take from matrix non-zero rows per column - matlab

I have a matrix A. Suppose it is:
A=[1 0 8;
0 0 2;
3 0 5;
4 8 0;
0 5 3;
6 1 3;
1 6 5;
0 7 1]
and I want to get the non-zero rows subscripts per column in a new matrix.
In my example that will be,
B = [ 1 3 4 6 7 0 0 0;
4 5 6 7 8 0 0 0;
1 2 3 5 6 7 8 0]
In terms of just size, if A=(m,n), B will be B=(n,m) (the transpose). In terms of content, B contains the subscripts of the non-zero rows in A as described above.

Here is one way:
mask = ~sort(~A); %// destination of row indexes in output
[ii,~]=find(A); %// get the row indexes
B = zeros(size(A));
B(mask) = ii; B=B.' %'//write indexes to output and transpose

I think this does what you want (get the non-zero row indices per column). It's very similar to this other question:
[r c] = size(A);
M = bsxfun(#times, A~=0, 1:size(A,2)).'; %'// substitute values by indices
[~, rows] = sort(M~=0,'descend'); %//'' push zeros to the end
cols = repmat(1:r,c,1);
ind = sub2ind([c r],rows(:),cols(:));
B = repmat(NaN,c,r);
B(:) = M(ind).';
B = B.';
Result:
>> B
B =
1 3 4 6 7 0 0 0
4 5 6 7 8 0 0 0
1 2 3 5 6 7 8 0

Related

Indexing a matrix in matlab according to conditions set on other matrices

I am trying to index my matrix based on two conditions, I'll explain.
Let's say I have two matrices:
a = [7 3 4; 5 6 7; 4 8 0];
b = [1 9 8; 2 4 6; 6 1 6];
And a third matrix to index:
c = [1 2 3; 4 5 6; 7 8 9];
My aim is to index c in a way that I get a 3x3 matrix in which only the values of c are copied over for whose indexes the following conditions are met and the rest are zeros.
a <= 5, b >= 6
Resulting matrix:
result = [0 2 3; 0 0 0; 7 0 9]
I hope I was able to explain my problem.
Given
a = [7 3 4; 5 6 7; 4 8 0];
b = [1 9 8; 2 4 6; 6 1 6];
c = [1 2 3; 4 5 6; 7 8 9];
result = zeros(size(c);
Using logical indexing,
>> d = (a <= 5) & (b >= 6)
d =
0 1 1
0 0 0
1 0 1
>> result(d) = c(d)
result =
0 2 3
0 0 0
7 0 9
Loop throw rows and columns and set the result.
for row=1:size(a,1)
for col=1:size(a,2)
if(a(row,col)> b(row,col))
result(row,col) = 0
else
result(row,col) = c(row,col)
end
end
end

Shift rows in matrix with respect to vector values in Octave/MATLAB

Can I shift rows in matrix A with respect to values in vector v?
For instance A and v specified as follows:
A =
1 0 0
1 0 0
1 0 0
v =
0 1 2
In this case I want to get this matrix from A:
A =
1 0 0
0 1 0
0 0 1
Every i-th row in A has been shifted by i-th value in v
Can I do this operation with native functions?
Or should I write it by myself?
I've tried circshift function, but I couldn't figure out how to shift rows separately.
The function circshift does not work as you want and even if you use a vector for the amount of shift, that is interpreted as the amount of shift for each dimension. While it is possible to loop over the rows of your matrix, that will not be very efficient.
More efficient is if you compute the indexing for each row which is actually quite simple:
## First, prepare all your input
octave> A = randi (9, 4, 6)
A =
8 3 2 7 4 5
4 4 7 3 9 1
1 6 3 9 2 3
7 4 1 9 5 5
octave> v = [0 2 0 1];
octave> sz = size (A);
## Compute how much shift per row, the column index (this will not work in Matlab)
octave> c_idx = mod ((0:(sz(2) -1)) .- v(:), sz(2)) +1
c_idx =
1 2 3 4 5 6
5 6 1 2 3 4
1 2 3 4 5 6
6 1 2 3 4 5
## Convert it to linear index
octave> idx = sub2ind (sz, repmat ((1:sz(1))(:), 1, sz(2)) , c_idx);
## All you need is to index
octave> A = A(idx)
A =
8 3 2 7 4 5
9 1 4 4 7 3
1 6 3 9 2 3
5 7 4 1 9 5
% A and v as above. These could be function input arguments
A = [1 0 0; 1 0 0; 1 0 0];
v = [0 1 2];
assert (all (size (v) == [1, size(A, 1)]), ...
'v needs to be a horizontal vector with as many elements as rows of A');
% Calculate shifted indices
[r, c] = size (A);
tmp = mod (repmat (0 : c-1, r, 1) - repmat (v.', 1, c), c) + 1;
Out = A(sub2ind ([r, c], repmat ([1 : r].', 1, c), tmp))
Out =
1 0 0
0 1 0
0 0 1
If performance is an issue, you can replace repmat with an equivalent bsxfun call which is more efficient (I use repmat here for simplicity to demonstrate the approach).
With focus on performance, here's one approach using bsxfun/broadcasting -
[m,n] = size(A);
idx0 = mod(bsxfun(#plus,n-v(:),1:n)-1,n);
out = A(bsxfun(#plus,(idx0*m),(1:m)'))
Sample run -
A =
1 7 5 7 7
4 8 5 7 6
4 2 6 3 2
v =
3 1 2
out =
5 7 7 1 7
6 4 8 5 7
3 2 4 2 6
Equivalent Octave version to use automatic broadcasting would look something like this -
[m,n] = size(A);
idx0 = mod( ((n-v(:)) + (1:n)) -1 ,n);
out = A((idx0*m)+(1:m)')
Shift vector with circshift in loop, iterating row index.

Permute the Matrix with Given Index

Given A is symmetry matrix with size n and
A =
1 2 3 4 5 % The Position
1 [0 5 2 4 1
2 5 0 3 0 2
3 2 3 0 0 0
4 4 0 0 0 5
5 1 2 0 5 0]
B is a row vector that permute the matrix A row and column
B = [2 4 1 5 3]
The output that I want is
C =
2 4 1 5 3 % The New Position given by Matrix B
2 [0 0 5 2 3
4 0 0 4 5 0
1 5 4 0 1 2
5 2 5 1 0 0
3 3 0 2 0 0]
I can get the output by using simple for loop
index = [2,4,1,5,3];
C = zeros(5,5);
for i = 1:5
for j = 1:5
% Position of in square matrix n
% (i,j) = (i-1)*n + j
C(i,j) = A((index(i)-1)*5+index(j));
end
end
However, if I want to permute a matrix with size 80x80, then I need to run 1600 times in order to get the output.
Is there any simple trick to do it instead of using for loop?
You should be able to rearrange your matrices as follows:
C = A(index,index);
This rearranges each dimension according to the index variable independently.

Find position of vector in matrix [duplicate]

This question already has answers here:
General method to find submatrix in matlab matrix
(3 answers)
Closed 8 years ago.
I have the vector:
1 2 3
and the matrix:
4 1 2 3 5 5
9 8 7 6 3 1
1 4 7 8 2 3
I am trying to find a simple way of locating the vector [1 2 3] in my matrix.
A function returning either coordinates (Ie: (1,2:4)) or a matrix of 1s where there is a match a 0s where there isn't, Ie:
0 1 1 1 0 0
0 0 0 0 0 0
0 0 0 0 0 0
So far, the only function I've found is is 'ismember', which however only tells me if the individual components of the vector appear in the matrix. Suggestions?
Use strfind with a linearized version of the matrix, and then convert linear indices to subindices. Care should be taken to remove matches of the vector spanning different rows.
mat = [1 2 3 1 2 3 1 2;
3 0 1 2 3 5 4 4]; %// data
vec = [1 2 3]; %// data
ind = strfind(reshape(mat.',[],1).', vec);
[col row] = ind2sub(fliplr(size(mat)), ind);
keep = col<=size(mat,2)-length(vec)+1; %// remove result split across rows
row = row(keep);
col = col(keep);
Result for this example:
>> row, col
row =
1 1 2
col =
1 4 3
meaning the vector appears three times: row 1, col 1; row 1, col 4; row 2, col 3.
The result can be expressed in zero-one form as follows:
result = zeros(fliplr(size(mat)));
ind_ones = bsxfun(#plus, ind(keep).', 0:numel(vec)-1);
result(ind_ones) = 1;
result = result.';
which gives
>> result
result =
1 1 1 1 1 1 0 0
0 0 1 1 1 0 0 0
One way to get the starting location of the vector in the matrix is using colfilt:
>> A = [1 2 3 1 2 3 1 2; ...
3 0 1 2 3 5 4 4]; % matrix from Luis Mendo
>> T = [1 2 3];
>> colFun = #(x,t) all(x==repmat(t,1,size(x,2)),1);
>> B = colfilt(A,size(T),'sliding',colFun,T(:))
B =
0 1 0 0 1 0 0 0
0 0 0 1 0 0 0 0
That gives a mask of the center points, which translate to (row,col) coordinates:
>> [ii,jj]=find(B);
>> locs = bsxfun(#minus,[ii jj],floor((size(T)-1)/2))
locs =
1 1
2 3
1 4

Greatest values in a matrix, row by row - matlab

I have an m-by-n matrix. For each row, I want to find the position of the k greatest values, and set the others to 0.
Example, for k=2
I WANT
[1 2 3 5 [0 0 3 5
4 5 9 3 0 5 9 0
2 6 7 1] 0 6 7 0 ]
You can achieve it easily using the second output of sort:
data = [ 1 2 3 5
4 5 9 3
2 6 7 1 ];
k = 2;
[M N] = size(data);
[~, ind] = sort(data,2);
data(repmat((1:M).',1,N-k) + (ind(:,1:N-k)-1)*M) = 0;
In the example, this gives
>> data
data =
0 0 3 5
0 5 9 0
0 6 7 0
You can use prctile command to find the threshold per-line.
prctile returns percentiles of the values in the rows of data and thus can be easily tweaked to return the threshold value above which the k-th largest elements at each row exist:
T = prctile( data, 100*(1 - k/size(data,2)), 2 ); % find the threshold
out = bsxfun(#gt, data, T) .* data; % set lower than T to zero
For the data matrix posted in the question we get
>> out
out =
0 0 3 5
0 5 9 0
0 6 7 0