My matlab code with interp3 is not providing me correct answer. Please help.

I have a data (shown on left). I have prepared a matlab code (shown on right). The output should have come 13 for (x,y,z)=(1,2,3) but I am getting the value 18. Please show where should I do the necessary correction.

[Stephen23]

Please upload your CSV file by clicking the paperclip button.

[Junaed Hossain]

Here it is.

Answer 1

[Stephen23]

format compact
T = readtable('interpcheck.csv')

T = 24×5 table
    index    x    y    z    result
    _____    _    _    _    ______
      1      1    1    1       2  
      2      1    1    2       4  
      3      1    1    3       6  
      4      1    1    4       8  
      5      1    2    1       7  
      6      1    2    2      10  
      7      1    2    3      13  
      8      1    2    4      16  
      9      1    3    1      12  
     10      1    3    2      16  
     11      1    3    3      20  
     12      1    3    4      24  
     13      2    1    1      15  
     14      2    1    2      18  
     15      2    1    3      21  
     16      2    1    4      24  

A = accumarray([T.x,T.y,T.z],T.result)

A = 
A(:,:,1) =
     2     7    12
    15    21    27
A(:,:,2) =
     4    10    16
    18    26    34
A(:,:,3) =
     6    13    20
    21    31    41
A(:,:,4) =
     8    16    24
    24    36    48

X = unique(T.x);
Y = unique(T.y);
Z = unique(T.z);
interpn(X,Y,Z,A,1,2,3)

ans = 13

But using GRIDDATA is simpler:

griddata(T.x,T.y,T.z,T.result,1,2,3)

ans = 13

Answer 2

[Cris LaPierre]

I suggest looking at the description of what the inputs to interp3 can be.

By taking the unique value of X, Y, and Z, you are losing the relationship between the values. Since you have all the data, I'd be inclided to use reshape to have the inputs be 3D arrays. When doing this, note that rows correspond to y, and columns to x. That means needing to sort your data so that the output of reshape correctly organizes the data.

file = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/1123055/interpcheck.csv';
data = readtable(file);
data = sortrows(data,["z","x","y"])

data = 24×5 table
    index    x    y    z    result
    _____    _    _    _    ______

      1      1    1    1       2  
      5      1    2    1       7  
      9      1    3    1      12  
     13      2    1    1      15  
     17      2    2    1      21  
     21      2    3    1      27  
      2      1    1    2       4  
      6      1    2    2      10  
     10      1    3    2      16  
     14      2    1    2      18  
     18      2    2    2      26  
     22      2    3    2      34  
      3      1    1    3       6  
      7      1    2    3      13  
     11      1    3    3      20  
     15      2    1    3      21  

x=reshape(data.x,[3,2,4]);
y=reshape(data.y,[3,2,4]);
z=reshape(data.z,[3,2,4]);

V = reshape(data.result,[3,2,4]);

r = interp3(x,y,z,V,1,2,3)

r = 13

Your example data set does allow you to use use unique here. You do have to keep in mind that the size of v must be [length(Y) length(X) length(Z)]. However, you can't just arbitrarily make it the size you want. That will cause a disconnect between your x,y,z values and the corresponding result value. This is why you are getting 18. You must either sort the data so that the output of reshape treats the rows as y and columns as x

data = sortrows(data,["z","x","y"])

x = unique(data.x);

y = unique(data.y);

z = unique(data.z);

V = reshape(data.result,3,2,4);

r = interp3(x,y,z,V,1,2,3)

or reshape the data to match the format in the table, and then permute to get it to be what is needed.

x = unique(data.x);

y = unique(data.y);

z = unique(data.z);

V = reshape(data.result,4,3,2);

v = permute(V,[2,3,1]);

r = interp3(x,y,z,v,1,2,3)

[Torsten]

I wish "interp3" could do this kind of stuff internally given that the three columns x,y and z in the Excel-file surely stem from a regular grid.

The most natural way to call interp3 would then be

M = 24x4 matrix;
x = M(:,1);
y = M(:,2);
z = M(:,3);
V = M(:,4);
v = interp3(x,y,z,V,1,2,3)

and all the ordering should be part of interp3.

[Cris LaPierre]

It does seem like that would be easier, and there is a function for that - griddata, as Stephen23 pointed out.

[Torsten]

But griddata usually is for scattered data ... So equivalent to scatteredInterpolant, I guess.

It should be possible to indicate that the data stem from a regular grid, but one doesn't need to care about the ordering.