Skip to main content

Interpolation The coordinates do not lie on a structured tensor product grid


I have a big array of multidimentional data 50 Mb, 500 000 elements. and I want to interpolate it and make a normal function.


Please do not mark this question as a duplicate straightaway, because I read many answers and they actually do not answer my question, they are a little bit different. I do not ask how to fix this problem, but more about definition and a way to find where my data is wrong.


Data example is this:


{
{{-0.5, -0.4898989898989899, 1., 0., 0.1}, 0.10120921662021362},
{{-0.5, -0.4898989898989899, 1., 0.12566370614359174, 0.1}, 0.1012092163684851},
{{-0.5, -0.4898989898989899, 1., 0.25132741228718347, 0.1}, 0.10120921611675658},
{{-0.5, -0.4898989898989899, 1., 0.37699111843077515, 0.1}, 0.10120921586502805},

{{-0.5, -0.4898989898989899, 1., 0.5026548245743669, 0.1}, 0.10120921561329953},
{{-0.5, -0.4898989898989899, 1., 0.6283185307179586, 0.1}, 0.101209215361571}
}

This small example works fine, but when I try to interpolate all my data, I get this error


Interpolation::indim: The coordinates do not lie on a structured tensor product grid.


My questions are:




  1. What is "structured tensor product grid"? Can someone give me example of "structured tensor product grid" and "NOT structured tensor product grid"? Might be I will be able to change my data accordingly, but I could not find definition of this term anywhere.





  2. Is there any way to find in my big data list (50 Mb) this place, where deviation (something wrong) happens? In other words how to find where my data is wrong?






Comments

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...