how can I create a 4D matrix and use it for interpolation

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Hello everybody,
I have 3 vectors conditions:
first vector: Wpig=0.5:0.5:7;
second vector: Chla=0.5:0.01:0.6;
third vector: Starch=0:0.04:0.24;
for each possible condition I calculate Ea using a function I named "proprad(Wpig,Chla,Starch)", so for exemple for proprad(0.5,0.5,0)=Ea and Ea is a vector composed by 31 values (it's for this I created a vector named Wavelength having the same lenght that Ea vector result). Summarizing, usign my function, when you put 3 scalars: Wpig,Chla,Starch, you get a vector result (Ea).
So, I want to create a 4D matrix in wich the 3 firsts dimensions will correspond to my 3 conditions (Wpig,Chla,Starch) and the 4th dimension will be the vectors estimated by my function.
My first idea is to create a zeros 4D matrix like this:
and then remplace each dimension by the value, giving something like this:
1 dimension : Wpig
2 dimension: Chla
3 dimension: Starch
4 dimension: Ea
finally, my goal is to use the 4D matrix, for interpolation. So for exemple, if I want to know what's the value of Ea for conditions like Wpig=0.93,Chla=0.57 and Starch=0.12, I cand interpolate in the 4D matrix to estimate it.
Could someone help me to solve this coding problem?
Thank you very much for your time and your help!

Answers (1)

Fabio Freschi
Fabio Freschi on 29 Oct 2019
Edited: Fabio Freschi on 30 Oct 2019
% your vectors
Now you need to sample uniformly the space using your vectors. Use may use ndgrid for this
[X,Y,Z] = ndgrid(Wpig,Chla,Starch);
X, Y, and Z are now 3d matrices, where
  • X: Wpig
  • Y: Chla
  • Z: Starch
Note that you have numel(Wpig)*numel(Chla)*numel(Starch) = 1078 elements in these matrices.
You must now evaluate your function. If it admits matrices as inputs, you can supply directly the 3d matrices. For example
Ea = cos(X)+sin(Y).*tan(Z);
If it admits vectors as inputs or you evaluate each value of Ea providing only scalar values, e.g. in a for loop, you can create Ea as a vector, then reshape it. For example
% this three lines are not necessary, but makes things more clear
X1 = X(:);
Y1 = Y(:);
Z1 = Z(:);
% preallocation
Ea = zeros(numel(X),1);
% evaluation
for i = numel(X1)
Ea = cos(X1(i))+sin(Y1(i)).*tan(Z1(i));
% reshape the result vector to fit X,Y,Z dimensions
Ea = reshape(Ea,size(X));
Now you can use intepolation. interpn can interpolate n-d gridded data in WpigQ, ChlaQ, StarchQ query points
% query points
WpigQ = [5.5; 6.3];
ChlaQ = [0.53; 0.58];
StarchQ = [0.111; 0.134];
% interp
EaInterp = interpn(X,Y,Z,Ea,WpigQ,ChlaQ,StarchQ);
Fernando Robert Ferrel Ballestas
No, i can't. because for Wpig, Chla and Starch scalar combinaison like for exemple:
proprad0.5,0.5,0) I obtain Ea vector of 31 elements. (31x1) .
I put the vector Wavelength because it has the same dimension of Ea and it could be used for the 4D-matrix construction but I'm not sure.
What do you recommend me to do? Thanks!

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