Skip to main content

interpolation - Interpolating 2D data with missing values


I have a list (21 x 21) containing values. I want to eliminate slots containing zeros by interpolating the nearest values and overwriting the zeros. How do I use the Mathematica's ListInterpolation function to do that?



Answer



You have to use Interpolation because there it is possible to give values which do not lie on a structured grid. Let's create some test data which has zeroes in it


data = Table[ Sin[x] + Cos[y], {x, 0, Pi/2, Pi/2/29.}, {y, 0, Pi/2, Pi/2/29.}]*
   RandomInteger[{0, 1}, {30, 30}];
ListPlot3D[data]

Mathematica graphics



Now you attach the position of every value to it so you get tuples of the form {{x,y},value} and Select only those, where value is not zero. This can then be interpolated


data2 = Select[Flatten[MapIndexed[{#2, #1} &, data, {2}], 1], 
   Last[#] != 0 &];
ip = Interpolation[data2];
Plot3D[ip[y, x], {x, 1, 30}, {y, 1, 30}]

Mathematica graphics


Note, that with such data you always have an InterpolationOrder of 1.


Update regarding your comment


Yes, this is indeed a problem and you have to decide what to do. First you have to understand the issue. Let's assume the following grid with values, where all white cells are zero and have to be interpolated



Mathematica graphics


When you look at cell {3,1}, you see that such a situation is not a problem, because the value can be interpolated since it is place in between the cells {1,2} and {1,4}.


On the other hand, the cell {5,5} is a problem, because no surrounding cells with values are left which can be used for interpolation. Therefore, what you have to ensure is, that you have values on all 4 corners of your matrix. When they got selected out because they were zero, then you have to fill them with values. When they are indeed zero, and got kicked out accidentally, then you have to fill them back in.


You can ignore the corners when you Select non-zero values by changing the condition in the end


{ny, nx} = Dimensions[data];
data2 = Select[Flatten[MapIndexed[{N@#2, #1} &, data, {2}], 1], 
   Last[#] != 0 && 
   (First[#] =!= {1, 1} || First[#] =!= {1, nx} || 
    First[#] =!= {ny, 1} || First[#] =!= {ny, nx}) &];

Comments

Post a Comment

Popular posts from this blog

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...
Post a Comment
Read more

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...
Post a Comment
Read more

How to remap graph properties?

Graph objects support both custom properties, which do not have special meanings, and standard properties, which may be used by some functions. When importing from formats such as GraphML, we usually get a result with custom properties. What is the simplest way to remap one property to another, e.g. to remap a custom property to a standard one so it can be used with various functions? Example: Let's get Zachary's karate club network with edge weights and vertex names from here: http://nexus.igraph.org/api/dataset_info?id=1&format=html g = Import[ "http://nexus.igraph.org/api/dataset?id=1&format=GraphML", {"ZIP", "karate.GraphML"}] I can remap "name" to VertexLabels and "weights" to EdgeWeight like this: sp[prop_][g_] := SetProperty[g, prop] g2 = g // sp[EdgeWeight -> (PropertyValue[{g, #}, "weight"] & /@ EdgeList[g])] // sp[VertexLabels -> (# -> PropertyValue[{g, #}, "name"]...
Post a Comment
Read more