Is there a vectorized, automated way to fill a row vector l times with repeating numbers x such that x is increased by y after a certain number k of elements? k, l, x, and y are given.
Two examples:
(k = 4, l = 4, x = 0, y = 1): $A = [0 0 0 0; 1 1 1 1; 2 2 2 2; 3 3 3 3];$
(k = 2, l = 3, x = 0, y = 0.1): $B = [0 0; 0.1 0.1; 0.2 0.2]$
You can use repmat together with a:b
This way your fist example would look like this:
repmat((0:3)', 1,4)
The second one:
repmat((0:0.1:0.2)', 1,2)
You can also try linspace or similar functions to be as close to what you want as possible
Related
I have a list of vertices where each row corresponds to a (x, y) coordinate.
For example, the following includes the vertices (0, 0), (1, 0), and (0, 1)
V = [0 0;
1 0;
0 1];
I also have a list of edges where the first column specifies the row of the starting vertex and the second column specifies the row of the ending vertex.
For example, the following includes the edges (0, 0) to (1, 0) and (0, 0) to (0, 1)
E = [1 2; % V(1) -> V(2) = (0, 0) -> (1, 0)
1 3] % V(1) -> V(3) = (0, 0) -> (0, 1)
I need to produce a list of edges with their actual coordinates from these two lists. That is, from V and E, I need
edge1 = [0 0]; % = E(1, 1) = V(1)
edge2 = [0 0]; % = E(2, 1) = V(1)
edge3 = [1 0]; % = E(1, 2) = V(2)
edge4 = [0 1]; % = E(2, 2) = V(3)
I know how to do this with for loops, but my supervisor said there is a more optimal solution using the function find(x), which returns the nonzero indices in an array. I do not see how this could be done with find. Is there a way that this could be done without using for loops but using the find function?
As far as I remember find is not really recommended when it comes to runtime, and for loops are not as bad as they where in the past taking JIT into consideration and MATLAB's effort to improve them.
However one possible solution without using for-loops (and without find) would be:
E = [1 2;
1 3];
V = [0 0;
1 0;
0 1];
Edges=V(E(:),:)
Edges =
0 0
0 0
1 0
0 1
So the output is not a list of different variables / edges but rather a matrix holding all of them row-wise.
I have a symmetric m-by-m matrix A. Each element has a value between 0 and 1. I now want to choose n rows / columns of A which form an n-by-n sub-matrix B.
The criteria for choosing these elements, is that the sum of all elements of B must be the minimum out of all possible n-by-n sub-matrices of A.
For example, suppose that A is a 4-by-4 matrix:
A = [0 0.5 1 0; 0.5 0 0.5 0; 1 0.5 1 1; 0 0 1 0.5]
And n is set to 3. Then, the best B is the one taking the first, second and fourth rows / columns of A:
B = [0 0.5 0; 0.5 0 0; 0 0 0.5]
Where the sum of these elements is 0 + 0.5 + 0 + 0.5 + 0 + 0 + 0 + 0 + 0.5 = 1.5, which is smaller than another other possible 3-by-3 sub-matrices (e.g. using the first, third and fourth rows / columns).
How can I do this?
This is partly a mathematics question, and partly a Matlab one. Any help with either would be great!
Do the following:
m = size(A,1);
n=3;
sub = nchoosek(1:m,n); % (numCombinations x n)
subR = permute(sub,[2,3,1]); % (n x 1 x numCombinations), row indices
subC = permute(sub,[3,2,1]); % (1 x n x numCombinations), column indices
lin = bsxfun(#plus,subR,m*(subC-1)); % (n x n x numCombinations), linear indices
allB = A(lin); % (n x n x numCombinations), all possible Bs
sumB = sum(sum(allB,1),2); % (1 x 1 x numCombinations), sum of Bs
sumB = squeeze(sumB); % (numCombinations x 1), sum of Bs
[minB,minBInd] = min(sumB);
fprintf('Indices for minimum B: %s\n',mat2str(sub(minBInd,:)))
fprintf('Minimum B: %s (Sum: %g)\n',mat2str(allB(:,:,minBInd)),minB)
This looks only for submatrices where the row indices are the same as the column indices, and not necessarily consecutive. That is how I understood the question.
This is a bit brute force, but should work
A = [0 0.5 1 0; 0.5 0 0.5 0; 1 0.5 1 1; 0 0 1 0.5];
sizeA = size(A,1);
size_sub=3;
idx_combs = nchoosek(1:sizeA, size_sub);
for ii=1:size(idx_combs,1)
sub_temp = A(idx_combs(ii,:),:);
sub = sub_temp(:,idx_combs(ii,:));
sum_temp = sum(sub);
sums(ii) = sum(sum_temp);
end
[min_set, idx] = min(sums);
sub_temp = A(idx_combs(idx,:),:);
sub = sub_temp(:,idx_combs(idx,:))
Try to convolve the matrix A with a smaller matrix M. Eg if you is interested in finding the 3x3 submatrix then let M be ones(3). This code shows how it works.
A = toeplitz(10:-1:1) % Create a to eplitz matrix (example matrix)
m = 3; % Submatrix size
mC = ceil(m/2); % Distance to center of submatrix
M = ones(m);
Aconv = conv2(A,M); % Do the convolution.
[~,minColIdx] = min(min(Aconv(1+mC:end-mC,1+mC:end-mC))); % Find column center with smallest sum
[~,minRowIdx] = min(min(Aconv(1+mC:end-mC,minColIdx+mC),[],2)); % Find row center with smlest sum
minRowIdx = minRowIdx+mC-1 % Convoluted matrix is larger than A
minColIdx = minColIdx+mC-1 % Convoluted matrix is larger than A
range = -mC+1:mC-1
B = A(minRowIdx+range, minColIdx+range)
The idea is to imitate a fir filter y(n) = 1*x(n-1)+1*x(n)+1*x(n+1). For now it only finds the first smallest matrix though. Notice the +1 adjustment because first matrix element is 1. Then notice the the restoration right below.
I have a matrix M that looks similar to this:
M = [ 1, 2, 3, 0, 0;
1, 2, 0, 0, 0;
2, 3, 4, 5, 0;
4, 5, 6, 0, 0;
1, 2, 3, 4, 5;
]
I'm trying to get a column vector with the rightmost non-zero value of each row in A, but ONLY for the rows that have the first column == 1.
I'm able to calculate a filter for the rows:
r = M( :, 1 ) == 1;
> r = [ 1; 1; 0; 0; 1 ]
And I have a set of indices for "the rightmost non-zero value of each row in M":
> c = [ 3, 2, 4, 3, 5 ]
How do I combine these in a slicing of A in order to get what I'm looking for? I'm looking for something like:
A( r, c )
> ans = [ 3; 2; 5 ]
But doing this gets me a 3x3 matrix, for some reason.
The shortest way I can think of is as follows:
% Get the values of the last non-zero entry per row
v = M(sub2ind(size(M), 1:size(M,1), c))
% Filter out the rows that does not begin with 1.
v(r == 1)
This seems to work (I assume other operations defining r,c have been performed):
M(sub2ind(size(A),find(r==1).',c(r==1))).'
Short interpretation of the problem and solution:
M( r, c )
gives a 3 x 5 matrix (not 3 x 1 as desired) due to mixing of logical and subscript indices. The logical indices in r pick out rows in A with r==1. Meanwhile row array c picks out elements from each row according to the numeric index:
ans =
3 2 0 3 0
0 2 0 0 0
3 2 4 3 5
What you really want are indices into the rightmost nonzero elements in each row starting with 1. The solution uses linear indices (numeric) to get the correct elements from the matrix.
I think this should do the trick. I wonder if there is more elegant way of doing this though.
% get only rows u want, i.e. with first row == 1
M2 = M(r,:);
% get indices of
% "the rightmost non-zero value of each row in M"
% for the rows u want
indicesOfinterest = c(r==1);
noOfIndeciesOfinterest = numel(indicesOfinterest);
% desired output column vector
output = zeros(noOfIndeciesOfinterest, 1);
% iterate through the indeces and select element in M2
% from each row and column indicated by the indice.
for idx = 1:noOfIndeciesOfinterest
output(idx) = M2(idx, indicesOfinterest(idx));
end
output % it is [3; 2 ; 5]
You can use
arrayfun(#(x) M(x,c(x)), find(r))
But unless you need r and c for other purposes, you can use
arrayfun(#(x) M(x,find(M(x,:),1,'last')), find(M(:,1)==1))
Here is a way to do it using linear indexing:
N = M';
lin_index = (0:size(N,1):prod(size(N))-1) + c;
v = N(lin_index);
v(r)
y = 0;
for m = 0:variable
for n = 0:m
y = y + f(n,m);
end
end
I vectorized the inner loop this way,
y = 0;
for m = 0:variable
n = 0:m
y = y + f(n,m);
end
This resulted in around 60% speed increase for my code. How do I also vectorize the outer loop?
You are probably looking for the meshgrid function. It is designed to fill in the sort of m by n combinations that it looks like you need. For example:
>> m = 1:4;
>> n = 1:3;
>> [mGridValues, nGridValues] = meshgrid(m,n)
mGridValues =
1 2 3 4
1 2 3 4
1 2 3 4
nGridValues =
1 1 1 1
2 2 2 2
3 3 3 3
This is a little more complicated since your inner loop depends on the value of your outer loop. So you will need to mask out the undesired [n, m] pairs (see below).
Modifying the prototype code that you have provided, you would end up with something like this:
[mValues, nValues] = meshgrid(0:variable, 0:variable); %Start with a full combination of values
mask = mValues >= nValues; %Identify all values where m >= n
mValues = mValues(mask); % And then remove pairs which do not
nValues = nValues(mask); % meet this criteria
y = f(nValues, mValues ); %Perform whatever work you are performing here
I have a matrix M(x,y). I want to apply a threshold in all values in x, such that if x
Example:
M = 1, 2;
3, 4;
5, 6;
If t = 5 is applied on the 1st dimension, the result will be
R = 0, 2;
0, 4;
5, 6;
One way (use M(:,1) to select the first column; M(:,1)<5 returns row indices for items in the first column that are lest than 5))-
> R = M;
> R(M(:,1)<5,1) = 0
R =
0 2
0 4
5 6
Another -
R = M;
[i,j]=find(M(:,1)<5); % locate rows (i) and cols (j) where M(:,1) < 5
% so j is just going to be all 1
% and i has corresponding rows
R(i,1)=0;
To do it in a matrix of arbitrary dimensions:
thresh_min = 5;
M(M < thresh_min) = 0;
The statement M < thresh_min returns indices of M that are less than thresh_min. Then, reindexing into M with these indices, you can set all of these valuse fitting your desired criterion to 0 (or whatever else).