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Generate a matrix containing all combinations of elements taken from n vectors
(4 answers)
Closed 7 years ago.
I need to combine all data of n (random) arrays with different lengths.
ex:
a=[1 3 2 7 8], b=[2 5 3 9] and c=[5 6] and maybe we have d, e, f etc....
I need the combination of all elements like:
M={[1 2 5], [1 2 6], [1 5 5], [1 5 6], [1 3 5], [1 3 6] ....}.
Solution for 3 arrays:
[A,B,C] = meshgrid(a, b, c);
M = [A(:), B(:), C(:)];
Solution for n arrays iterating over the short dimension n:
a=[1 3 2 7 8];
b=[2 5 3 9];
c=[5 6];
d=[1 3 5];
arrays = { a, b, c, d };
M = a';
for i = 2:length(arrays)
A1 = M;
A2 = arrays{i}';
[i1, i2] = meshgrid(1:length(A1), 1:length(A2));
M = [A1(i1(:), :) A2(i2(:))];
end
Related
I have a column vector A (6x1) with values [6 3 10 4 2 8]'; and a matrix B (6x5) with values
B = [1 2 3 0 4 ;
3 7 8 5 0 ;
0 9 1 0 1 ;
5 0 3 1 2 ;
4 6 7 6 4 ;
3 1 2 7 3]
I want to make five matrices with size 6x2 using Matlab.
The first column is vector A
The second column is columns from B, like [A, B(first col)], [A, B(second col)]
First matrix is [6 1; 3 3; 10 0; 4 5; 2 4; 8 3];
2nd matrix is [6 2; 3 7; 10 9; 4 0; 2 6; 8 1]
... and so on
Any help I really appreciate it
You could use a loop
C = NaN( size(B,1), 2, size(B,2) );
for ii = 1:size(B,2)
C(:,:,ii) = [A, B(:,ii)];
end
This gives you a 3D array, where each slice in the 3rd dimension is a 6x2 matrix (for this example) as desired. You would access the nth slice with C(:,:,n).
You can do this slightly more concisely with arrayfun, but it's basically a loop in disguise
C = arrayfun( #(ii) [A, B(:,ii)], 1:size(B,2), 'uni', 0 );
C = cat(3, C{:} );
You could omit the cat function if you're happy with results in a cell array, where you access the nth matrix with C{n}.
You could first make a copy of the columns of A, then concatenate A and B, and reshape:
At = repmat(A, 1, size(B,2));
C = reshape([At;B], 6, 2, []);
Or oneliner:
C = reshape([repmat(A, 1, size(B,2));B], 6, 2, []);
Then retrieve your matrices with C(:,:,k)
you can use this
first_matrix=[A,B(:,1)];
second_matrix=[A,B(:,2)];
third_matrix=[A,B(:,3)];
... and so on
I am having difficulty concatenating vectors in MATLAB.
A = [1
2
3]
B = [6
7
8
9
10]
Desired result:
C = [1
2
3
6
7
8
9
10]
where the sizes of A and B are different in every iteration of my script and I want to form the concatenated resulting vector, C, which has a dynamic size.
This is what I have tried:
A = [1
2
3];
B = [6
7
8
9
10];
Vertical concatenation of two vectors/matrices is what you want, done like this...
C = [A; B];
... or this...
C = [A
B];
... or this...
C = vertcat(A,B);
All three of these give
C = [1
2
3
6
7
8
9
10]
% As you requested...
You were running into trouble because you were trying to use horzcat
C = horzcat(A',B');
Horizontal concatenation merges matrices horizontally, i.e.
C = [1, 6
2, 7
3, 8
?, 9
?, 10]
So to avoid this, you've transposed the matrices to make them rows instead of columns, then transposed the result back?? You just need vertcat! I have shown the shorthand and full form for this above.
Try:
A = [1 2 3];
B = [4 5 6 7 8 9 10];
C = [A B]
For vertical vectors A' and B' use:
C = [A;B]
The fool-proof way is this:
C = [A(:);B(:)];
If you use this method then it does not matter if A and B are row vectors, column vectors, or even matrices.
I am tring to get the mean of three vectors but the mean function is not working.
Example:
A = [1 2 3 4 5];
B = [2 3 4 5 6];
C = [3 4 5 6 7];
V = mean(A,B,C); % should be [2 3 4 5 6] as each column is the some of the same column in A, B and C divided by three.
Any Help?
For a general case (row or column vector case), you can use this -
mean_vals = mean(cat(2,A(:),B(:),C(:)),2)
The following codes runs in Matlab:
a = [1 2 3 4]
b = [ 1 2 3; 1 2 3; 1 2 3]
a(b)
The result of a(b) is a matrix:
[ 1 2 3; 1 2 3; 1 2 3]
Can anyone explain what happened here? Why a vector can be indexed by a matrix, how to interpret the result?
That's a very standard MATLAB operation that you're doing. When you have a vector or a matrix, you can provide another vector or matrix in order to access specific values. Accessing values in MATLAB is not just limited to single indices (i.e. A(1), A(2) and so on).
For example, what you have there is a vector of a = [1 2 3 4]. When you try to use b to access the vector, what you are essentially doing is a lookup. The output is basically the same size as b, and what you are doing is creating a matrix where there are 3 rows, and each element accesses the first, second and third element. Not only can you do this for a vector, but you can do this for a matrix as well.
Bear in mind that when you're doing this for a matrix, you access the elements in column major format. For example, supposing we had this matrix:
A = [1 2
3 4
5 6
7 8]
A(1) would be 1, A(2) would be 3, A(3) would be 5 and so on. You would start with the first column, and increasing indices will traverse down the first column. Once you hit the 5th index, it skips over to the next column. So A(5) would be 2, A(6) would be 4 and so on.
Here are some examples to further your understanding. Let's define a matrix A such that:
A = [5 1 3
7 8 0
4 6 2]
Here is some MATLAB code to strengthen your understanding for this kind of indexing:
A = [5 1 3; 7 8 0; 4 6 2]; % 3 x 3 matrix
B = [1 2 3 4];
C = A(B); % C should give [5 7 4 1]
D = [5 6 7; 1 2 3; 4 5 6];
E = A(D); % E should give [8 6 3; 5 7 4; 1 8 6]
F = [9 8; 7 6; 1 2];
G = A(F); % G should give [2 0; 3 6; 5 7]
As such, the output when you access elements this way is whatever the size of the vector or matrix that you specify as the argument.
In order to be complete, let's do this for a vector:
V = [-1 9 7 3 0 5]; % A 6 x 1 vector
B = [1 2 3 4];
C = V(B); % C should give [-1 9 7 3]
D = [1 3 5 2];
E = V(D); % E should give [-1 7 0 9]
F = [1 2; 4 5; 6 3];
G = V(F); % G should give [-1 9; 3 0; 5 7]
NB: You have to make sure that you are not providing indexes that would make the accessing out of bounds. For example if you tried to specify the index of 5 in your example, it would give you an error. Also, if you tried anything bigger than 9 in my example, it would also give you an error. There are 9 elements in that 3 x 3 matrix, so specifying a column major index of anything bigger than 9 will give you an out of bounds error.
Notice that the return value of a(b) is the same size as b.
a(b) simply takes each element of b, call it b(i,j), as an index and returns the outputs a(b(i,j)) as a matrix the same size as b. You should play around with other examples to get a more intuitive feel for this:
b = [4 4 4; 4 4 4];
a(b) % Will return [4 4 4; 4 4 4]
c = [5; 5];
a(c) % Will error as 5 is out of a's index range
In matlab, If an m by 3 matrix has rows that all exist in a bigger n by 3 matrix, how can I create a (n-m) by 3 matrix that does not contain the rows of the first (m by 3) matrix?
e.g. if the first matrix is [1 4 6] and the second matrix [1 2 3; 1 4 6; 8 7 4], how can I come up with the matrix: [1 2 3;8 7 4]?
That's a job for ismember with the 'rows' option:
a = [1 4 6];
b = [1 2 3; 1 4 6; 8 7 4];
eq_rows = ismember(b,a,'rows');
result = b(~eq_rows,:)