MATLAB: Indexing multidimensional matrices with elements is a vector

indexindexingMATLABmatricesmultidimensionalvectors

I have a multidimensional matrix M and a vector V of indeces that i use in this way:

M(V(1),V(2),V(3),...)

Is there a better way to do that? If V has 100 elements is not a good idea write the code in this way.

Moreover if i have 2 vector of indeces V1 and V2, is there a better way that combine them in a single vector

V=[V1 V2];

and use it as previously.

And finally: if V is not a vector but a Matrix and i would like use it like

M(V(1,1),V(1,2),...,V(2,1),V(2,2),...,...)

can i write something to avoid me to reshape V in a vector form?

Thank you in advance.

Best Answer

V=num2cell(V);
matrix(V{:})

Related Solutions

MATLAB: How to write a single line code for ‘n’ number of functions.

For at least the last 15 years, the only time that you can have an array of functions indexed with () is if the functions are symbolic. However if you do create an array of symbolic functions indexed by () then it is difficult to extract the individual functions without accidentally triggering executing all of the functions with the index as the parameter.

So... if you need an array of functions, you should use a cell array of function handles.

Next, you are missing some information on how symbolic variables work. You have

    n=10;
    syms v theta
    for i=1:n
    f(i)= v(i)*cos(theta(i));
    end

The syms you give there is the same in part as

v = sym('v')

Notice this assigns the scalar value sym('v') to v. With it being a scalar, you can reference v(1) and pull back that sym('v') scalar. But then when you try v(2) then it would attempt to index the scalar sym('v') at offset 2, and that would fail because it is only length 1.

Any time you have a scalar symbol name in MATLAB, like v after the

syms v

then MATLAB will treat it as a scalar. There is no way in MATLAB to declare that "This symbol will refer to a vector of length n, and I just want you to use the symbol and array indexing notation in the formulae." There is also no way to use a symbol to index something. Instead, each time you have a symbol indexed, the array has to exist at that location and the value stored there will be brought into the equation.

What you can do is:

    n=10;
    v = sym('v', [1 n]);
    theta = sym('theta', [1 n]);
    for i=1:n
      f{i} = v(i)*cos(theta(i));
    end

and the result of that would be a cell array that contains symbolic expressions, with the first expression containing v1*cos(theta1) and the second expression containing v2*cos(theta2) and so on to v10*cos(theta10) . Notice that these are no longer indexed references: the value stored at the index was looked up and used in the expression.

This is not really so bad, because you can later do things like

Pi = sym('pi');
v_vals = rand() * 2 * Pi;
subs(f{8}, v, v_vals)

Here, because v is a vector of symbol names, that would expand to

subs(f{8}, [v1, v2, v3, v4, v5, v6, v7, v8, v9, v10], v_vals)

which would instruct it to replace v1 with v_vals(1), v2 with v_vals(2) and so on. It is an arrangement that is mostly usable -- but it does make it difficult to program symbolic functions that are intended to accept arrays of different sizes.

MATLAB: Combination of vectors to build a matrix

As per Stephen's answer do not use numbered variables. As all your vectors are the same size, you could all store them as rows of a single matrix. If you don't like that, you could store the vectors as elements of a cell array.

%direct conversion of your code. Not the most elegant way of generating the cell array
V{1} = [2;4;2;1];
V{2} = [3;3;5;1];
V{3} = [4;1;2;1];
V{4} = [7;8;1;1];
V{5} = [5;4;2;1];
V{6} = [1;8;7;1];
V{7} = [3;2;0;1];
V{8} = [9;8;1;1];
V{9} = [1;4;7;1];
V{10} = [2;1;5;1];

Once you've got your vectors in a cell or matrix, it's easy to generate all possible combinations of rows/vectors: use nchoosek.

vectorcombinations = nchoosek(1:numel(V), 4); %all combinations of 4 vector indices out of however many there are

You can then use the indices to create your matrices. You can use a loop iterating over the rows of vectorcombinations, or more advanced techniques such as cellfun:

allmatrices = cellfun(@(c) [V{c}], num2cell(vectorcombinations, 2), 'UniformOutput', false);

The important bit in the line above is just [V{c}], where c is the content of just one row of vectorcombinations. This just concatenates the 4 vectors referred by the indices of that row.

Best Answer

Related Solutions

MATLAB: How to write a single line code for ‘n’ number of functions.

MATLAB: Combination of vectors to build a matrix

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