The input is an N-by-1 matrix. I need to reshape it to L-by-M matrix. The following is an example.
Input:
b =
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Set length = 18, Output:
X =
1 2 3
2 3 4
3 4 5
4 5 6
5 6 7
6 7 8
7 8 9
8 9 10
9 10 11
10 11 12
11 12 13
12 13 14
13 14 15
14 15 16
15 16 17
16 17 18
17 18 19
18 19 20
Because I have a very big matrix, using a loop to reshape is very inefficient. How can I improve the reshape speed?
Your example output matrix X is the perfect matrix to index a vector of length N to get what you want. It's also very easy to create using bsxfun:
N = 20;
b = rand(N,1);
M = 3; %// number of columns
L = N-M; %// Note that N-M is an upper limit for L!
idx = bsxfun(#plus, (0:L)', 1:M)
X = b(idx)
That's exactly what im2col (from the Image Processing Toolbox) does:
b = (1:20).'; %'// example data
L = 18; % // desired length of sliding blocks
x = im2col(b, [L 1]); % // result
I'd use horzcat. For example:
function X = reshaper(b,len)
diff = length(b) - len + 1;
X = b(1:len);
for i=2:diff
X = horzcat(X,b(i:len+(i-1)));
end
You could probably remove the for loop with some further thought.
Related
I want to create matrix B from matrix A, with the following rules:
Non-diagonal elements A are like non-diagonal elements of B.
The main diagonal of A is the antidiagonal of B
The antidiagonal of A is the main diagonal of B.
For example:
A = [ 1 2 3 4;
7 8 9 10;
13 14 15 16;
19 20 21 22 ];
B = [ 4 2 3 1;
7 9 8 10;
13 15 14 16;
22 20 21 19 ];
How can I create B given A?
You can create all of the indices, then it's a single assignment.
% Get size of square matrix A
n = size(A,1);
% Indicies are 1:n^2 by default
idx = 1:n^2;
% Swap diagonal and antidiagonal indices
idx( [1:(n+1):n^2, n^2-n+1:1-n:n] ) = [n^2-n+1:1-n:n, 1:(n+1):n^2];
% Use the indexing array to create B from A, reshape to be n*n
B = reshape( A( idx ), n, n );
Output for your example A:
B =
4 2 3 1
7 9 8 10
13 15 14 16
22 20 21 19
There are so many ways to reach that results, it is just an indexing exercise. Here is one (of the many) way to reach that result for any square matrix of size n:
%% input
A=[ 1 2 3 4 ;
7 8 9 10 ;
13 14 15 16 ;
19 20 21 22 ];
%% Calculate linear indices for the diagonal and antidiagonal
n=size(A,1) ;
idxdiag = 1:(n+1):n^2 ; % => idxdiag = [1 6 11 16]
idxantidiag = n:(n-1):n^2-1 ; % => idxantidiag = [4 7 10 13]
%% Generate B
B = A ; % start with a simple copy (for the non-diagonal elements)
% Method 1: direct indice assignment
B(idxdiag) = diag(fliplr(A)) ; % Assign diagonal elements of B
B(idxantidiag) = flipud(diag(A)) ; % Assign antidiagonal elements of B
% Method 2: summation
B([idxdiag idxantidiag]) = 0 ;
B = B + diag(diag(fliplr(A))) + fliplr(diag(diag(A))) ;
B =
4 2 3 1
7 9 8 10
13 15 14 16
22 20 21 19
Both methods return exactly the same matrix B.
I suggest you familiarise yourself with the MATLAB function used to understand what is going on behind the scene:
fliplr
flipud
diag
and may be have a read at:
Matrix Indexing in MATLAB
I thought a little differently and came to a conclusion
A=[1 2 3 4;7 8 9 10;13 14 15 16; 19 20 21 22];;
n=size(A,1) ;
B=zeros(n,n) ;
for i=1:n
for j=1:n
if i==j
B(i,j)=A(i,n-i+1);
elseif j==n-i+1
B(i,j)=A(i,i);
else
B(i,j)=A(i,j);
end
end
end
B
Here's a variant using eye, find, and flip to generate linear indices:
ind1 = find(eye(size(A)));
ind2 = flip(find(flip(eye(size(A)))));
B = A;
B([ind1 ind2]) = B([ind2 ind1]);
B =
4 2 3 1
7 9 8 10
13 15 14 16
22 20 21 19
And here's a variant of the above that uses just eye and flip to generate logical indices:
ind1 = eye(size(A), 'logical');
ind2 = flip(ind1);
B = A;
B(ind1) = flip(A(ind2));
B(ind2) = flip(A(ind1));
B =
4 2 3 1
7 9 8 10
13 15 14 16
22 20 21 19
I have a matrix A in Matlab of dimension Nx(N-1), e.g.
N=5;
A=[1 2 3 4;
5 6 7 8;
9 10 11 12;
13 14 15 16;
17 18 19 20];
I want to rearrange the elements of A in a certain way. Specifically I want to create a matrix B of dimension (N-1)xN such that:
for i=1,...,N,
B(:,i) collects
1) the first i-1 elements of the i-1th column of A and
2) the last N-i elements of the ith column of A.
Notice that for i=1 the i-1th column of A does not exist and therefore 1) is skipped; similarly, for i=N theith column of A does not exist and therefore 2) is skipped.
In the example above
B=[5 1 2 3 4
9 10 6 7 8
13 14 15 11 12
17 18 19 20 16];
This code does what I want. I am asking your help to vectorise it in an efficient way.
B=zeros(N-1,N);
for i=1:N
if i>1 && i<N
step1=A(1:i-1,i-1);
step2=A(i+1:N,i);
B(:,i)=[step1;step2];
elseif i==1
B(:,i)=A(i+1:N,i);
elseif i==N
B(:,i)=A(1:i-1,i-1);
end
end
Extract the lower and upper triangular matrices of A. Then reassemble them with a "diagonal shift":
u = triu(A);
l = tril(A,-1);
B = padarray(u(1:end-1,:),[0 1],'pre') + padarray(l(2:end,:),[0 1],'post');
Another valid approach using logical indexing combined with tril and triu:
B = zeros(size(A'));
B(tril(true(size(B)))) = A(tril(true(size(A)), -1));
B(triu(true(size(B)), 1)) = A(triu(true(size(A))));
Result:
>> B
B =
5 1 2 3 4
9 10 6 7 8
13 14 15 11 12
17 18 19 20 16
I have two matrices in Matlab A and B respectively of dimension MxN and GxN.
M can be greater or smaller than G.
A and B do not contain identical rows.
I want to construct a matrix C of dimension Hx(N+2) in the following way
C=[];
for i=1:size(A,1)
%if A(i,1:end-1) coincides with a row in B(:,1:end-1) (it can coincide with only one row at most)
%then C=[C;A(i,1:end) B(j,end)]; %where j is the index of the identical row in B
%otherwise impose C=[C;A(i,1:end) 0]
end
for i=1:size(B,1)
%if B(i,1:end-1) does not coincide with any row in A(:,1:end-1)
%then impose C=[C; B(i,1:end-1) 0 B(i,end)];
end
For example:
A=[1 2 3 4 5 100; 6 7 8 9 10 101; 11 12 13 14 15 102];
B=[6 7 8 9 10 103; 15 16 17 18 19 104]
C=[1 2 3 4 5 100 0; 6 7 8 9 10 101 103; 11 12 13 14 16 102 0; 15 16 17 18 19 0 104]
As M and G can be very high, I am looking for the fastest way to perform this.
You can use ismember + indexing to do your task:
[idx1,idx2] = ismember(A(:,1:end-1), B(:,1:end-1), 'rows');
idx3 = ~ismember(B(:,1:end-1), A(:,1:end-1), 'rows');
C(idx1,:) = [A(idx1,:) B(idx2(idx1),end)];
C(~idx1,:) = [A(~idx1,:) zeros(sum(~idx1),1)];
C=[C;B(idx3,1:end-1) zeros(sum(idx3),1) B(idx3,end)];
You could also use intersect with a bit of preallocation to speed up the assignment (if M or G gets really large).
A=[1 2 3 4 5 100; 6 7 8 9 10 101; 11 12 13 14 15 102];
B=[6 7 8 9 10 103; 15 16 17 18 19 104];
C=[1 2 3 4 5 100 0; 6 7 8 9 10 101 103; 11 12 13 14 16 102 0; 15 16 17 18 19 0 104];
[M,N] = size(A);
G = size(B,1);
[tmp, idxA, idxB] = intersect(A(:,1:end-1),B(:,1:end-1),'rows')
idxBnotA = setdiff([1:G],idxB);
H = M + G - length(idxA);
C1 = zeros(H,N+1);
C1(1:M,1:N) = A;
C1(idxA,end) = B(idxB,end);
C1(M+1:end,1:end-2) = B(idxBnotA,1:end-1);
C1(M+1:end,end) = B(idxBnotA,end)
I have a 2 dimensional matrix and I want to get the data along a particular line. Similar to what 'Slice' does to a 3D matrix. Is there a a way to do a similar thing on a 2D matrix.
Thanks in advance.
Extracting all values of a column or a line:
>> M = magic(4)
M =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> particular_row = 3;
>> M(particular_row,:)
ans =
9 7 6 12
>> particular_column = 2;
>> M(:,particular_column)
ans =
2
11
7
14
Extracting values along a diagonal:
What if I want to get the data along any direction say along a line joining matrix index (1,1) to (4,4) of a 5x5 matrix?
I'd use linear indexing and the sub2ind function for this task. Demo:
(1,1) to (4,4):
>> M = magic(5)
M =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
>> M(sub2ind(size(M), 1:4, 1:4))
ans =
17 5 13 21
Another example: (1,2) to (3,4):
M(sub2ind(size(M), 1:3, 2:4))
ans =
24 7 20
I made a matrix in Matlab, say,
A = magic(5);
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
Now I found the indices I want using the find function as:
ind = find(A(:,5)>3 & A(:,4)>= 8);
ind =
1
2
3
Now if I want to get a subset of matrix A for those indices using B = A(ind) function, I only get the first column of the matrix:
B = A(ind)
B =
17
23
4
How can I get all the columns as subset??
Oops ... I got it
B = A(ind,:);