Every possible sum combination in a vector - matlab

Assuming I'm having a vectors of numbers A, for example: A=[1 3 5 3 9 6](A's length >= 2) and an Integer X=6. Need to find how many pairs (A[i],A[j]) where i<j exist in the vector which answer this condition: A[i]+A[j]=X. The number of pairs is printed.
Not allowed to use for/while. Allowed only ceil,floor,mod,repmat,reshape,size,length,transpose,sort,isempty,all,any,find ,sum,max,min.


With repmat, length and sum -
integer1 = 6; %// One of the paramters
A_ind = 1:length(A) %// Get the indices array
%// Expand A_ind into rows and A_ind' into columns, to form a meshgrid structure
A_ind_mat1 = repmat(A_ind,[length(A) 1])
A_ind_mat2 = repmat(A_ind',[1 length(A)]) %//'
%// Expand A into rows and A' into columns, to form a meshgrid structure
A_mat1 = repmat(A,[length(A) 1])
A_mat2 = repmat(A',[1 length(A)]) %//'
%// Form the binary matrix of -> (A[i],A[j]) where i<j
cond1 = A_ind_mat1 < A_ind_mat2
%// Use the binary matrix as a logical mask to select elements from the two
%// matrices and see which element pairs satisfy -> A[i]+A[j]=X and get a
%// count of those pairs with SUM
pairs_count = sum((A_mat1(cond1) + A_mat2(cond1))==integer1)
Outputs from code run to make it clearer -
A =
1 3 5 3 9 6
A_ind =
1 2 3 4 5 6
A_ind_mat1 =
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
A_ind_mat2 =
1 1 1 1 1 1
2 2 2 2 2 2
3 3 3 3 3 3
4 4 4 4 4 4
5 5 5 5 5 5
6 6 6 6 6 6
A_mat1 =
1 3 5 3 9 6
1 3 5 3 9 6
1 3 5 3 9 6
1 3 5 3 9 6
1 3 5 3 9 6
1 3 5 3 9 6
A_mat2 =
1 1 1 1 1 1
3 3 3 3 3 3
5 5 5 5 5 5
3 3 3 3 3 3
9 9 9 9 9 9
6 6 6 6 6 6
cond1 =
0 0 0 0 0 0
1 0 0 0 0 0
1 1 0 0 0 0
1 1 1 0 0 0
1 1 1 1 0 0
1 1 1 1 1 0
pairs_count =
2
A bit more explanation -
Taking few more steps to clarify why pairs_count must be 2 here -
Set all values in A_mat1 and A_mat2 to be zeros that do not satisfy the less than criteria
>> A_mat1(~cond1)=0
A_mat1 =
0 0 0 0 0 0
1 0 0 0 0 0
1 3 0 0 0 0
1 3 5 0 0 0
1 3 5 3 0 0
1 3 5 3 9 0
>> A_mat2(~cond1)=0
A_mat2 =
0 0 0 0 0 0
3 0 0 0 0 0
5 5 0 0 0 0
3 3 3 0 0 0
9 9 9 9 0 0
6 6 6 6 6 0
Now, add A_mat1 and A_mat2 and see how many 6's you got -
>> A_mat1 + A_mat2
ans =
0 0 0 0 0 0
4 0 0 0 0 0
6 8 0 0 0 0
4 6 8 0 0 0
10 12 14 12 0 0
7 9 11 9 15 0
As you can see there are two 6's and thus our result is verified.

Related

Bin interaction frequencies

I have 10 bins, and each bin contains a specific number of observations, e.g.:
a = [0,0,1,0,0,2,0,0,0,2]
I'd like to subsequently tally how many times any given pair of (non-zero) bins co-occur - based on the number of observations.
Given the above example, bin#3 = 1, bin#6 = 2 and bin#10 = 2.
This means that bin 3 and 6 co-occurred once, bin 3 and 10 co-occurred once, and bin 6 and 10 co-occurred twice (the minimum value of the pair is taken).
My desired output is a full matrix, listing every possible bin combination (columns 1-2) and the tally of what was observed (column 3):
1 2 0
1 3 0
1 4 0
1 5 0
1 6 0
1 7 0
1 8 0
1 9 0
1 10 0
2 3 0
2 4 0
2 5 0
2 6 0
2 7 0
2 8 0
2 9 0
2 10 0
3 4 0
3 5 0
3 6 1
3 7 0
3 8 0
3 9 0
3 10 1
4 5 0
4 6 0
4 7 0
4 8 0
4 9 0
4 10 0
5 6 0
5 7 0
5 8 0
5 9 0
5 10 0
6 7 0
6 8 0
6 9 0
6 10 2
7 8 0
7 9 0
7 10 0
8 9 0
8 10 0
9 10 0
Is there a short and/or fast way of doing this?

You can get all combinations of the bin numbers in many ways. I'll use combvec for ease.
Then it's relatively simple to vectorise this using min...
a = [0,0,1,0,0,2,0,0,0,2];
n = 1:numel(a);
% Use unique and sort to get rid of duplicate pairs when order doesn't matter
M = unique( sort( combvec( n, n ).', 2 ), 'rows' );
% Get rid of rows where columns 1 and 2 are equal
M( M(:,1) == M(:,2), : ) = [];
% Get the overlap count for bins
M( :, 3 ) = min( a(M), [], 2 );

Try this.
bin_output = [....];
bin_matrix = [0,0,1,0,0,2,0,0,0,2];
bin_nonzero = find(bin_matrix);
for j = 1:length(bin_nonzero);
if isequal(j,length(bin_nonzero))
break;
end
for k = (j+1):(length(bin_nonzero))
for m = 1:length(bin_output)
if isequal(bin_output(m,1),j) && isequal(bin_output(m,2),k)
bin_output(m,3) = bin_output(m,3) + min([bin_matrix(1,bin_nonzero(1,j)),bin_matrix(1,bin_nonzero(1,k))]);
end
end
end
end

MATLAB: How do you add all the first n rows of a matrix within the same column, and save the result to the last row?

It was hard to phrase the question, but here's an example of what I'm looking for:
1 2 3 4
2 1 1 1
2 2 3 1
0 0 0 0
and in column one, I add all the value of all of the first three rows and save it to the third and so on, so that it becomes:
1 2 3 4
2 1 1 1
2 2 3 1
5 5 7 6

I think you can use sum:
octave:23> m = [1 2 3 4; 2 1 1 1; 2 2 3 1; 0 0 0 0]
m =
1 2 3 4
2 1 1 1
2 2 3 1
0 0 0 0
octave:24> m(length(m), :) = sum(m)
m =
1 2 3 4
2 1 1 1
2 2 3 1
5 5 7 6

Matlab: Unique values between two matrices

I have 2 matrices:
T3(:,:,1) =
0 0 0 0 1 0 0 0 0
0 0 0 0 2 0 0 0 0
0 0 0 0 3 0 0 0 0
0 1 0 1 4 2 0 4 0
0 3 0 2 6 3 0 5 0
2 4 2 5 7 5 4 6 5
4 5 5 7 8 8 5 7 6
5 6 6 8 9 9 8 9 8
T3(:,:,2) =
2 1 1 1 1 1 1 1 1
3 3 2 2 2 2 2 2 2
4 4 4 3 3 3 3 3 3
5 5 5 5 4 4 4 4 4
6 6 6 6 6 5 5 5 5
7 7 7 7 7 7 6 6 6
8 8 8 8 8 8 8 7 7
9 9 9 9 9 9 9 9 8
How do I make values present in T3(:,:,1) turn to zero in T3(:,:,2)?
e.g. in the first column of T3(:,:,1) the values are 2,4,5. I'd like the first column of T3(:,:,2) to have the the values 2,4,5 as zero.
T3(:,:,2) =
0 0 1 0 0 1 1 1 1
3 0 0 0 0 0 2 2 2
0 0 4 3 0 0 3 3 3
0 0 0 0 0 4 0 0 4
6 0 0 6 0 0 0 0 0
7 7 7 0 0 7 6 0 0
8 8 8 0 0 0 0 0 7
9 9 9 9 0 0 9 0 0
I wonder if there is a way to do this using setdiff or unique.
for y=1:H-1
for z=1:H-1
for h=1:H
for d=1:D-1
if T3(y,h,d+1) == T3(z,h,d)
T3(y,h,d+1)=0;
end
end
end
end
end
I can do it as a loop where H=number of columns (9) and D= number of dimensions (2). There must be a better way :)?
Many thanks guys.

matlab efficient copying of matrix

I have matrix (a) with (1:10),<10 x 1> double. I would like to copy the values and rearrange them column wise into another matrix var. (b). See example below. Also, what method would be most efficient at this task?
matrix a matrix b
1 1
2 2 2
3 3 3 3
4 4 4 4 4
5 5 5 5 5 5
6 6 6 6 6 6 6
7 7 7 7 7 7 7 7
8 8 8 8 8 8 8 8 8
9 9 9 9 9 9 9 9 9 9
10 10 10 10 10 10 10 10 10 10 10
update:
Hi once again Amro. How about if I wanted to define which values to copy. See below example:
matrix a matrix b
column: 1 2 3 4 5 6 7
1 1
2 2 2
3 3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10 10

Try:
>> a = (1:10)'
a =
1
2
3
4
5
6
7
8
9
10
>> b = tril(repmat(a,1,10))
b =
1 0 0 0 0 0 0 0 0 0
2 2 0 0 0 0 0 0 0 0
3 3 3 0 0 0 0 0 0 0
4 4 4 4 0 0 0 0 0 0
5 5 5 5 5 0 0 0 0 0
6 6 6 6 6 6 0 0 0 0
7 7 7 7 7 7 7 0 0 0
8 8 8 8 8 8 8 8 0 0
9 9 9 9 9 9 9 9 9 0
10 10 10 10 10 10 10 10 10 10

I think in the second matrix you specified you made an error. I'm assuming you wanted to do something like this:
b =
1 0 0 0 0 0
2 2 0 0 0 0
0 3 3 0 0 0
0 0 4 4 0 0
0 0 0 5 5 0
0 0 0 0 6 6
this is simple to do:
%define vector of arbitrary length
a=1:6;
%generate b with shifted diagonal matrices
b=diag(a)+diag(a(2:end),-1);
the second argument of diag just shifts the resulting diagonal.

Replace duplicate elements from vector with 0 (Matlab/Octave)

I want to replace duplicate elements from a vector with 0, and keep only the first occurrence.
If I have a vector like
[ 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 5 6 6 6 ]
how could I transform it into
[ 1 0 2 0 0 3 0 0 4 0 0 0 5 0 0 0 6 0 0 ] ?
Thanks.

a = [ 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 5 6 6 6 ];
[c, ia] = unique(a, 'first');
t = a;
t(ia) = 0;
filtered_vect = a - t;
edit: That in a more concise way, destroying the original vector:
a = [ 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 5 6 6 6 ];
[c, ia] = unique(a, 'first');
a(~ismember(1:length(a),ia)) = 0;