4D Table Interpolation

I have a data set in four variables (alpha,beta,gamma,lambda).

Here alpha is a 10 element vector, beta is a 8 element vector, both gamma and lambda have four values each.

The data is given such that for each value of lambda, there are 4 tables, and those 4 tables correspond to each value of gamma. Each of those four tables is a 8x10 matrix whose rows correspond to values of beta and columns correspond to values of alpha.

I tried to implement it this way (sample code using random values):

alpha  = 1:10;
beta   = 1:8;
gamma  = 1:4;
lambda = 1:4;

m = length(beta);
n = length(alpha);

Data(:,:,1,1) = rand(m,n); % alpha in first dimension, beta is 2nd dimension, gamma in 3rd and lambda in 4th
Data(:,:,2,1) = rand(m,n);
Data(:,:,3,1) = rand(m,n);
Data(:,:,4,1) = rand(m,n);

Data(:,:,1,2) = rand(m,n);
Data(:,:,2,2) = rand(m,n);
Data(:,:,3,2) = rand(m,n);
Data(:,:,4,2) = rand(m,n);

Data(:,:,1,3) = rand(m,n);
Data(:,:,2,3) = rand(m,n);
Data(:,:,3,3) = rand(m,n);
Data(:,:,4,3) = rand(m,n);

Data(:,:,1,4) = rand(m,n);
Data(:,:,2,4) = rand(m,n);
Data(:,:,3,4) = rand(m,n);
Data(:,:,4,4) = rand(m,n);

idat = interpn(alpha,beta,gamma,lambda,Data,1,2,3,4);

Error using griddedInterpolant
Sample points vector corresponding to grid dimension 1 must contain 8 elements.

Error in interpn (line 149)
F = griddedInterpolant(X, V, method,extrap);

This code gives me errors. How can I resolve it? Do I need to create an n-dimensional grid? or am I making some mistake in the making of 4D tables.

Answer 1

[Voss]

Swap your definitions of m and n (or equivalently use rand(n,m)). Like you said, alpha is 1st dimension, beta is 2nd.

alpha  = 1:10;
beta   = 1:8;
gamma  = 1:4;
lambda = 1:4;

m = length(alpha);
n = length(beta);

Data(:,:,1,1) = rand(m,n); % alpha in first dimension, beta is 2nd dimension, gamma in 3rd and lambda in 4th
Data(:,:,2,1) = rand(m,n);
Data(:,:,3,1) = rand(m,n);
Data(:,:,4,1) = rand(m,n);

Data(:,:,1,2) = rand(m,n);
Data(:,:,2,2) = rand(m,n);
Data(:,:,3,2) = rand(m,n);
Data(:,:,4,2) = rand(m,n);

Data(:,:,1,3) = rand(m,n);
Data(:,:,2,3) = rand(m,n);
Data(:,:,3,3) = rand(m,n);
Data(:,:,4,3) = rand(m,n);

Data(:,:,1,4) = rand(m,n);
Data(:,:,2,4) = rand(m,n);
Data(:,:,3,4) = rand(m,n);
Data(:,:,4,4) = rand(m,n);

idat = interpn(alpha,beta,gamma,lambda,Data,1,2,3,4);

disp(idat)

    0.7127

Edit to show that the interpolated value matches the input table:

Data(1,2,3,4)

ans = 0.7127

[Fawad Khan]

You're right. But, I actually followed the 2D interpolation first. Like I said, that the matrices have size 8 by 10, where the rows correspond to beta and columns correspond to alpha. If I ignore 3rd and 4th dimensions for now. Then, the following code works

alpha  = 1:10;
beta   = 1:8;

m = length(beta);
n = length(alpha);

Data = rand(m,n);

idat = interp2(alpha,beta,Data,1,2)

idat = 0.7148

However, if I were to swap the dimensions in this case:

alpha  = 1:10;
beta   = 1:8;

m = length(alpha);
n = length(beta);

Data = rand(m,n);

idat = interp2(alpha,beta,Data,1,2)

Error using griddedInterpolant
Sample points vector corresponding to grid dimension 1 must contain 8 elements.

Error in interp2>makegriddedinterp (line 226)
F = griddedInterpolant(varargin{:});

Error in interp2 (line 126)
F = makegriddedinterp({X, Y}, V, method,extrap);

then I get the same error.

[Fawad Khan]

Also, if you print the corresponding data table value from your solution

Data(1,2,3,4)

The interpolated value corresponds to a value for beta = 1 and alpha = 2 whereas I wanted the value corresponding to alpha = 1 and beta = 2

[Fawad Khan]

You can also check the documentation of interp2. It says "The default grid points cover the rectangular region, X=1:n and Y=1:m, where [m,n] = size(V)."

[Voss]

From the interp2 documentation:

"If X and Y are grid vectors, then V must be a matrix containing length(Y) rows and length(X) columns."

From the interpn documentation:

"If X1,X2,...,Xn are grid vectors, then V is an array whose ith dimension is the same length as grid vector Xi, where i= 1,2,...n."

So interp2 is reversed relative to what you'd expect going by how interpn works.

[Voss]

Also, Data(1,2,3,4) matches the result from interpn. I've edited my answer to show that.

[Fawad Khan]

Yes, you're actually right. Thank you for your help.

[Voss]

You're welcome.