I'd like to transform a vector
v = [1,2,3,4]
into a matrix (4x4) with diagonals like this:
1 2 3 4
2 1 2 3
3 2 1 2
4 3 2 1
You want to generate a Toeplitz matrix, so you should use the toeplitz function.
v = [ 1 2 3 4 ];
out = toeplitz(v)
out =
1 2 3 4
2 1 2 3
3 2 1 2
4 3 2 1
If A is your 4x4 array, just do:
A(1:5:end) = 1:4;
Best
v = [1 2 3 4];
A = gallery('circul',v);
B = triu(A,0)+triu(A,1)';
Related
I'm trying to create a symmetric n by n matrix where the symmetry line is linearly decreasing from n to 1.
For example a 5 by 5 would be:
5 4 3 2 1
4 4 3 2 1
3 3 3 2 1
2 2 2 2 1
1 1 1 1 1
Thanks
Using implicit expansion, the min function will generate a square matrix from the combination of a row and a column vector, so the result can be gained by doing:
N = 5;
A = min( (N:-1:1).', (N:-1:1) );
You may use:
numRows = 5;
mI = repmat((1:numRows)', 1, numRows);
mJ = repmat((1:numRows), numRows, 1);
mA = flip(flip(min(mI, mJ), 1), 2)
With the answer given by:
mA =
5 4 3 2 1
4 4 3 2 1
3 3 3 2 1
2 2 2 2 1
1 1 1 1 1
Supose there is a Matrix
A =
1 3 2 4
4 2 5 8
6 1 4 9
and I have a Vector containing the "class" of each column of this matrix for example
v = [1 , 1 , 2 , 3]
How can I sum the columns of the matrix to a new matrix as column vectors each to the column of their class? In this example columns 1 and 2 of A would added to the first column of the new matrix, column 2 to the 3 to the 2nd, column 4 the the 3rd.
Like
SUM =
4 2 4
6 5 8
7 4 9
Is this possible without loops?
One of the perfect scenarios to combine the powers of accumarray and bsxfun -
%// Since we are to accumulate columns, first step would be to transpose A
At = A.' %//'
%// Create a vector of linear IDs for use with ACCUMARRAY later on
idx = bsxfun(#plus,v(:),[0:size(A,1)-1]*max(v))
%// Use ACCUMARRAY to accumulate rows from At, i.e. columns from A based on the IDs
out = reshape(accumarray(idx(:),At(:)),[],size(A,1)).'
Sample run -
A =
1 3 2 4 6 0
4 2 5 8 9 2
6 1 4 9 8 9
v =
1 1 2 3 3 2
out =
4 2 10
6 7 17
7 13 17
An alternative with accumarray in 2D. Generate a grid with the vector v and then apply accumarray:
A = A.';
v = [1 1 2 3];
[X, Y] = ndgrid(v,1:size(A,2));
Here X and Y look like this:
X =
1 1 1
1 1 1
2 2 2
3 3 3
Y =
1 2 3
1 2 3
1 2 3
1 2 3
Then apply accumarray:
B=accumarray([X(:) Y(:)],A(:)),
SUM = B.'
SUM =
4 2 4
6 5 8
7 4 9
As you see, using [X(:) Y(:)] create the following array:
ans =
1 1
1 1
2 1
3 1
1 2
1 2
2 2
3 2
1 3
1 3
2 3
3 3
in which the vector v containing the "class" is replicated 3 times since there are 3 unique classes that are to be summed up together.
EDIT:
As pointed out by knedlsepp you can get rid of the transpose to A and B like so:
[X2, Y2] = ndgrid(1:size(A,1),v);
B = accumarray([X2(:) Y2(:)],A(:))
which ends up doing the same. I find it a bit more easier to visualize with the transposes but that gives the same result.
How about a one-liner?
result = full(sparse(repmat(v,size(A,1),1), repmat((1:size(A,1)).',1,size(A,2)), A));
Don't optimize prematurely!
The for loop performs fine for your problem:
out = zeros(size(A,1), max(v));
for i = 1:numel(v)
out(:,v(i)) = out(:,v(i)) + A(:,i);
end
BTW: With fine, I mean: fast, fast, fast!
given matrix A of size 6 by 6 contain blocks of numbers,each block of size 2 by 2, and outher reference matrix R of size 2 by 12 also contain blocks of numbers, each block of size 2 by 2. the perpse of the whole process is to form a new matrix, called the Index matrix, contain index's that refer to the position of the blocks within the matrix A based on the order of the blocks within the reference matrix R. and here is an exemple
matrix A:
A =[1 1 2 2 3 3;
1 1 2 2 3 3;
1 1 3 3 4 4;
1 1 3 3 4 4;
4 4 5 5 6 6;
4 4 5 5 6 6 ]
matrix R:
R=[1 1 2 2 3 3 4 4 5 5 6 6;
1 1 2 2 3 3 4 4 5 5 6 6 ]
the new matrix is:
Index =[1 2 3;
1 3 4;
4 5 6]
any ideas ?
With my favourite three guys - bsxfun, permute, reshape for an efficient and generic solution -
blksz = 2; %// blocksize
num_rowblksA = size(A,1)/blksz; %// number of blocks along rows in A
%// Create blksz x blksz sized blocks for A and B
A1 = reshape(permute(reshape(A,blksz,num_rowblksA,[]),[1 3 2]),blksz^2,[])
R1 = reshape(R,blksz^2,1,[])
%// Find the matches with "bsxfun(#eq" and corresponding indices
[valid,idx] = max(all(bsxfun(#eq,A1,R1),1),[],3)
%// Or with PDIST2:
%// [valid,idx] = max(pdist2(A1.',reshape(R,blksz^2,[]).')==0,[],2)
idx(~valid) = 0
%// Reshape the indices to the shapes of blocked shapes in A
Index = reshape(idx,[],num_rowblksA).'
Sample run with more random inputs -
>> A
A =
2 1 1 2
1 2 2 1
1 1 1 1
2 2 2 2
1 2 2 1
1 2 1 1
>> R
R =
2 1 1 1 1 2 2 2 1 1 1 1
2 1 2 1 1 2 2 1 2 2 2 1
>> Index
Index =
0 0
5 5
3 0
Is there an efficient way (e.g., without using for loops manually) to create a matrix in Matlab that enumerates the 2-D coordinates of a matrix of a given size?
For example, if I'm given an m x n matrix, I want the resulting mn x 2 matrix to be as follows:
1 1
1 2
1 3
...
1 n
2 1
2 2
...
m 1
m 2
...
m n
Thanks in advance!
mat = [1 2;3 4;5 6;7 8;9 10];
[m,n] = size(mat);
vec = [kron(1:m,ones(1,n)); kron(ones(1,m),1:n)]'
1 1
1 2
2 1
2 2
3 1
3 2
4 1
4 2
5 1
5 2
Robert P. has a correct (and elegant) answer with a nifty use of kron, but just for fun here's the alternative with ndgrid,
>> mat=zeros(5,2);
>> [nn,mm] = ndgrid(1:size(mat,2),1:size(mat,1))
>> vec = [mm(:) nn(:)]
vec =
1 1
1 2
2 1
2 2
3 1
3 2
4 1
4 2
5 1
5 2
I need to transform a matrix:
X = [1 2; 3 4]
X = 1 2
3 4
to
X = [1 2; 1 2; 1 2; 3 4; 3 4; 3 4]
X = 1 2
1 2
1 2
3 4
3 4
3 4
and do this operation for a matrix with any number of rows.
How can I achieve this in MATLAB?
Here is a nice and easy way to do this using kron
kron(X,[1 1 1]')
this produces
1 2
1 2
1 2
3 4
3 4
3 4