Given a matrix A (mxn) and a vector B (mx1) I want to create a vector C (mx1) in which each row element is the row element of A from a column indexed by B.
Is it possible to do this, without using loops?
A = [1 2; 3 4; 5 6];
B = [2 1 1].';
Then I want:
C = [2 3 5].';
Convert the column subscripts of B to linear indices and then use them to reference elements in A:
idx = sub2ind(size(A), (1:size(A, 1)).', B);
C = A(idx);
(for more information, read the part about linear indexing in this answer).
Related
Lets say I have matrices A = [1 2; 3 4], B = [4 3; 2 1]. I want to multiply each column from matrix A ([1; 3], [2; 4]) by the corresponding row in matrix B ([4 3], [2 1]) and sum resulting matrices. I have came up with the following code:
C = zeros(size(A));
for i = 1 : size(A, 1)
C = C + A(:, i) * B(i, :);
end
Could it be rewritten using some math trick or matlab function to get rid of the for loop?
I see there is unclarity in my question regarding the result I want. The result should exactly mimic provided Matlab code, therefore I seek one matrix which is given by the matrix summation of the intermediate matrices that are created by multiplying each column vector with corresponding row vector from both matrices. For this specific example, it would be given by
C = A(:, 1) * B(1, :) + A(:, 2) * B(2, :);
I am just looking for some generic, for-loop less version for any matrices of compatible dimensions.
I just tried out my suggestion in the comments, and it seems to work with this octave tester:
Short form (only works in Octave):
A = [1 2; 3 4], B = [4 3; 2 1]
X = sum((A * B)(:))
Long form (Matlab):
A = [1 2; 3 4]
B = [4 3; 2 1]
C = A * B % Stop here if you want the exact result from your Matlab code
x = sum(C(:)) % To get the sum of the resulting matrix
Sources:
https://www.tutorialspoint.com/matlab/matlab_matrix_multiplication.htm
https://www.mathworks.com/matlabcentral/newsreader/view_thread/51252
Update, based on your update:
Output of A * B:
8 5
20 13
Output of your code:
8 5
20 13
It appears that
C = zeros(size(A));
for i = 1 : size(A, 1)
C = C + A(:, i) * B(i, :);
end
is equivalent to the matrix multiplication
C = A*B
for square matrices A and B.
You can also do this in MATLAB, to get the sum.
C=ones(1,2)*A*B*ones(2,1)
The general form would be
C=ones(1,size(A,1))*(A*B)*ones(size(B,2),1);
EDIT
I see you updated your question for clarity. The matrix product can be calculated directly
C = A*B;
as pointed out by jodag.
This works provided you follow rules of linear algebra where inner dimensions of your matrices are the same (i.e. when number of columns in A match the number of rows in B; size(A,2)==size(B,1)).
Given the matrix A = [6 4 1; 1 4 3; 3 4 2;7 6 8] and the array of pairs b = [4 6; 4 1; 1 6], I want to find the pairs given in b in the rows of A without a for loop.
For example, the first pairs is (4,6) or (6,4) , which occurs in the first row of A.
Assuming, you want to find the rows of A which contain the exact pairs given in b, this is how you can do it without a loop:
% Create a matrix of pairs in A
pairs = cat(3, A(:, 1:end-1), A(:, 2:end));
% Reshape b to use bsxfun
b_ = reshape(b', [1 1 size(b')]);
% Get the matches for the pairs and for the flipped pairs
indices = all( bsxfun(#eq, pairs, b_), 3) | all( bsxfun(#eq, pairs, flip(b_,3)), 3);
% Find the indices of the rows with a match
row_indices = find(squeeze(any(any(indices,4),2)));
Please refer to the reference on vectorization for more information on how to make fast computations in Matlab without loops.
I have 2 matrices A and B.
I find the max values in the columns of A, and keep their indices in I. So far so good.
Now, I need to choose those arrays of B with the same index as stored in I. I don't know how to do this.
See below:
A = [1,2,3; 0,8,9]
B = [0,1,2; 4,2,3]
[~,I] = max(A)
h = B(I)
I need to get these values of B:
h = [0 2 3]
But the code results in a different one. How can I fix it?
A =
1 2 3
0 8 9
B =
0 1 2
4 2 3
I =
1 2 2
h =
0 4 4
Thanks in advance
The max function how you used it works like
If A is a matrix, then max(A) is a row vector containing the maximum value of each column.
so M = max(A) is equivalent to M = max(A,[],1). But rather use the third input if you're not sure.
If you use max to find the maxima in the columns of the matrix, it returns the row indices. The column indices are for your case simply 1:size(A,2) = [1 2 3].
Now you need to convert your row and column indices to linear indices with sub2ind:
%// data
A = [1,2,3; 0,8,9]
B = [0,1,2; 4,2,3]
%// find maxima of each column in A
[~, I] = max( A, [], 1 ) %// returns row indices
%// get linear indices for both, row indices and column indices
I = sub2ind( size(A), I, 1:size(A,2) )
%// index B
h = B(I)
returns:
h =
0 2 3
I have two vectors, X of bases and N of exponents. I want to get the matrix of all values e = xn for each x in X and n in N.
For example, the following input:
X = [2 3 4]'
N = [1 2 3]
should produce:
ans = [2 4 8; 3 9 27; 4 16 64]
Is there a way to get this without looping (just like you can get all values of x×n by using the column by row product)?
Use bsxfun:
bsxfun(#power, X, N)
This assumes that X is a column vector and N is a row vector. If you want to guarantee that, use the following syntax which is more robust:
bsxfun(#power, X(:), N(:).')
This is probably a bit sloppier than the bsxfun answer, but you could use meshgrid:
E = X.^(meshgrid(N)')
This assumes both X and N are row vectors. If both are column vectors then it becomes:
E = X.^(meshgrid(N))
a = [1 2; 3 4; 5 6] I want to extract the first and third row of a, so I have x = [1; 3] (indices of rows).
a(x) doesn't work.
Like this: a([1,3],:)
The comma separates the dimensions, : means "entire range", and square brackets make a list.
In MATLAB if one parameter is given when indexing, it is so-called linear indexing. For example if you have 4x3 matrix, the linear indices of the elements look like this, they are growing by the columns:
1 5 9
2 6 10
3 7 11
4 8 12
Because you passed the [1 3] vector as a parameter, the 1st and 3rd elements were selected only.
When selecting whole columns or rows, the following format shall be used:
A(:, [list of columns]) % for whole columns
A([list of rows], :) % for whole rows
General form of 2d matrix indexing:
A([list of rows], [list of columns])
The result is the elements in the intersection of the indexed rows and columns. Results will be the elements marked by X:
A([2 4], [3 4 5 7])
. . C C C . C
R R X X X R X
. . C C C . C
R R X X X R X
Reference and some similar examples: tutorial on MATLAB matrix indexing.
x = a([1 3]) behaves like this:
temp = a(:) % convert matrix 'a' into a column wise vector
x = temp([1 3]) % get the 1st and 3rd elements of 'a'
you could write a loop to iterate across the rows of the matrix:
for i = [1,3]
a(i,:)
end
type this: a([1 3],[1 2])
the output is
ans =
1 2
5 6