Use vpasolve for vectors of two inputs.

Hello,

I have the inputs A and B as vectors. Moreover I got the constants c and d. My equotations look like (c-d-x)^2+y^2=d^2 and x^2+(c-d-y)^2=d^2. Those should give for each row of the input vector two pairs of solutions (x(1),y(1) and x(2),y(2)).

I found a solution with a for loop, but vpasolve has to run a lot of times, which consumes a lot of time:

A=[1,2,3,4];
B=[5,6,7,8];
c=9;
d=10;
%those numbers are just for the example and do not lead to real solution

    for i=1:length(A)

          clear x
          clear y
          syms x y 
          S = vpasolve([(c-A(i)-x)^2+y^2==d^2, x^2+(c-B(i)-y)^2==d^2],[x,y]);

          L(1,:,i)=[double(S.x(1));double(S.y(1))];
          L(2,:,i)=[double(S.x(2));double(S.y(2))];

    end

This however takes some time for a long input vector, so I do wonder if it is possible to speed this up (maybe get rid of the for-loop)?

Thank you in advance.

Answer 1

[Walter Roberson]

A = [1, 2, 3, 4];
B = [5, 6, 7, 8];
c=9;
d=10;
syms As Bs x y
sol = solve((c-As-x)^2+y^2==d^2, x^2+(c-Bs-y)^2==d^2,x,y);
Rx = double(subs(sol.x, {As, Bs}, {A, B}));
Ry = double(subs(sol.y, {As, Bs}, {A, B}));

I am not sure what the output dimensions of Rx and Ry would be.

[AndreasO]

Thanks for the answer.

The code works very well for me. Rx and Ry output vectors with twice the length of A/B, in which the first entries are always c/d and can be deleted.

So i had to add:

Rx(1:length(Rx)/2)=[];
Ry(1:length(Ry)/2)=[];

And i was able to get very quickly the solutions for my parameters.