Storing a loop index value in a dynamic array?

This really is a made-up example computationally, I'm not sure if those random constraints are ever satisfied or not, but it still illustrates what I am trying to do. Essentially, my program uses ndgrid to find all of the values that meet the constraints that I specify. One of these values, though, cannot be used with ndgrid because it is used as an input to a function that requires a scalar value. Because of this, I am using the loop to fill the rest of the possible combinations. However, I can no longer keep track of which value of W is correlated with each row in the Locations matrix. It is almost useless for me to even increment W if I don't know which of its values caused an output row that I am interested in. Is there any way to store the current value of W in the last column of the locations matrix, without knowing how many rows are concatenated to the matrix with each iteration? (it changes dynamically in my program, and one increment of W may add 50 rows while another may add 2)

clear
clc

Locations = [];
for W = 0:0.01:1
    [X,Y,Z] = ndgrid(1:0.1:1);

    F = X.^2 + Y - 3.*Z + W^2;
    G = Y.^2 + Z.^4 - 6*W;      % random functions
    H = X + Y + Z.^3;

    idx=(F<=1 & G>=5 & H>=5); % random constraints
    Locations = unique([Locations; X(idx),Y(idx),Z(idx)],'rows');
    % I want the value of W that was used for the calculations
    % that the indices reference
    % Locations = unique([Locations; X(idx),Y(idx),Z(idx),W],'rows');
end

[J. Alex Lee]

In trying to understand your ultimate goal, I guess I'm confused if you have a criterion for which set of coordinates you'd want to keep on a collision. Since you are stepping sequentially, if you want to track the value of W you are forced to make a decision on "which W, the previous or the current". In the end, you will either keep the first W that satisfied your criteria, or the last one.

Conceptually, is it easier to make the full 4D grid including the span of W, and just analyze the whole block later? Then you will have in one shot all the values of W that meet your criteria, and it may become clearer what you want to do with them...

[Craig Atkinson]

I was going to get back to this question, but yes, I did end up making the full 4D grid and lumping my "W" value in along with the others. Intiially, I was trying to avoid rewriting a function that I was calling within the script, which would round the value of W to the one that was closest to the value found in a defined array. Since I couldn't find a way to concatenate the index of W into the locations array I decided to just write my own version of the function which ended up being easier than I had anticipated, though it does seem to take a bit longer. So to put it simply, I wanted all possible combinations of X, Y, and Z, which can be millions, but the value of W is constrained to a set of about 50.

If you're curious, though, they aren't being used for coodinates, they're actually dimensions and I am using ndgrid to find the optimal combinations for my script. I was just trying to avoid giving too much information about the code so that others wouldn't search for it because this was a technical aspect of a design project. Though it wouldn't help anybody by itself, if I posted my actual code someone may have stumbled across it and found the formulas that I was plugging the dimensions into.

[J. Alex Lee]

I'm still not sure I understand...but on thinking about it more if you literally want to just do what you have in your sample code and create a vector of height the same height as the final Locations array that tracks which W you are appending locations from, then you can use ismember to test for collision between your current list of coordinates and your growing history:

CurLoc = [X(idx),Y(idx),Z(idx)]
mask = ismember(CurLoc,Locations)

LocAppend = CurLoc(~mask,:)

Locations = [Locations ; LocAppend]
WList = [WList ; W .* ones(size(LocAppend,1),1)]

But I guess you will always lose information about other values of W that satisfied your criteria

Answer 1

[J. Alex Lee]

Without trying to get into the weeds of your need, did you know that "unique" can additionally output indices into each argument, and would tha thelp you? Per the help screen:

[C,IA,IC] = unique(A,'rows') also returns index vectors IA and IC such
    that C = A(IA,:) and A = C(IC,:). 

[Craig Atkinson]

Interesting, I actually didn't know that I might be able to use that for other portions of my program. Unfortunately I still need to figure out a way a way to track that looping value