Say I have a matrix
x = [1 2 3 4 ]
and I want to create a matrix that adds two elements and outputs a third?
y = [1+2 3+4]
y = [3 7]
For four values, I can just do y=[x(1)+x(2) x(3)+x(4)].
How would I go about doing that if x was bigger and variable (say a thousand elements)? How would I program y?
I've been struggling with this for two days now... thanks in advance...
A simple way would be to reshape the original array x into a matrix containing k rows, k being the number of elements you are summing together (here 2, sorry I don't know how to explain this), and then simply call sum on this matrix which will calculate the sum of each column and output it into a new vector y.
Example:
x = [1:10]
block = 2
r = reshape(x,block,[])
So here r looks like this:
r =
1 3 5 7 9
2 4 6 8 10
Therefore calling sum with the 1st dimension on r yields the following:
y = sum(reshape(x,block,[]),1)
y =
3 7 11 15 19
Related
I simplify my problem, let says I have three matrices.
I want to extract the red-boxed sub-matrices. I define
S = [1 4;
2 5]
that are the linear indices of the above matrices. So, A(S), B(S) and C(S) can extract the entries of the three matrices.
I pack them into vector by V = [ A(S)(:); B(S)(:); C(S)(:) ]. Let says after some manipulations, I obtain a new vector
V_new = [12 9 8 12 21 8 7 5 3 12 11 10]'
Here comes to my problem:
E.g for matrix A, I want to obtain
2->12, 5->9, 4->8 and 6->12
which are the first four entries of my V_new.
Since I have around 200 matrices, I have no idea to swap along the 200 matrices and the updated vector, V_new at the same time. Is writing a for-loop best way to do this purpose?
Thanks in advance.
Assuming that your A, B and C matrices have the same dimensions, rather work with a 3D matrix.
e.g. assuming your example matrices
M = cat(3,A,B,C)
No to extract those 4 upper left elements:
M_subset = M(1:2,1:2,:)
And then to reshape them into the vector you had:
V = M_subset(:)
then manipulate it to get V_new and finally put it back in the original:
M(1:2,1:2,:) = reshape(V_new,2,2,[])
We've got a columnvector m x 1 and a matrix m x n.
For the value in row i in the columnvector we want to multiply this value with each value in the same row i of the matrix, and then sum all of these up. This is to be repeated for every row i in the vector so that we end up with a columnvector.
Want to do this with a for-loop, have this so far (where M is the matrix and v is the initial columnvector we start out with) which returns an error that says "Subscripted assignment dimension mismatch.", so I guess I messed up with my indices somehow:
for i = 1:nv
for k = 1:mM
columnvectorendresult(i,) = columnvectorendresult(i,) + v(i,:)*M(i,:);
end
end
Don't know if I'm close with what I have so far, but not fully into this just yet. Any suggestions?
In case you want to sum after multiplication, the answer of knedlsepp using the distributive property of multiplication is the logical choice. If you want to use other operations than sums or differences, than the following answer can be applied more generically
Here we go:
%// columnvector m x 1
a = randi(5,3,1)
%// matrix m x n
B = randi(5,3,2)
%// multiplication
Ba = bsxfun(#times,B,a(:))
%// sum
BaSum = sum(Ba,2)
Example:
a =
3
4
4
B =
2 5
3 1
1 1
Ba =
6 15
12 4
4 4
BaSum =
21
16
8
Instead of multiplying each entry with the same factor and then doing the summation, you should sum the rows of the matrix first and then do the multiplication. ("Use the distributive property of multiplication.")
This is how you do this in MATLAB:
columnvectorendresult = v.*sum(M,2);
I have a <206x193> matrix A. It contains the values of a parameter at 206 different locations at 193 time steps. I am interested in the maximum value at each location over all times as well as the corresponding indices. I have another matrix B with the same dimensions of A and I'm interested in values for each location at the time that A's value at that location was maximal.
I've tried [max_val pos] = max(A,[],2), which gives the right maximum values, but A(pos) does not equal max_val.
How exactly does this function work?
I tried a smaller example as well. Still I don't understand the meaning of the indices....
>> H
H(:,:,1) =
1 2
3 4
H(:,:,2) =
5 6
7 8
>> [val pos] = max(H,[],2)
val(:,:,1) =
2
4
val(:,:,2) =
6
8
pos(:,:,1) =
2
2
pos(:,:,2) =
2
2
The indices in idx represent the index of the max value in the corresponding row. You can use sub2ind to create a linear index if you want to test if A(pos)=max_val
A=rand(206, 193);
[max_val, idx]=max(A, [], 2);
A_max=A(sub2ind(size(A), (1:size(A,1))', idx));
Similarly, you can access the values of B with:
B_Amax=B(sub2ind(size(A), (1:size(A,1))', idx));
From your example:
H(:,:,2) =
5 6
7 8
[val pos] = max(H,[],2)
val(:,:,2) =
6
8
pos(:,:,2) =
2
2
The reason why pos(:,:,2) is [2; 2] is because the maximum is at position 2 for both rows.
max is a primarily intended for use with vectors. In normal mode, even the multi-dimensional arrays are treated as a series of vectors along which the max function is applied.
So, to get the values in B at each location at the time where A is maximum, you should
// find the maximum values and positions in A
[c,i] = max(A, [], 2);
// iterate along the first dimension, to retrieve the corresponding values in B
C = [];
for k=1:size(A,1)
C(k) = B(k,i(k));
end
You can refer to #Jigg's answer for a more concise way of creating matrix C
I have multiple matrices of the same size and want to compare them.
As a result I need a matrix which gives me the biggest of the 3 for every value.
I will clarify what i mean with an example:
I have 3 matrices with data of 3 persons.
I would like to compare these 3 and get a matrix as result.
In that matrix every cell/value should be the name of the matrix who had the highest value for that cell. So if in the 3 matrices the first value (1 colum, 1 row) is accordingly 2, 5, 8 the first value of the result matrix should be 3 (or the name of the 3 matrix).
If the three matrices are A, B, C, do this:
[~, M] = max(cat(3,A,B,C),[],3);
It creates a 3D "matrix" and maximizes across the third dimension.
Concatenate them on the 3rd dimension, and the use the SECOND output from max to get exactly what you want
A = rand(3,3);
B = rand(3,3);
C = rand(3,3);
D = cat(3, A, B, C)
[~, Solution] = max(D, [], 3)
e.g.:
D =
ans(:,:,1) =
0.70101 0.31706 0.83874
0.89421 0.33783 0.55681
0.68520 0.11697 0.45631
ans(:,:,2) =
0.268715 0.213200 0.124450
0.869847 0.999649 0.153353
0.345447 0.023523 0.338099
ans(:,:,3) =
0.216665 0.297900 0.604734
0.103340 0.767206 0.660668
0.127052 0.430861 0.021584
Solution =
1 1 1
1 2 3
1 3 1
edit
As I did not know about the second argument of the max-function, here is what you should NOT use:
old
Well, quick&dirty:
x=[2 5 8];
w=max(x)
[~,loc] = ismember(w,x)
I would like to average every 3 values of an vector in Matlab, and then assign the average to the elements that produced it.
Examples:
x=[1:12];
y=%The averaging operation;
After the operation,
y=
[2 2 2 5 5 5 8 8 8 11 11 11]
Therefore the produced vector is the same size, and the jumping average every 3 values replaces the values that were used to produce the average (i.e. 1 2 3 are replaced by the average of the three values, 2 2 2). Is there a way of doing this without a loop?
I hope that makes sense.
Thanks.
I would go this way:
Reshape the vector so that it is a 3×x matrix:
x=[1:12];
xx=reshape(x,3,[]);
% xx is now [1 4 7 10; 2 5 8 11; 3 6 9 12]
after that
yy = sum(xx,1)./size(xx,1)
and now
y = reshape(repmat(yy, size(xx,1),1),1,[])
produces exactly your wanted result.
Your parameter 3, denoting the number of values, is only used at one place and can easily be modified if needed.
You may find the mean of each trio using:
x = 1:12;
m = mean(reshape(x, 3, []));
To duplicate the mean and reshape to match the original vector size, use:
y = m(ones(3,1), :) % duplicates row vector 3 times
y = y(:)'; % vector representation of array using linear indices