# Brute force combination of two vectors. Yet, the combination only gets written in a matrix if it fulfils two constraints.

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Abdelmajid Ben yahya il 9 Mar 2020
Modificato: Ameer Hamza il 9 Mar 2020
I have two vectors:
L_1=[30:10:500];
L_2=[30:10:500];
and two values that are known:
a=250;
b=482;
These vectors are now of the same size, but this is not always the case. Thus, I would like to create a matrix (2 columns) that has every possible combination L_1,L_2 that fulfils the following constraints.
L_1< (a/theta_a); AND L_1< (b/theta_b);
The values theta_a and theta_b are calculated through on behalf of the values L_1 and L_2 with the following formula:
Theta_a=acosd((a^2+L_1^2-L_2^2)/(2*a*L_1);
Theta_b=acosd((b^2+L_1^2-L_2^2)/(2*b*L_1);
It would be great if the computational time can be reduced by an efficient script.
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Ameer Hamza il 9 Mar 2020
For the values of L_1 and L_2, a and b you gave, the function acosd can return complex value. The domain of acosd is -1 to 1 for real-valued output. But the input of acosd
(a^2+L_1^2-L_2^2)/(2*a*L_1)
can take any value beyong -1 to 1. How will you do comparison in that case.

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### Risposta accettata

Ameer Hamza il 9 Mar 2020
Modificato: Ameer Hamza il 9 Mar 2020
L_1=30:1:500;
L_2=30:1:500;
a=250;
b=482;
combinations = combvec(L_1, L_2)';
Theta_a=acos((a^2+combinations(:,1).^2-combinations(:,2).^2) ...
./(2*a*combinations(:,1)));
Theta_b=acos((b^2+combinations(:,1).^2-combinations(:,2).^2) ...
./(2*b*combinations(:,1)));
mask = imag(Theta_a) == 0 & imag(Theta_b) == 0; % only keep rows where both angles are real
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Abdelmajid Ben yahya il 9 Mar 2020
the first assumptions is not correct, as the formua is the derivation of the cosine rule.
These constraints are made to erase certain mechanical configurations, within a physical crank-shaft mechanism.
I attached some drawings to explainthe idea.
the first two drawings (top) show the mechanism, while the drawings underneath show the derivation of the constraints.
So, i think that the made assumptions can be rejected.
Ameer Hamza il 9 Mar 2020
Ok, your formula is correct. I think it produces an imaginary number in some cases because it is impossible to create a real triangle for some combinations of L_1, L_2, a, and b. I corrected the code and added another condition that both angles should be real.

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