Summation of column elements of matrix A from index values of matrix B

Suppose I have matrix A=3x3 and B=3x3. I sort each column of B and get index matrix I by using [C,I]=sort(B). Now I will take first column Indices of matrix I and want to sum the corresponding elements of column A pertaining to these indices. Now I will take second column index of matrix I and sum the corresponding elements of A and so on till 4th element. I want to store these 4 sum values.

E.g. A=[1 2 3;2 3 4; 4 5 6] , B=[10 13 2; 23 24 3; 21 19 21]

Now [C,I] =sort (B), then I= [1 1 1 ;3 3 2;2 2 3]. The first column of I is [1 3 2]. Now I want to sum elements of A i.e. 1st element from first column, 3rd element from 2nd column and 2nd element from 3rd column ( 1+5+4). Store this value. Then I take 2nd column of I i.e. [1 3 2]. Again repeat summation of A as stated for 1st column (1+5+4). Then I take 3rd column of I and repeat step for A for summation (1+3+6). Now I want to store these 3 summation values in D( i.e. 10 10 10).

Pls suggest code.

Answer 1

[Matt J]

 A=randi(10,3)  , B=randi(10,3);

A = 3×3

9 9 6 10 6 9 1 2 6

 
 [m,n]=size(B);
 
 [~,I]=sort(B),

I = 3×3

3 2 2 1 1 3 2 3 1

 J=repmat((1:n)',1,m);
 
 D=sum( A( sub2ind(size(A),I,J) ) )

D = 1×3

19 25 18