sorting a matrix of 4 rows by the fourth element and outputting of combinations that make the 4th row element

My project so far has been to create a vector of numbers:

%x: a vector of numbers
x = 1:4;

and then create a 3 column matrix of the all the possible combinations of the vector x

%n: number of elements to pick (with repetetition) from x. n must be less than or equal to numel(x)
n = 3;
assert(n < numel(x), 'n can''t be greater than numel(x)')
combs = cell(1, n);
[combs{:}] = ndgrid(x);
combs = reshape(cat(n+1, combs{:}), [], n);  %a numel(x)^n X n matrix of combinations

and add a 4th column to the matrix which is the energy of the the 3 columns which is equal

length = length(combs);
for x=1:length
    combs(x,4) = combs(x, 1)^2+combs(x, 2)^2+combs(x, 3)^2;
    E(x,:) = combs(x,4);
end

This produces a matrix similiar to the picture below:

This code works great but I want to re oragnize the rows according to the energy (4th) column to look like this:

So the rows will start with 4th column is 3 and then the next three are 6, and so fourth. I'm not sure how to do this, and would appreciate any help. Just a FYI I plan to change the vector from 4 to 14, this simulation is for Griffth's Quantum mechanics problem 4.2.B, I already know the answer but I figured it would be a fun to see the matrix blow up as well as practice coding. I remember doing something similiar in Java but its been a long time ago.

Thank you,

-Leo Q

Answer 1

[KSSV]

NOTE: Never use a function name as the variable. You have used length as variable, this is problematic.

clc; clear all ;
%x: a vector of numbers
x = 1:4;
%n: number of elements to pick (with repetetition) from x. n must be less than or equal to numel(x)
n = 3;
assert(n < numel(x), 'n can''t be greater than numel(x)')
combs = cell(1, n);
[combs{:}] = ndgrid(x);
combs = reshape(cat(n+1, combs{:}), [], n);  %a numel(x)^n X n matrix of combinations
thelength = length(combs);
for x=1:thelength
    combs(x,4) = combs(x, 1)^2+combs(x, 2)^2+combs(x, 3)^2;
    E(x,:) = combs(x,4);
end
%% Arrange combs 
v = combs(:,end) ; 
[c,ia,ib] = unique(v) ;
iwant = cell(length(c),1) ; 
for i = 1:length(c)
    iwant{i} = combs(ib==i,:) ; 
end
celldisp(iwant)

 
iwant{1} =
 
     1     1     1     3

 
 
iwant{2} =
 
     2     1     1     6
     1     2     1     6
     1     1     2     6

 
 
iwant{3} =
 
     2     2     1     9
     2     1     2     9
     1     2     2     9

 
 
iwant{4} =
 
     3     1     1    11
     1     3     1    11
     1     1     3    11

 
 
iwant{5} =
 
     2     2     2    12

 
 
iwant{6} =
 
     3     2     1    14
     2     3     1    14
     3     1     2    14
     1     3     2    14
     2     1     3    14
     1     2     3    14

 
 
iwant{7} =
 
     3     2     2    17
     2     3     2    17
     2     2     3    17

 
 
iwant{8} =
 
     4     1     1    18
     1     4     1    18
     1     1     4    18

 
 
iwant{9} =
 
     3     3     1    19
     3     1     3    19
     1     3     3    19

 
 
iwant{10} =
 
     4     2     1    21
     2     4     1    21
     4     1     2    21
     1     4     2    21
     2     1     4    21
     1     2     4    21

 
 
iwant{11} =
 
     3     3     2    22
     3     2     3    22
     2     3     3    22

 
 
iwant{12} =
 
     4     2     2    24
     2     4     2    24
     2     2     4    24

 
 
iwant{13} =
 
     4     3     1    26
     3     4     1    26
     4     1     3    26
     1     4     3    26
     3     1     4    26
     1     3     4    26

 
 
iwant{14} =
 
     3     3     3    27

 
 
iwant{15} =
 
     4     3     2    29
     3     4     2    29
     4     2     3    29
     2     4     3    29
     3     2     4    29
     2     3     4    29

 
 
iwant{16} =
 
     4     4     1    33
     4     1     4    33
     1     4     4    33

 
 
iwant{17} =
 
     4     3     3    34
     3     4     3    34
     3     3     4    34

 
 
iwant{18} =
 
     4     4     2    36
     4     2     4    36
     2     4     4    36

 
 
iwant{19} =
 
     4     4     3    41
     4     3     4    41
     3     4     4    41

 
 
iwant{20} =
 
     4     4     4    48

 

[Leo Quintanar]

Thanks that worked perfectly, also thank you for your comment about my stupidity regrading my varaible names.

Answer 2

[Scott MacKenzie]

At the end of your code, add

sortrows(combs,4)

[Leo Quintanar]

thxs