Assume matrix M:
1 2 3
3 5 6
6 8 9
How do I store I extract the following row vector a from it?
1
5
9
You just need to use diag:
octave-3.4.0:1> A = [ 1 2 3; 3 5 6; 6 8 9 ]
A =
1 2 3
3 5 6
6 8 9
octave-3.4.0:2> D = diag(A)
D =
1
5
9
Note that you can also extract other diagonals by passing a second parameter to diag, e.g.
octave-3.4.0:3> D = diag(A, 1)
D =
2
6
octave-3.4.0:4> D = diag(A, -1)
D =
3
8
If you know the dimensions of your matrix (square or otherwise), you can extract any diagonal you like, or even modified diagonals (such as numbers in (1,1), (2,3), (3,5), etc), somewhat faster than using diag, by simply using an index call like this:
a=M(1:4:9)
(note: this produces a row vector; for a column vector, just transpose) For an NxN matrix, simply start at the desired value (1 for the top-left corner, 2 for next one down vertically, and so on), then increment by N+1 until you reach the appropriate value.
octave:35> tic; for i=1:10000 diag(rand(3)); end; toc;
Elapsed time is 0.13973 seconds.
octave:36> tic; for i=1:10000 rand(3)(1:4:9); end; toc;
Elapsed time is 0.10966 seconds.
For reference:
octave:49> tic; for i=1:10000 rand(3); end; toc;
Elapsed time is 0.082429 seconds.
octave:107> version
ans = 3.6.3
So the overhead for the for loop and the rand function, subtracted off, shows that using indices is about twice as fast as using diag. I suspect that this is purely due to the overhead of calling diag, as the operation itself is very straightforward and fast, and is almost certainly how diag itself works.
Related
I need this for Lagrange polynomials. I'm curious how one would do this without a for loop. The code currently looks like this:
tj = 1:n;
ti = zeros(n,n-1);
for i = 1:n
ti(i,:) = tj([1:i-1, i+1:end]);
end
My tj is not really just a 1:n vector but that's not important. While this for loop gets the job done, I'd rather use some matrix operation. I tried looking for some appropriate matrices to multiply it with, but no luck so far.
Here's a way:
v = [10 20 30 40]; %// example vector
n = numel(v);
M = repmat(v(:), 1, n);
M = M(~eye(n));
M = reshape(M,n-1,n).';
gives
M =
20 30 40
10 30 40
10 20 40
10 20 30
This should generalize to any n
ti = flipud(reshape(repmat(1:n, [n-1 1]), [n n-1]));
Taking a closer look at what's going on. If you look at the resulting matrix closely, you'll see that it's n-1 1's, n-1 2's, etc. from the bottom up.
For the case where n is 3.
ti =
2 3
1 3
1 2
So we can flip this vertically and get
f = flipud(ti);
1 2
1 3
2 3
Really this is [1, 2, 3; 1, 2, 3] reshaped to be 3 x 2 rather than 2 x 3.
In that line of thinking
a = repmat(1:3, [2 1])
1 2 3
1 2 3
b = reshape(a, [3 2]);
1 2
1 3
2 3
c = flipud(b);
2 3
1 3
1 2
We are now back to where you started when we bring it all together and replace 3's with n and 2's with n-1.
Here's another way. First create a matrix where each row is the vector tj but are stacked on top of each other. Next, extract the lower and upper triangular parts of the matrix without the diagonal, then add the results together ensuring that you remove the last column of the lower triangular matrix and the first column of the upper triangular matrix.
n = numel(tj);
V = repmat(tj, n, 1);
L = tril(V,-1);
U = triu(V,1);
ti = L(:,1:end-1) + U(:,2:end);
numel finds the total number of values in tj which we store in n. repmat facilitates the stacking of the vector tj to create a matrix that is n x n large. After, we use tril and triu so that we extract the lower and upper triangular parts of the matrices without the diagonal. In addition, the rest of the matrix is all zero except for the relevant triangular parts. The -1 and 1 flags for tril and triu respectively extract this out successfully while ensuring that the diagonal is all zero. This creates a column of extra zeroes appearing at the last column when calling tril and the first column when calling triu. The last part is to simply add these two matrices together ignoring the last column of the tril result and the first column of the triu result.
Given that tj = [10 20 30 40]; (borrowed from Luis Mendo's example), we get:
ti =
20 30 40
10 30 40
10 20 40
10 20 30
I have a problem with sorting some finance data based on firmnumbers. So given is a matrix that looks like:
[1 3 4 7;
1 2 7 8;
2 3 7 8;]
On Matlab i would like the matrix to be sorted as follows:
[1 0 3 4 7 0;
1 2 0 0 7 8;
0 2 3 0 7 8;]
So basically every column needs to consist of 1 type of number.
I have tried many things but i cant get the matrix sorted properly.
A = [1 3 4 7;
1 2 7 8;
2 3 7 8;]
%// Get a unique list of numbers in the order that you want them to appear as the new columns
U = unique(A(:))'
%'//For each column (of your output, same as columns of U), find which rows have that number. Do this by making A 3D so that bsxfun compares each element with each element
temp1 = bsxfun(#eq,permute(A,[1,3,2]),U)
%// Consolidate this into a boolean matrix with the right dimensions and 1 where you'll have a number in your final answer
temp2 = any(temp1,3)
%// Finally multiply each line with U
bsxfun(#times, temp2, U)
So you can do that all in one line but I broke it up to make it easier to understand. I suggest you run each line and look at the output to see how it works. It might seem complicated but it's worthwhile getting to understand bsxfun as it's a really useful function. The first use which also uses permute is a bit more tricky so I suggest you first make sure you understand that last line and then work backwards.
What you are asking can also be seen as an histogram
A = [1 3 4 7;
1 2 7 8;
2 3 7 8;]
uniquevalues = unique(A(:))
N = histc(A,uniquevalues' ,2) %//'
B = bsxfun(#times,N,uniquevalues') %//'
%// bsxfun can replace the following instructions:
%//(the instructions are equivalent only when each value appears only once per row )
%// B = repmat(uniquevalues', size(A,1),1)
%// B(N==0) = 0
Answer without assumptions - Simplified
I did not feel comfortable with my old answer that makes the assumption of everything being an integer and removed the possibility of duplicates, so I came up with a different solution based on #lib's suggestion of using a histogram and counting method.
The only case I can see this not working for is if a 0 is entered. you will end up with a column of all zeros, which one might interpret as all rows initially containing a zero, but that would be incorrect. you could uses nan instead of zeros in that case, but not sure what this data is being put into, and if it that processing would freak out.
EDITED
Includes sorting of secondary matrix, B, along with A.
A = [-1 3 4 7 9; 0 2 2 7 8.2; 2 3 5 9 8];
B = [5 4 3 2 1; 1 2 3 4 5; 10 9 8 7 6];
keys = unique(A);
[counts,bin] = histc(A,transpose(unique(A)),2);
A_sorted = cell(size(A,1),1);
for ii = 1:size(A,1)
for jj = 1:numel(keys)
temp = zeros(1,max(counts(:,jj)));
temp(1:counts(ii,jj)) = keys(jj);
A_sorted{ii} = [A_sorted{ii},temp];
end
end
A_sorted = cell2mat(A_sorted);
B_sorted = nan(size(A_sorted));
for ii = 1:size(bin,1)
for jj = 1:size(bin,2)
idx = bin(ii,jj);
while ~isnan(B_sorted(ii,idx))
idx = idx+1;
end
B_sorted(ii,idx) = B(ii,jj);
end
end
B_sorted(isnan(B_sorted)) = 0
You can create at the beginning a matrix with 9 columns , and treat the values in your original matrix as column indexes.
A = [1 3 4 7;
1 2 7 8;
2 3 7 8;]
B = zeros(3,max(A(:)))
for i = 1:size(A,1)
B(i,A(i,:)) = A(i,:)
end
B(:,~any(B,1)) = []
i want to create 1D vector in matlab from given matrix,for this i have implemented following algorithm ,which use trivial way
% create one dimensional vector from 2D matrix
function [x]=one_dimensional(b,m,n)
k=1;
for i=1:m
for t=1:n
x(k)=b(i,t);
k=k+1;
end
end
x;
end
when i run it using following example,it seems to do it's task fine
b=[2 1 3;4 2 3;1 5 4]
b =
2 1 3
4 2 3
1 5 4
>> one_dimensional(b,3,3)
ans =
2 1 3 4 2 3 1 5 4
but generally i know that,arrays are not good way to use in matlab,because it's performance,so what should be effective way for transformation matrix into row/column vector?i am just care about performance.thanks very much
You can use the (:) operator...But it works on columns not rows so you need to transpose using the 'operator before , for example:
b=b.';
b(:)'
ans=
2 1 3 4 2 3 1 5 4
and I transposed again to get a row output (otherwise it'll the same vector only in column form)
or also, this is an option (probably a slower one):
reshape(b.',1,[])
My data is a 2096x252 matrix of double values. I need a for loop or an equivalent which performs the following:
Each time the matrix is reproduced the first array is deleted and the second becomes the first. When the loop runs again, the remaining matrix is reproduced and the first array is deleted and the next becomes the first and so on.
I've tried using repmat but it is too slow and tedious when dealing with large matrices (2096x252).
Example input:
1 2 3 4
3 4 5 6
3 5 7 5
9 6 3 2
Desired output:
1 2 3 4
3 4 5 6
3 5 7 5
9 6 3 2
3 4 5 6
3 5 7 5
9 6 3 2
3 5 7 5
9 6 3 2
9 6 3 2
Generally with Matlab it is much faster to pre-allocate a large array than to build it incrementally. When you know in advance the final size of the large array there's no reason not to follow this general advice.
Something like the following should do what you want. Suppose you have an array in(nrows, ncols); then
indices = [0 nrows:-1:1];
out = zeros(sum(indices),ncols);
for ix = 1:nrows
out(1+sum(indices(1:ix)):sum(indices(1:ix+1)),:) = in(ix:end,:);
end
This worked on your small test input. I expect you can figure out what is going on.
Whether it is the fastest of all possible approaches I don't know, but I expect it to be much faster than building a large matrix incrementally.
Disclaimer:
You'll probably have memory issues with large matrices, but that is not the question.
Now, to the business:
For a given matrix A, the straightforward approach with the for loop would be:
[N, M] = size(A);
B = zeros(sum(1:N), M);
offset = 1;
for i = 1:N
B(offset:offset + N - i, :) = A(i:end, :);
offset = offset + size(A(i:end, :), 1);
end
B is the desired output matrix.
However, this solution is expected to be slow as well, because of the for loop.
Edit: preallocated B instead of dynamically changing size (this optimization should achieve a slight speedup).
I have a question.
Suppose I have matrix
A =
1 2 3
4 5 6
7 8 9
10 11 12
I need to select n rolling rows from A and transpose elements in new matrix C in rows.
The loop that I use is:
n = 3; %for instance every 3 rows of A
B = [];
for i = 1:n
Btemp = transpose(A(i:i+size(A,1)-n,:));
B = [B;Btemp];
end
C=B';
and that produces matrix C which is:
C =
1 2 3 4 5 6 7 8 9
4 5 6 7 8 9 10 11 12
This is what i want too do, but can I do the same job without the loop?
It takes 4 minutes to calculate for an A matrix of 3280x35 size.
I think you can make it work very fast if you make initialization. And one other trick is to take the transpose first, since MATLAB uses columns as first index instead of rows.
tic
A = reshape(1:3280*35,[3280 35])'; %# Generate an example A
[nRows, nCols] = size(A);
n = 3; %for instance every 3 rows of A
B = zeros(nRows-n+1,nCols*n);
At = A';
for i = 1:size(B,1)
B(i,:) = reshape(At(:,i:i+n-1), [1 nCols*n]);
end
toc
The elapsed time is
Elapsed time is 0.004059 seconds.
I would not use reshape in the loop, but transform A first to one single row (actually a column will also work, doesn't matter)
Ar = reshape(A',1,[]); % the ' is important here!
then the selecting of elements out of Ar is really simple:
[nrows, ncols] = size(A);
new_ncols = ncols*n;
B = zeros(nrows-(n-1),new_ncols);
for ii = 1:nrows-(n-1)
B(ii,:) = Ar(n*(ii-1)+(1:new_ncols));
end
Still, the preallocation of B, gives you the largest improvement: more info at http://www.mathworks.nl/help/techdoc/matlab_prog/f8-784135.html
I don't have Matlab on me right now but I think you can do this without loops like this:
reshape(permute(cat(A(1:end-1,:),A(2:end,:),3),[3,2,1]), [2, size(A,2)*(size(A,1) - 1)]);
and in fact won't this do what you want?:
A1 = A(1:end-1,:);
A2 = A(2:end,:);
answer = [A1(:) ; A2(:)]