Re: multivariate interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg110936] Re: multivariate interpolation*From*: Silvio Abruzzo <silvio.abruzzo at gmail.com>*Date*: Mon, 12 Jul 2010 07:21:50 -0400 (EDT)*References*: <i1e7pb$95b$1@smc.vnet.net>

Dear Ingolf Dahl, thank you very much. It is exactly what I was looking for. I tried with other data that I have and the interpolation with the small numbers works very good, better than the interpolation with the big numbers. Best regards, Silvio On Jul 12, 7:04 am, "Ingolf Dahl" <ingolf.d... at telia.com> wrote: > 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 smal= l > y, where x = 1/y^2. The limits will then be very small number instead o= f > 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 Dahlhttp://www.familydahl.se/mathematica > > > > > -----Original Message----- > > From: Silvio Abruzzo [mailto:silvio.abru... at gmail.com] > > Sent: den 11 juli 2010 12:20 > > To: mathgr... at smc.vnet.net > > Subject: 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