I'm trying to compute a vector A for which the ith element is the sum of the first i elements of a different vector B (this vector is given).
I couldn't work out how to do this and the internet wasn't much help either.
I am very new to matlab so an easy solution would be preferred :)
Use MATLAB's cumsum function.
code example:
%generates random vector b
b = rand(5,1);
%calculates accomulative sum
a = cumsum(b);
Result:
b = [0.4319 0.9616 0.5671 0.8731 0.5730]
a = [0.4319 1.3935 1.9606 2.8338 3.4068]
Related
In an attempt to create my own covariance function in MatLab I need to perform matrix multiplication on a row to create a matrix.
Given a matrix D where
D = [-2.2769 0.8746
0.6690 -0.4720
-1.0030 -0.9188
2.6111 0.5162]
Now for each row I need manufacture a matrix. For example the first row R = [-2.2770, 0.8746] I would want the matrix M to be returned where M = [5.1847, -1.9915; -1.9915, 0.7649].
Below is what I have written so far. I am asking for some advice to explain how to use matrix multiplication on a rows to produce matrices?
% Find matrices using matrix multiplication
for i=1:size(D, 1)
P1 = (D(i,:))
P2 = transpose(P1)
M = P1*P2
end
You are trying to compute the outer product of each row with itself stored as individual slices in a 3D matrix.
Your code almost works. What you're doing instead is computing the inner product or the dot product of each row with itself. As such it'll give you a single number instead of a matrix. You need to change the transpose operation so that it's done on P1 not P2 and P2 will now simply be P1. Also you are overwriting the matrix M at each iteration. I'm assuming you'd like to store these as individual slices in a 3D matrix. To do this, allocate a 3D matrix where each 2D slice has an equal number of rows and columns which is the number of columns in D while the total number of slices is equal to the total number of rows in D. Then just index into each slice and place the result accordingly:
M = zeros(size(D,2), size(D,2), size(D,1));
% Find matrices using matrix multiplication
for ii=1:size(D, 1)
P = D(ii,:);
M(:,:,ii) = P.'*P;
end
We get:
>> M
M(:,:,1) =
5.18427361 -1.99137674
-1.99137674 0.76492516
M(:,:,2) =
0.447561 -0.315768
-0.315768 0.222784
M(:,:,3) =
1.006009 0.9215564
0.9215564 0.84419344
M(:,:,4) =
6.81784321 1.34784982
1.34784982 0.26646244
Depending on your taste, I would recommend using bsxfun to help you perform the same operation but perhaps doing it faster:
M = bsxfun(#times, permute(D, [2 3 1]), permute(D, [3 2 1]));
In fact, this solution is related to a similar question I asked in the past: Efficiently compute a 3D matrix of outer products - MATLAB. The only difference is that the question wanted to find the outer product of columns instead of the rows.
The way the code works is that we shift the dimensions with permute of D so that we get two matrices of the sizes 2 x 1 x 4 and 1 x 2 x 4. By performing bsxfun and specifying the times function, this allows you to efficiently compute the matrix of outer products per slice simultaneously.
In matlab, I have a matrix and index vector v (in real problem, v vector is very long)
A = [1,2,3;4,5,6;7,8,9]; % 3-by-3 matrix
v = [1,2,3,2,3,3,1]
How can I generate a matrix like
[A(1,:);A(2,:);A(3,:);A(2,:);A(3,:);A(3,:);A(1,:)]
without using loop or write out everything explicitly?
You can use vectors to index, A([1,1,1]) would give you three times the first element.
A(v,:)
I have a vector created from linspace between specific numbers and have dimensions of 1*150. Now i want to multiply each element of the above created vector with another vector whose dimension is 1*25. The detail of my code is given below
c_p = linspace(1,.3*pi,150);
c = c_p';
C = zeros([150,25]);
for i= 1:1:size(C,1)
wp= c(i);
for n= 1:25
c_wp(n) = cos(n*wp);
end
C(i,25)= c_wp;
end
The vector is actually a multiple of cosine of length 25 and here wp is the elements of first vector of dimension 1*150. SO by the logic, I must have an output of 150*25 but instead giving me "subscripted assignment dimension mismatch". Any help would be appreciated, as i am new to matlab.
To multiply each element of a row vector a with each element of another row vector b, we can use linear algebra. We transpose a to make it a column vector and then use matrix multiplication:
a.' * b
That way you don't even need a for loop.
For a 3N by 3N by 3N matrix A, I would like to derive a N by N by N matrix B whose entries come from summation over blocks in A.
For example, B(1,1,1) = sum of all elements of A(1:3,1:3,1:3).
Basically, A is kind of a high resolution matrix and B is a low resolution matrix from summing over entries in A.
If memory is not a concern, you can use a "labelling" approach: build a 3-component label to group the elements of A, and use that label as the first input argument to accumarray to do the sum. The label uses integers from 1 to N, so the result of accumarray already has the desired shape (NxNxN).
N = 5;
F = 3; %// block size per dimension
A = rand(15,15,15); %// example data. Size FN x FN x FN
[ii jj kk] = ind2sub(size(A), 1:numel(A));
label = ceil([ii.' jj.' kk.']/F);
result = accumarray(label, A(:));
reshape + sum based approach and as such has to be pretty efficient -
sumrows = sum(reshape(A,3,[]),1); %// Sum along rows
sumcols = sum(reshape(sumrows,N,3,[]),2); %// Sum along cols
B = reshape(sum(reshape(sumcols,N*N,3,[]),2),N,N,N); %// Sum along 3rd dim
If you are crazy about one-liners, here's that combining all steps into one -
B = reshape(sum(reshape(sum(reshape(sum(reshape(A,3,[]),1),N,3,[]),2),N*N,3,[]),2),N,N,N);
For a 2D matrix, this would work:
B = reshape(sum(im2col(A, [3 3], 'distinct')), [N N]);
NB: You need the image processing toolbox.
But for 3D matrices, I don't know of any built-in function equivalent to im2col. You might have to use a loop. Left as an exercise to the reader ;)
Which of the following statements will find the minimum difference between any pair of elements (a,b) where a is from the vector A and b is from the vector B.
A. [X,Y] = meshgrid(A,B);
min(abs(X-Y))
B. [X,Y] = meshgrid(A,B);
min(abs(min(Y-X)))
C. min(abs(A-B))
D. [X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
Can someone please explain to me?
By saying "minimum difference between any pair of elements(a,b)", I presume you mean that you are treating A and B as sets and you intend to find the absolute difference in any possible pair of elements from these two sets. So in this case you should use your option D
[X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
Explanation: Meshgrid turns a pair of 1-D vectors into 2-D grids. This link can explain what I mean to say:
http://www.mathworks.com/help/matlab/ref/meshgrid.html?s_tid=gn_loc_drop
Hence (X-Y) will give the difference in all possible pairs (a,b) such that a belongs to A and b belongs to B. Note that this will be a 2-D matrix.
abs(X-Y) would return the absolute values of all elements in this matrix (the absolute difference in each pair).
To find the smallest element in this matrix you will have to use min(min(abs(X-Y))). This is because if Z is a matrix, min(Z) treats the columns of Z as vectors, returning a row vector containing the minimum element from each column. So a single min command will give a row vector with each element being the min of the elements of that column. Using min for a second time returns the min of this row vector. This would be the smallest element in the entire matrix.
This can help:
http://www.mathworks.com/help/matlab/ref/min.html?searchHighlight=min
Options C is correct if you treat A and B as vectors and not sets. In this case you won't be considering all possible pairs. You'll end up finding the minimum of (a-b) where a,b are both in the same position in their corresponding vectors (pair-wise difference).
D. [X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
meshgrid will generate two grids - X and Y - from the vectors, which are arranged so that X-Y will generate all combinations of ax-bx where ax is in a and bx is in b.
The rest of the expression just gets the minimum absolute value from the array resulting from the subtraction, which is the value you want.
CORRECT ANSWER IS D
Let m = size(A) and n = size(B)
You want to subtract each pair of (a,b) such that a is from vector A and b is from vector B.
meshgrid(A,B) creates two matrices X Y both of size nxm where X have rows sames have vector A while Yhas columns same as vector B .
Hence , Z = X-Y will give you a matrix with n*m values corresponding to the difference between each pair of values taken from A and B . Now all you have to do is to find the absolute minimum among all values of Z.
You can do that by
req_min = min(min(abs(z)))
The whole code is
[X Y ] = meshgrid(A,B);
Z= X-Y;
Z = abs(Z);
req_min = min(min(Z));
You could also use bsxfun instead of meshgrid:
min(min(abs(bsxfun(#minus, A(:), B(:).'))))
Or use pdist2:
min(min(pdist2(A(:),B(:))))