I have a given matrix H and I would like to unfold (expand) it to find a matrix B by following the method below :
Let H be a matrix of dimension m × n. Let x = gcd (m,n)
The matrix H is cut in two parts.
The cutting pattern being such that :
The "diagonal cut" is made by alternately moving c = n/x units to the right (we move c units to the right several times).
We alternately move c-b = m/x units down (i.e. b = (n-m)/x) (we move b units down several times).
After applying this "diagonal cut" of the matrix, we copy and paste the two parts repeatedly to obtain the matrix B.
Exemple : Let the matrix H of dimension m × n = 5 × 10 defined by :
1 0 1 1 1 0 1 1 0 0
0 1 1 0 0 1 1 0 1 1
1 1 0 1 1 1 0 1 0 0
0 1 1 0 1 0 1 0 1 1
1 0 0 1 0 1 0 1 1 1
Let's calculate x = gcd (m,n) = gcd (5,10) = 5,
Alternatively move to the right : c = n/x = 10/5 = 2,
Alternatively move down : b = (n-m)/x = (10-5)/5 = 1.
Diagonal cutting diagram : The matrix H is cut in two parts.
The cutting pattern is such that :
We move c = 2 units to the right several times c = 2 units to the right,
We repeatedly move c - b = 1 unit downwards.
We get :
After applying this "diagonal cut" of the matrix, we copy and paste the two parts repeatedly to obtain the matrix :
Remark : In the matrices X, X1 and X2 the dashes are zeros.
The resulting matrix B is (L is factor) :
Any suggestions?
This can be done by creating a logical mask with the cutting pattern, and then element-wise multiplying the input by the mask and by its negation. Repeating by L can be done with blkdiag.
H = [1 0 1 1 1 0 1 1 0 0
0 1 1 0 0 1 1 0 1 1
1 1 0 1 1 1 0 1 0 0
0 1 1 0 1 0 1 0 1 1
1 0 0 1 0 1 0 1 1 1];
L = 2;
[m, n] = size(H);
x = gcd(m, n);
c = n / x;
b = (n-m)/x;
mask = repelem(tril(true(m/b)), b, c);
A = [H.*mask; H.*~mask];
A = repmat({A}, L, 1);
B = blkdiag(A{:});
Related
I have a matrix B and I would like to obtain a new matrix C from B by adding its last w*a rows to the first w*a rows (w and a will be defined afterwards).
My matrix B is generally defined by :
I would like to obtain matrix C defined in a general way by:
The characteristics of matrices B and C are:
L and w are defined real values;
B0,B1,...,Bw are of dimension: a by b;
B is of dimension: [(L+w)×a] by (L×b);
C is of dimension: (L×a) by (L×b).
Example: For L = 4 and w = 2 I obtain the following matrix B:
The w*a = 2*1 = 2 last rows of B are:
The w*a = 2*1 = 2 first rows of B are:
By adding the two matrices we have:
The matrix C thus obtained is then:
For B0 = [1 0], B1 = [0 1] and B2 = [1 1]. We obtain :
B0, B1 and B2 are of dimension a by b i.e. 1 by 2;
B is of dimension: [(L+w )×(a)] by (L×b) i.e. [(4+2)×1] by (4×2) i.e. 6 by 8;
C is of dimension: (L×a) by (L×b) i.e. (4×1) by (4×2) i.e. 4 by 8.
The matrices B and C that I get are as follows:
B =
1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0
1 1 0 1 1 0 0 0
0 0 1 1 0 1 1 0
0 0 0 0 1 1 0 1
0 0 0 0 0 0 1 1
C =
1 0 0 0 1 1 0 1
0 1 1 0 0 0 1 1
1 1 0 1 1 0 0 0
0 0 1 1 0 1 1 0
I would like to have some suggestions on how to program this construction so that from a given matrix B I can deduce the matrix C.
Matlab's range indexing should help you do this in a few steps. The key things to remember are that ranges are inclusive, i.e. A[1:3] is a three 3x1 matrix, and that you can use the keyword end to automatically index the end of the matrix row or column.
%% Variables from OP example
w = 2;
L = 4;
B0 = [1 0];
B1 = [0 1];
B2 = [1 1];
[a, b] = size(B0);
% Construct B
BX = [B0;B1;B2]
B = zeros((L+w)*a, L*b);
for ii = 0:L-1
B(ii+1:ii+w+1, ii*b+1:ii*b+b) = BX;
end
%% Construct C <- THIS PART IS THE ANSWER TO THE QUESTION
% Grab first rows of B
B_first = B(1:end-w*a, :) % Indexing starts at first row, continues to w*a rows before the end, and gets all columns
% Grab last rows of B
B_last = B(end-w*a+1:end, :); % Indexing starts at w*a rows before the end, continues to end. Plus one is needed to avoid off by one error.
% Initialize C to be the same as B_first
C = B_first;
% Add B_last to the first rows of C
C(1:w*a, :) = C(1:w*a, :) + B_last;
I get the output
C =
1 0 0 0 0 0 1 1 0 1
0 1 1 0 0 0 0 0 1 1
1 1 0 1 1 0 0 0 0 0
0 0 1 1 0 1 1 0 0 0
0 0 0 0 1 1 0 1 1 0
I need some information on how to program the sliding window of matrix.
I have a diagonal matrix B defined below by:
I would like to deduce from the given matrix B and the size of the window W the different matrix for t ranging from 1 to the size L of the matrix.
Note: Each window has the same width and height. And the window moves on the diagonal.
Example: We have a matrix with size 5 by 8 and the size of the window is 3 by 4 and moves on the diagonal. The matrix B of the example is:
My code:
% Sliding window matrix
B = [ 1 1 0 0 0 0 0 0
2 2 1 1 0 0 0 0
0 0 2 2 1 1 0 0
0 0 0 0 2 2 1 1
0 0 0 0 0 0 2 2]; % Matrix B
W = 4; % Size of the window wanted here is 4
n = size(B,2) - W + 1;
X = zeros(size(B,1),W*n);
k = W-1:-1:0;
for i = 1:n
window = B(:,i:i+W-1)';
X(:,i*W - k) = B(:,i:i+W-1);
end
window;
With W = 4 and n of the for loop set to 1 I get:
window = [1 2 0 0 0
1 2 0 0 0
0 1 2 0 0
0 1 2 0 0];
Whereas I should get:
window = [1 1 0 0
2 2 1 1
0 0 2 2];
With my code I don't get exactly the different sub-matrix obtained by sliding window.
I would like my program to be able, depending on the matrix B and the choice of dimensions of my window, to return the diagonal matrix representing the window and shift one step to also recover the next diagonal matrix which is identical to the previous one, and so on until the end.
Any suggestions?
You need to specify window dimensions separately. Try this:
B = [ 1 1 0 0 0 0 0 0
2 2 1 1 0 0 0 0
0 0 2 2 1 1 0 0
0 0 0 0 2 2 1 1
0 0 0 0 0 0 2 2];
[bh, bw] = size(B); % matrix size
wh = 3; % window height
ww = 4; % window width
sx = 2; % sliding step length along 2nd dim
sy = 1; % sliding step length along 1st dim
wx = 1:sx:(bw-ww+1); % window left
wy = 1:sy:(bh-wh+1); % window top
n = min(numel(wx), numel(wy)); % number of windows which fit in matrix
for ii = 1:n
X = B((1:wh)+wy(ii)-1, (1:ww)+wx(ii)-1)
end
Note that the sliding window, as it is described in your question, does not necessarily visit the entire matrix diagonal. Unless you calculate the sx and sy based on the dimensions of the matrix.
B = randi(3, [8 13])
[bh, bw] = size(B); % matrix size
wh = 3; % window height
ww = 4; % window width
sx = 3; % slideing step length along 2nd dim
sy = 1; % slideing step length along 1st dim
I would like to create a square matrix of size n x n where the diagonal elements as well as the left-diagonal are all equal to 1. The rest of the elements are equal to 0.
For example, this would be the expected result if the matrix was 5 x 5:
1 0 0 0 0
1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 1 1
How could I do this in MATLAB?
Trivial using the tril function:
tril(ones(n),0) - tril(ones(n),-2)
And if you wanted a thicker line of 1s just adjust that -2:
n = 10;
m = 4;
tril(ones(n),0) - tril(ones(n),-m)
If you prefer to use diag like excaza suggested then try
diag(ones(n,1)) + diag(ones(n-1,1),-1)
but you can't control the 'thickness' of the stripe this way. However, for a thickness of 2, it might perform better. You'd have to test it though.
You can also use spdiags too to create that matrix:
n = 5;
v = ones(n,1);
d = full(spdiags([v v], [-1 0], n, n));
We get:
>> d
d =
1 0 0 0 0
1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 1 1
The first two lines define the desired size of the matrix, assuming a square n x n as well as a vector of all ones that is of length n x 1. We then call spdiags to define where along the diagonal of this matrix this vector will be populating. We want to define the main diagonal to have all ones as well as the diagonal to the left of the main diagonal, or -1 away from the main diagonal. spdiags will adjust the total number of elements for the diagonal away from the main to compensate.
We also ensure that the output is of size n x n, but this matrix is actually sparse . We need to convert the matrix to full to complete the result.,
With a bit of indices juggling, you can also do this:
N = 5;
ind = repelem(1:N, 2); % [1 1 2 2 3 3 ... N N]
M = full(sparse(ind(2:end), ind(1:end-1), 1))
Simple approach using linear indexing:
n = 5;
M = eye(n);
M(2:n+1:end) = 1;
This can also be done with bsxfun:
n = 5; %// matrix size
d = [0 -1]; %// diagonals you want set to 1
M = double(ismember(bsxfun(#minus, 1:n, (1:n).'), d));
For example, to obtain a 5x5 matrix with the main diagonal and the two diagonals below set to 1, define n=5 and d = [0 -1 -2], which gives
M =
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
0 1 1 1 0
0 0 1 1 1
Apologies in advance if this question is a duplicate, or if the solution to this question is very straightforward in Matlab. I have a M x N matrix A, a 1 x M vector ind, and another vector val. For example,
A = zeros(6,5);
ind = [3 4 2 4 2 3];
val = [1 2 3];
I would like to vectorize the following code:
for i = 1 : size(A,1)
A(i, ind(i)-1 : ind(i)+1) = val;
end
>> A
A =
0 1 2 3 0
0 0 1 2 3
1 2 3 0 0
0 0 1 2 3
1 2 3 0 0
0 1 2 3 0
That is, for row i of A, I want to insert the vector val in a certain location, as specificied by the i'th entry of ind. What's the best way to do this in Matlab without a for loop?
It can be done using bsxfun's masking capability: build a mask telling where the values will be placed, and then fill those values in. In doing this, it's easier to work with columns instead of rows (because of Matlab's column major order), and transpose at the end.
The code below determines the minimum number of columns in the final A so that all values fit at the specified positions.
Your example applies a displacement of -1 with respect to ind. The code includes a generic displacement, which can be modified.
%// Data
ind = [3 4 2 4 2 3]; %// indices
val = [1 2 3]; %// values
d = -1; %// displacement for indices. -1 in your example
%// Let's go
n = numel(val);
m = numel(ind);
N = max(ind-1) + n + d; %// number of rows in A (rows before transposition)
mask = bsxfun(#ge, (1:N).', ind+d) & bsxfun(#le, (1:N).', ind+n-1+d); %// build mask
A = zeros(size(mask)); %/// define A with zeros
A(mask) = repmat(val(:), m, 1); %// fill in values as indicated by mask
A = A.'; %// transpose
Result in your example:
A =
0 1 2 3 0
0 0 1 2 3
1 2 3 0 0
0 0 1 2 3
1 2 3 0 0
0 1 2 3 0
Result with d = 0 (no displacement):
A =
0 0 1 2 3 0
0 0 0 1 2 3
0 1 2 3 0 0
0 0 0 1 2 3
0 1 2 3 0 0
0 0 1 2 3 0
If you can handle a bit of bsxfun overdose, here's one with bsxfun's adding capability -
N = numel(ind);
A(bsxfun(#plus,N*[-1:1]',(ind-1)*N + [1:N])) = repmat(val(:),1,N)
Sample run -
>> ind
ind =
3 4 2 4 2 3
>> val
val =
1 2 3
>> A = zeros(6,5);
>> N = numel(ind);
>> A(bsxfun(#plus,N*[-1:1]',(ind-1)*N + [1:N])) = repmat(val(:),1,N)
A =
0 1 2 3 0
0 0 1 2 3
1 2 3 0 0
0 0 1 2 3
1 2 3 0 0
0 1 2 3 0
I have a logical matrix A, and I would like to select all the elements to the left of each of my 1s values given a fixed distant. Let's say my distance is 4, I would like to (for instance) replace with a fixed value (saying 2) all the 4 cells at the left of each 1 in A.
A= [0 0 0 0 0 1 0
0 1 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 1 0 1]
B= [0 2 2 2 2 1 0
2 1 0 0 0 0 0
0 0 0 0 0 0 0
2 2 2 2 2 2 1]
In B is what I would like to have, considering also overwrting (last row in B), and cases where there is only 1 value at the left of my 1 and not 4 as the fixed searching distance (second row).
How about this lovely one-liner?
n = 3;
const = 5;
A = [0 0 0 0 0 1 0;
0 1 0 0 0 0 0;
0 0 0 0 0 0 0;
0 0 0 0 1 0 1]
A(bsxfun(#ne,fliplr(filter(ones(1,1+n),1,fliplr(A),[],2)),A)) = const
results in:
A =
0 0 5 5 5 1 0
5 1 0 0 0 0 0
0 0 0 0 0 0 0
0 5 5 5 5 5 1
here some explanations:
Am = fliplr(A); %// mirrored input required
Bm = filter(ones(1,1+n),1,Am,[],2); %// moving average filter for 2nd dimension
B = fliplr(Bm); %// back mirrored
mask = bsxfun(#ne,B,A) %// mask for constants
A(mask) = const
Here is a simple solution you could have come up with:
w=4; % Window size
v=2; % Desired value
B = A;
for r=1:size(A,1) % Go over all rows
for c=2:size(A,2) % Go over all columns
if A(r,c)==1 % If we encounter a 1
B(r,max(1,c-w):c-1)=v; % Set the four spots before this point to your value (if possible)
end
end
end
d = 4; %// distance
v = 2; %// value
A = fliplr(A).'; %'// flip matrix, and transpose to work along rows.
ind = logical( cumsum(A) ...
- [ zeros(size(A,1)-d+2,size(A,2)); cumsum(A(1:end-d-1,:)) ] - A );
A(ind) = v;
A = fliplr(A.');
Result:
A =
0 2 2 2 2 1 0
2 1 0 0 0 0 0
0 0 0 0 0 0 0
2 2 2 2 2 2 1
Approach #1 One-liner using imdilate available with Image Processing Toolbox -
A(imdilate(A,[ones(1,4) zeros(1,4+1)])==1)=2
Explanation
Step #1: Create a morphological structuring element to be used with imdilate -
morph_strel = [ones(1,4) zeros(1,4+1)]
This basically represents a window extending n places to the left with ones and n places to the right including the origin with zeros.
Step #2: Use imdilate that will modify A such that we would have 1 at all four places to the left of each 1 in A -
imdilate_result = imdilate(A,morph_strel)
Step #3: Select all four indices for each 1 of A and set them to 2 -
A(imdilate_result==1)=2
Thus, one can write a general form for this approach as -
A(imdilate(A,[ones(1,window_length) zeros(1,window_length+1)])==1)=new_value
where window_length would be 4 and new_value would be 2 for the given data.
Approach #2 Using bsxfun-
%// Paramters
window_length = 4;
new_value = 2;
B = A' %//'
[r,c] = find(B)
extents = bsxfun(#plus,r,-window_length:-1)
valid_ind1 = extents>0
jump_factor = (c-1)*size(B,1)
extents_valid = extents.*valid_ind1
B(nonzeros(bsxfun(#plus,extents_valid,jump_factor).*valid_ind1))=new_value
B = B' %// B is the desired output