I have the following vector u:
u=[a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4];
I want to permute the elements of of u to make the following vector, uNew:
uNew=[a1,b1,c1,a2,b2,c2,a3,b3,c3,a4,b4,c4];
I can think of no way of doing this other than with a for loop:
uNew=[];
for i=1:4
uNew=[uNew,u(i:4:end)];
end
But I'm hoping that a built-in function exits? Thanks!
Reshape it to a matrix which, read column by column, contains the order you want:
n=3 % number of categories (a,b,c)
u2=reshape(u,[],n).'
then convert it back to a vector:
u2=u2(:);
I'd use Daniel's approach. But just to provide an alternative:
m = 4; %// size of each initial "block"
[~, ind] = sort(mod(0:numel(u)-1,m)+1);
uNew = u(ind);
Note that this works because, as per sort's documentation,
The ordering of the elements in B (output) preserves the order of any equal elements in A (input)
Another approach:
N = 4;
uNew = u(mod(0:numel(u)-1, N) * N + floor((0:numel(u)-1)/N) + 1);
Related
I have two matrices A and B. A(:,1) corresponds to an x-coordinate, A(:,2) corresponds to a y-coordinate, and A(:,3) corresponds to a certain radius. All three values in a row describe the same circle. Now let's say...
A =
[1,4,3]
[8,8,7]
[3,6,3]
B =
[1,3,3]
[1, 92,3]
[4,57,8]
[5,62,1]
[3,4,6]
[9,8,7]
What I need is to be able to loop through matrix A and determine if there are any rows in matrix B that are "similar" as in the x value is within a range (-2,2) of the x value of A (Likewise with the y-coordinate and radius).If it satisfies all three of these conditions, it will be added to a new matrix with the values that were in A. So for example I would need the above data to return...
ans =
[1,4,3]
[8,8,7]
Please help and thank you in advance to anyone willing to take the time!
You can use ismembertol.
result = A(ismembertol(A,B,2,'ByRows',1,'DataScale',1),:)
Manual method
A = [1,4,3;
8,8,7;
3,6,3];
B = [1,3,3;
1,92,3;
4,57,8;
5,62,1;
3,4,6;
9,8,7]; % example matrices
t = 2; % desired threshold
m = any(all(abs(bsxfun(#minus, A, permute(B, [3 2 1])))<=t, 2), 3);
result = A(m,:);
The key is using permute to move the first dimension of B to the third dimension. Then bsxfun computes the element-wise differences for all pairs of rows in the original matrices. A row of A should be selected if all the absolute differences with respect to any column of B are less than the desired threshold t. The resulting variable m is a logical index which is used for selecting those rows.
Using pdist2 (Statistics and Machine Learning Toolbox)
m = any(pdist2(A, B, 'chebychev')<=t, 2);
result = A(m,:);
Ths pdist2 function with the chebychev option computes the maximum coordinate difference (Chebychev distance, or L∞ metric) between pairs of rows.
With for loop
It should work:
A = [1,4,3;
8,8,7;
3,6,3]
B = [1,3,3;
1,92,3;
4,57,8;
5,62,1;
3,4,6;
9,8,7]
index = 1;
for i = 1:size(A,1)
C = abs(B - A(i,:));
if any(max(C,[],2)<=2)
out(index,:) = A(i,:);
index = index + 1
end
end
For each row of A, computes the absolute difference between B and that row, then checks if there exists a row in which the maximum is less than 2.
Without for loop
ind = any(max(abs(B - permute(A,[3 2 1])),[],2)<=2);
out = A(ind(:),:);
Sorry about the bad title, I'm struggling to word this question well. Basically what I want to do is extract elements from a 2d matrix, from row by row, taking out a number of elements (N) starting at a particular column (k). In for loops, this would look like.
A = magic(6);
k = [2,2,3,3,4,4]; % for example
N = 3;
for j = 1:length(A)
B(j,:) = A(j,k(j):k(j)+N-1);
end
I figure there must be a neater way to do it than that.
You could use bsxfun to create an array of indices to use. Then combine this with the row numbers and pass it to sub2ind.
inds = sub2ind(size(A), repmat(1:size(A, 1), 3, 1), bsxfun(#plus, k, (0:(N-1))')).';
B = A(inds);
Or alternately without sub2ind (but slightly more cryptic).
B = A(bsxfun(#plus, 1:size(A,1), ((bsxfun(#plus, k, (0:(N-1)).')-1) * size(A,1))).');
Here's one approach using bsxfun's masking capability and thus logical indexing -
C = (1:size(A,2))';
At = A.';
B = reshape(At(bsxfun(#ge,C,k) & bsxfun(#lt,C,k+N)),N,[]).';
Say I have a nxm matrix and want to treat each row as vectors in a function. So, if I have a function that adds vectors, finds the Cartesian product of vectors or for some reason takes the input of several vectors, I want that function to treat each row in a matrix as a vector.
This sounds like a very operation in Matlab. You can access the ith row of a matrix A using A(i, :). For example, to add rows i and j, you would do A(i, :) + A(j, :).
Given an nxm matrix A:
If you want to edit a single column/row you could use the following syntax: A(:, i) for the ith-column and A(i, :) for ith-row.
If you want to edit from a column/row i to a column/row j, you could use that syntax: A(:, i:j) or A(i:j, :)
If you want to edit (i.e.) from the penultimate column/row to the last one, you could you: A(:, end-1:end) or A(end-1:end, :)
EDIT:
I can't add a comment above because I don't have 50 points, but you should post the function setprod. I think you should be able to do what you want to do, by iterating the matrix you're passing as an argument, with a for-next statement.
I think you're going to have to loop:
Input
M = [1 2;
3 4;
5 6];
Step 1: Generate a list of all possible row pairs (row index numbers)
n = size(M,1);
row_ind = nchoosek(1:n,2)
Step 2: Loop through these indices and generate the product set:
S{n,n} = []; //% Preallocation of cell matrix
for pair = 1:size(row_ind,1)
p1 = row_ind(pair,1);
p2 = row_ind(pair,2);
S{p1,p2} = setprod(M(p1,:), M(p2,:))
end
Transform the matrix into a list of row vectors using these two steps:
Convert the matrix into a cell array of the matrix rows, using mat2cell.
Generate a comma-separated list from the cell array, using linear indexing of the cell contents.
Example: let
v1 = [1 2];
v2 = [10 20];
v3 = [11 12];
M = [v1; v2; v3];
and let fun be a function that accepts an arbitrary number of vectors as its input. Then
C = mat2cell(M, ones(1,size(M,1)));
result = fun(C{:});
is the same as result = fun(v1, v2, v3).
Question title explains what I would like. For example, if there are 6 elements in a particular column, how do I randomly pick 1 element from that column. Please keep it simple if possible.
Thanks for the help.
Suppose you have a matrix A of size m-by-n. You wish to pick one element from each of the n columns at random:
>> rows = randsample( m, n ); % sample n times from integers 1:m
Now rows has n values, each represent a random entry at the corresponding column.
To access those values
>> sampledValues = A( sub2ind( size(A), rows, 1:n ) );
For more information see the doc on randsample and sub2ind.
You can use randi if your version of MATLAB is > R2008a
samples = A(sparse(randi(size(A,1),size(A,2),1), 1:size(A,2), true));
or,
[m, n] = size(A);
samples = A(sparse(randi(m,n,1), 1:n, true));
However for older versions you can replace randi with randsample but that requires Statistics Toolbox. Or introduce:
randi = #(imax, m, n) floor(1+rand(m,n)*imax);
Here is an easy way to do it. Note that a version without loops should be more efficient.
Assuming your variable is x loop over its n columns:
selected = zeros(1,n);
for c = 1:n
selected(c) = x(randperm(6,1),n);
end
I have two matrices A and B, both of which are Nx3 matrices.
I'm currently getting the maximum value and index for each row of matrix A using:
[maxA, idx] = max(A, [], 2)
idx(j) indicates which column contained the maximum for row j. Now I'd like to select those same positions from matrix B.
I've currently implemented this using a loop:
for j = 1:numel(idx)
maxB(j) = B(j, idx(j))
end
My current implementation is fast enough, although I prefer to avoid unneeded loops so is there a way to express this without a loop?
You can build a vector of linear indices (I expect B to be the same size as A):
vec_indices = sub2ind(size(A), 1:numel(idx), idx);
Then you can use that vector directly for lookup:
maxB = B(vec_indices)
You can construct the single dimension index into the matrix and get them that way. All multidimensional matrices in matlab can be addressed.
You can use
maxB = B(sub2ind([1:length(idx)]',idx(:)));
In one line:
maxB = B(A == max(A, [], 2) * ones(1, 3));
But this is not safe. It assumes unique values in every row of A.