0.193666},
{{ 2.966870, 0.174533}, -0.189150},
{{ 2.966870, 0.218166}, -0.187834},
{{ 2.966870, 0.261799}, -0.174997},
{{ 3.004664, 0.000000}, -0.194050},
{{ 3.004664, 0.043633}, -0.195418},
{{ 3.004664, 0.087266}, -0.195205},
{{ 3.004664, 0.130900}, -0.192492},
{{ 3.004664, 0.174533}, -0.191623},
{{ 3.004664, 0.218166}, -0.192395},
{{ 3.004664, 0.261799}, -0.181796},
{{ 3.042459, 0.000000}, -0.190913},
{{ 3.042459, 0.043633}, -0.192374},
{{ 3.042459, 0.087266}, -0.192580},
{{ 3.042459, 0.130900}, -0.191144},
{{ 3.042459, 0.174533}, -0.193806},
{{ 3.042459, 0.218166}, -0.196366},
{{ 3.042459, 0.261799}, -0.187872},
{{ 3.080253, 0.000000}, -0.187381},
{{ 3.080253, 0.043633}, -0.188943},
{{ 3.080253, 0.087266}, -0.189609},
{{ 3.080253, 0.130900}, -0.189813},
{{ 3.080253, 0.174533}, -0.195628},
{{ 3.080253, 0.218166}, -0.199759},
{{ 3.080253, 0.261799}, -0.193240},
{{ 3.118048, 0.000000}, -0.183492},
{{ 3.118048, 0.043633}, -0.185166},
{{ 3.118048, 0.087266}, -0.186363},
{{ 3.118048, 0.130900}, -0.188646},
{{ 3.118048, 0.174533}, -0.197061},
{{ 3.118048, 0.218166}, -0.202589},
{{ 3.118048, 0.261799}, -0.197915},
{{ 3.155842, 0.000000}, -0.179285},
{{ 3.155842, 0.043633}, -0.181090},
{{ 3.155842, 0.087266}, -0.182933},
{{ 3.155842, 0.130900}, -0.187658},
{{ 3.155842, 0.174533}, -0.198096},
{{ 3.155842, 0.218166}, -0.204871},
{{ 3.155842, 0.261799}, -0.201916},
{{ 3.193637, 0.000000}, -0.174801},
{{ 3.193637, 0.043633}, -0.176764},
{{ 3.193637, 0.087266}, -0.179435},
{{ 3.193637, 0.130900}, -0.186750},
{{ 3.193637, 0.174533}, -0.198733},
{{ 3.193637, 0.218166}, -0.206622},
{{ 3.193637, 0.261799}, -0.205261}
}]
Mathematica makes an "Interpolated" function by a polynomial of 3rd or 4th oder out of this.
The question is if there is an elegant option to extract the coefficients of this polynomial
(besides that of taking the 1st, 2nd, etc derivatives of the function, which is quite tedious).
Many thanks!
Hallo,
I have a question on the use of "Interpolation" function in Mathematica.
I am wondering whether it is possible to extract an analytical expression
for a function built using the "Interpolation" option. Say, I have the following
function of two variable f(x,y) represented on a grid:
Ra=Interpolation[{
{{ 2.777897, 0.000000}, -0.202683},
{{ 2.777897, 0.043633}, -0.203579},
{{ 2.777897, 0.087266}, -0.200988},
{{ 2.777897, 0.130900}, -0.192908},
{{ 2.777897, 0.174533}, -0.176695},
{{ 2.777897, 0.218166}, -0.155857},
{{ 2.777897, 0.261799}, -0.129889},
{{ 2.815692, 0.000000}, -0.202618},
{{ 2.815692, 0.043633}, -0.203585},
{{ 2.815692, 0.087266}, -0.201401},
{{ 2.815692, 0.130900}, -0.194172},
{{ 2.815692, 0.174533}, -0.179481},
{{ 2.815692, 0.218166}, -0.163498},
{{ 2.815692, 0.261799}, -0.140403},
{{ 2.853486, 0.000000}, -0.201962},
{{ 2.853486, 0.043633}, -0.203003},
{{ 2.853486, 0.087266}, -0.201219},
{{ 2.853486, 0.130900}, -0.194830},
{{ 2.853486, 0.174533}, -0.181844},
{{ 2.853486, 0.218166}, -0.170511},
{{ 2.853486, 0.261799}, -0.150171},
{{ 2.891281, 0.000000}, -0.200745},
{{ 2.891281, 0.043633}, -0.201863},
{{ 2.891281, 0.087266}, -0.200472},
{{ 2.891281, 0.130900}, -0.194926},
{{ 2.891281, 0.174533}, -0.184095},
{{ 2.891281, 0.218166}, -0.176901},
{{ 2.891281, 0.261799}, -0.159191},
{{ 2.929075, 0.000000}, -0.198999},
{{ 2.929075, 0.043633}, -0.200197},
{{ 2.929075, 0.087266}, -0.199196},
{{ 2.929075, 0.130900}, -0.194513},
{{ 2.929075, 0.174533}, -0.186552},
{{ 2.929075, 0.218166}, -0.182673},
{{ 2.929075, 0.261799}, -0.167464},
{{ 2.966870, 0.000000}, -0.196757},
{{ 2.966870, 0.043633}, -0.198037},
{{ 2.966870, 0.087266}, -0.197426},
{{ 2.966870, 0.130900}, -0.193666},
{{ 2.966870, 0.174533}, -0.189150},
{{ 2.966870, 0.218166}, -0.187834},
{{ 2.966870, 0.261799}, -0.174997},
{{ 3.004664, 0.000000}, -0.194050},
{{ 3.004664, 0.043633}, -0.195418},
{{ 3.004664, 0.087266}, -0.195205},
{{ 3.004664, 0.130900}, -0.192492},
{{ 3.004664, 0.174533}, -0.191623},
{{ 3.004664, 0.218166}, -0.192395},
{{ 3.004664, 0.261799}, -0.181796},
{{ 3.042459, 0.000000}, -0.190913},
{{ 3.042459, 0.043633}, -0.192374},
{{ 3.042459, 0.087266}, -0.192580},
{{ 3.042459, 0.130900}, -0.191144},
{{ 3.042459, 0.174533}, -0.193806},
{{ 3.042459, 0.218166}, -0.196366},
{{ 3.042459, 0.261799}, -0.187872},
{{ 3.080253, 0.000000}, -0.187381},
{{ 3.080253, 0.043633}, -0.188943},
{{ 3.080253, 0.087266}, -0.189609},
{{ 3.080253, 0.130900}, -0.189813},
{{ 3.080253, 0.174533}, -0.195628},
{{ 3.080253, 0.218166}, -0.199759},
{{ 3.080253, 0.261799}, -0.193240},
{{ 3.118048, 0.000000}, -0.183492},
{{ 3.118048, 0.043633}, -0.185166},
{{ 3.118048, 0.087266}, -0.186363},
{{ 3.118048, 0.130900}, -0.188646},
{{ 3.118048, 0.174533}, -0.197061},
{{ 3.118048, 0.218166}, -0.202589},
{{ 3.118048, 0.261799}, -0.197915},
{{ 3.155842, 0.000000}, -0.179285},
{{ 3.155842, 0.043633}, -0.181090},
{{ 3.155842, 0.087266}, -0.182933},
{{ 3.155842, 0.130900}, -0.187658},
{{ 3.155842, 0.174533}, -0.198096},
{{ 3.155842, 0.218166}, -0.204871},
{{ 3.155842, 0.261799}, -0.201916},
{{ 3.193637, 0.000000}, -0.174801},
{{ 3.193637, 0.043633}, -0.176764},
{{ 3.193637, 0.087266}, -0.179435},
{{ 3.193637, 0.130900}, -0.186750},
{{ 3.193637, 0.174533}, -0.198733},
{{ 3.193637, 0.218166}, -0.206622},
{{ 3.193637, 0.261799}, -0.205261}
}]
Mathematica makes an "Interpolated" function by a polynomial of 3rd or 4th oder out of this.
The question is if there is an elegant option to extract the coefficients of this polynomial
(besides that of taking the 1st, 2nd, etc derivatives of the function, which is quite tedious).
Many thanks!