Find all combinaisons of sum of two vector that corresponds to the value of a third vector

Hi community !

I have three vectors A, B and C.

A = [1561.28, 1561.64, 1562.00, 1562.36, 1562.72]; % signal
B = [1064.00, 1064.36, 1064.72, 1065.08, 1065.44]; % pump
C = [632.89, 633.02, 633.14, 633.27, 633.40];      % converted

I want to check all the possible combinaisons of A and B (see next function) that correspond to a value of C

func = 1./(1./A + 1./B) >> C

For example a correct anwser in the result vector would be [3 1 1] for :

1/( 1/A(3) + 1/B(1) ) = C(1) 

I've already check some functions like nchoosecrit() but it only take one scalar as an result argument so I don't know.

Answer 1

[Matt J]

tolerance=1e-6;

[A,B,C]=deal(A(:),B(:),C(:)); %Make everything a column vector

[Ar,Br,Cr]=deal(A,B.' , reshape(C,1,1,[]) ); 


lidx = abs(  1./Ar + 1./Br.' - 1./Cr  ) <= tolerance ;

[i,j,k]=ind2sub(size(lidx), find(lidx));

locations=[i,j,k],
combinations=[A(i),B(j),C(k)]

[anthony dall'agnol]

This is nicer indeed thank you, is there any chances to have the C value corresponding to each combinations ? Something like :

[i,j,k] = ..
combinations=[A(i),B(j),C(k)];

[Matt J]

See my edited answer.

[anthony dall'agnol]

Thx, have a good day !

Answer 2

[Adam]

Well, what you wrote:

1./(1./A + 1./B)

will give you answers you can compare to C as e.g.

abs( 1./(1./A + 1./B) - C )

to give an absolute difference of each from C which you can then test against some threshold to see of they are close enough to equal.

[anthony dall'agnol]

I don't see how doing this

1./(1./A + 1./B)

is going to give me all combinaisons of what I want. Because this operation will just do

for ii = 1:end
        someVector = 1/(1/A(ii) + 1/B(ii));
end

And I want something more like

for ii = 1:end
    for jj = 1:end
        someVector = 1/(1/A(ii) + 1/B(jj));
    end
end

and at the end be able to have the index of the value that respect the function. Ideally I would like something like :

[value, index] = nchoosecrit(someVector, @(x,y) function(x,y) == someResult);

Answer 3

[Stephen23]

Simpler to use ndgrid:

>> A = [1561.28, 1561.64, 1562.00, 1562.36, 1562.72]; % signal
>> B = [1064.00, 1064.36, 1064.72, 1065.08, 1065.44]; % pump
>> C = [632.89, 633.02, 633.14, 633.27, 633.40];      % converted
>> [Aa,Ba,Ca] = ndgrid(A,B,C);
>> idx = abs(1./(1./Aa + 1./Ba) - Ca) < 0.01; % adjust tolerance to suit data.
>> [X,Y,Z] = ind2sub(size(idx),find(idx));
>> [X,Y,Z] % indices corresponding to A,B,C:
ans =
   3   1   1
   1   2   1
   3   2   2
   1   3   2
   5   2   3
   3   3   3
   5   3   4
   3   4   4
   3   5   5

And checking (e.g. the last row):

>> 1/( 1/A(3) + 1/B(5) )
ans =  633.40
>> C(5)
ans =  633.40