Re: multivariate interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg110931] Re: multivariate interpolation*From*: "Ingolf Dahl" <ingolf.dahl at telia.com>*Date*: Mon, 12 Jul 2010 01:04:55 -0400 (EDT)

Here is my suggestion: Restructure the data matrix in two steps data1 = Flatten[data, 1]; data2 = Table[{{data1[[i, 1]], data1[[i, 2]]}, {data1[[i, 3]], data1[[i, 4]], data1[[i, 5]]}}, {i, Length[data1]}]; The list data2 can be used for interpolation f[a_, b_, x_] := Simplify[Interpolation[data2][a, b]] f[10.45, 0.065, x] gives {1000.67,8.09232*10^7,0.731501-22.7918 Sqrt[1/x]+151.976/x} Was this what you were looking for? I suggest that instead of working with large x, you should work with small y, where x = 1/y^2. The limits will then be very small number instead of very large. It seems plausible that linear interpolation should be more exact for small numbers than for large. x := 1/y^2 data3 = Table[{{data1[[i, 1]], data1[[i, 2]]}, {Sqrt[1./data1[[i, 4]]], Sqrt[1./data1[[i, 3]]], data1[[i, 5]]}}, {i, Length[data1]}] /. {Sqrt[y^2] -> y}; Instead of f we might define g. The first two elements in the result are then the limits for y. g[a_, b_, y_] := Expand[Simplify[Interpolation[data3][a, b]]] g[9., 0.09, y] gives {0.000140028,0.031607,0.651531-21.3675 y+128.192 y^2} I guess that g gives a "better" interpolation than f Best regards Ingolf Dahl http://www.familydahl.se/mathematica > -----Original Message----- > From: Silvio Abruzzo [mailto:silvio.abruzzo at gmail.com] > Sent: den 11 juli 2010 12:20 > To: mathgroup at smc.vnet.net > Subject: [mg110911] multivariate interpolation > > Dear Group, > I have the following problem. I have a matrix of this form > {{{9, 0.01, 1001, 269250000, > 0.944218 - 12.6734 Sqrt[1/x] + 72.8455/x}, {10, 0.01, 1001, > 269250000, 0.944134 - 13.1619 Sqrt[1/x] + 71.1457/x}, {11, 0.01, > 1001, 269250000, 0.944054 - 13.6278 Sqrt[1/x] + 69.5111/x},.... > > where the first two numbers are parameters and the third and fourth > number represent the bounds where the function in the last entries is > usable. I would like to interpolate the first, second and last column > in such a way that I have as result a function f[a_, b_, x_] were when > a and b are fixed and corresponds to some value in the matrix above > the function in the last column is used and when there is not the > corresponding entry the interpolation is used. A method to achieve my > goal is to calculate in some point between the min and the max the > function in the last column in order that I have a tensor product > structure and then to use the function Interpolation. Although this > method should work enough well, I would like to know if there is a > method to use all analytical information contained in the function in > the last column in order to produce a better interpolation. > > > Best regards, > > Silvio