How to sort the matrix rows based on a function over the rows

Let's say I have a Nx3 matrix M of double.

Consider, for example, a function Map(a,b,c) that returns a double

How can I sort M so that the rows with smallest Map come first?

For example, the first row should be i if Map(M(i,1), M(i,2), M(i,3)) value is the smallest between Map(M(j,1), M(j,2), M(j,3)) for any 1 ≤ j ≤ N and j ≠ i

Answer 1

[Jos (10584)]

I have no clue what a,b and c are but I assume the function Map(a,b,c) will return a vector of N elements:

X = Map(a,b,c) 
[sortX, idx] = sort(X) % sort X, retrieve the sorting indices
sortedM = M(idx,:)  % sort M accordingly

[Daniel Tex]

the values for a,b,c should be the the 3 elements of each row of M (and M is a double matrix)

sorry I didn't mention, thought it was implicit

I want row i to be the first if Map(M(i,1), M(i,2), M(i,3)) value is the minimum between Map of all other rows, and so on

[Jos (10584)]

Does Map allow vectors?

X = Map(M(:,1),M(:,2),M(:,3))

if not:

X = arrayfun(@(r) Map(M(r,1),M(r,2), M(r,3)), 1:size(M,1))

[Daniel Tex]

I tested and X was not M after sorting... let me give you an example

M1 = |1 2 3|
     |4 5 6|
     |7 8 9|

Map(a,b,c){
    if(a == 1 && b == 2 && c == 3) return 2
    if(a == 4 && b == 5 && c == 6) return 3
    if(a == 7 && b == 8 && c == 9) return 1
}

so after the sorting, the matrix I'm looking for is:

M2 = |7 8 9|
     |1 2 3|
     |4 5 6|

because Map(7,8,9) is the smallest value, followed by Map(1,2,3) and Map(4,5,6)

[Jos (10584)]

Did you try to run the arrayfun line on your matrix M as above? What does it return?

Retrieving the indices of a sort and use it to re-order another array is a classic trick ...

[Daniel Tex]

yes I did. Firstly I changed Map to receive an array as argument, then I did:

   X = arrayfun(@(r) Map(M(r,:)), 1:size(M,1))

X is the array with the outputs for Map of each row from 1 to N

[Jos (10584)]

so, then it should work ... or am I missing something?

Answer 2

[Andrei Bobrov]

[~ii] =  = sort(arrayfun(@(r) Map(M(r,:)), 1:size(M,1)));
out = M(ii,:);