MATLAB: Show All Possible Combination and Max. Value

combinationmatrixmax value

I have 6 different matrix (A,B,C,D,E,F).
A = [
Row1    Row2    Row3     Row4
30  30A  9.2588   0.2059
60  60A  18.5053   0.4054
90  90A  27.7393   0.5983
120  120A  36.961   0.7847
150  150A  46.1702   0.9645
180  180A  55.3671   1.1379
]
B = [
Row1    Row2    Row3     Row4
30  30B  9.2588   0.2059
60  60B  18.5053   0.4054
90  90B  27.7393   0.5983
120  120B  36.961   0.7847
150  150B  46.1702   0.9645
180  180B  55.3671   1.1379
]
C = [
Row1    Row2    Row3     Row4
30  30C  6.4351   0.314
60  60C  12.8844   0.6176
90  90C  19.3479   0.911
120  120C  25.8256   1.1941
150  150C  32.3175   1.4669
180  180C  38.8235   1.7294
]
D = [
Row1    Row2    Row3     Row4
30  30D  9.8998   0.2259
60  60D  19.6938   0.4449
90  90D  29.3821   0.657
120  120D  38.9645   0.8622
150  150D  48.4412   1.0606
180  180D  57.8121   1.2521
]
E = [
Row1    Row2    Row3     Row4
30  30E  6.4351   0.314
60  60E  12.8844   0.6176
90  90E  19.3479   0.911
120  120E  25.8256   1.1941
150  150E  32.3175   1.4669
180  180E  38.8235   1.7294
]
F = [
Row1    Row2    Row3     Row4
30  30F  9.8998   0.2259
60  60F  19.6938   0.4449
90  90F  29.3821   0.657
120  120F  38.9645   0.8622
150  150F  48.4412   1.0606
180  180F  57.8121   1.2521
]
I am looking for combination of A+B, A+C, A+D, A+E, A+F, B+C, ...., A+B+C, A+B+D, ... A+B+C+D, A+B+C+E, ... A+B+C+D+E+F.
For example, the result of A+B
A+B = [
Row1     Row2        Row3              Row4
30+30   30A+30B   9.2588+9.2588   0.2059+0.2059
30+60   30A+60B   9.2588+18.5053  0.2059+0.4054
...
60+30   60A+30B   18.5053+9.2588  0.4054+0.4054
180+180 180A+180B 55.3671+55.3671 1.1379+1.1379
]
= [
Row1     Row2        Row3       Row4
60      30A+30B     18.5176    0.4118
90      30A+60B     27.7641    0.6113
...
90      60A+30B     27.7641    0.6113
360    180A+180B   110.7342    2.27958
]
Finally, I hope to find the max value of row 4 when the value in row 1 is equal in all combination, such as 
Row 1 column1 (30) in A compare with Row 1 column 1 (30) in C,
Max value [
Row1  Row2  Row3   Row4
30    30C   6.4351  0.314
]
Thank you for your help!

Best Answer

Here is my approach to the first step (getting the sum of all combinations)
% step 0, create a small fake data set
A = randi(4,4,4) ; B = 10+randi(4,size(A)) ; C = 100+randi(4,size(A)) ;
% 1. put all matrices in a big 3D array
CM = cat(3,A,B,C)
% 2. make a list of all the combinations of 2 or more
acidx = nchoose(1:size(CM,3)) 
acidx(cellfun(@(c) numel(c)<2,acidx)) = [] 
% 3. sum all combinations
R = cellfun(@(c) sum(CM(:,:,c),3), acidx,'un',0)
The function NCHOOSE can be downloaded from the File Exchange: https://uk.mathworks.com/matlabcentral/fileexchange/20011-nchoose
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