Solve function. Warning: Explicit solution could not be found.

I'm working with a system of quadratic equations, my experiment has to go different lines from an initial distance Dist (1) and reach a distance 0.

The problem is that this code only reaches a minimum of approximately 0.00025.

It is a limitation of the solve function? or am I doing something wrong?

Of course, thank you very much.

Here is the code:

function SolveEcu()

% Coordenadas crom�ticas grises
  xg = 0.229;
  yg = 0.348;

    ug = 0.136;
    vg = 0.466;

    i=1;
    Dist(i) = 0.001; %Distancia inicial.

    while Dist(i) > 0
        syms ucTemp vcTemp        
        S = solve((vcTemp == (-0.1209*ucTemp) + 0.4827), (Dist(i)^2 == ((ucTemp-ug)^2+(vcTemp-vg)^2)), 'Real', true); %Resuelvo el sistema de ecuaciones

        uTemp = S.ucTemp;% Lo uso para evaluar
        vTemp = S.vcTemp;
        save(['E:\Labz\Experimento Color\Resultados\',datestr(now,'yymmdd')],'uTemp','vTemp','Dist');

        i=i+1;   
        Dist(i)=Dist(i-1)- 0.00001;

        disp(['Running.. i=',num2str(i)])
    end
    pause(0.5);
end

Matlab console:

Running.. i=76

d =

   2.5000e-04

Warning: Explicit solution could not be found.

> In solve at 169 In SolveEcu at 17

Comma separated list expansion has cell syntax for an array that is not a cell.

Error in sym/subsref (line 1575) [inds{k},refs{k}] = privformat(inds{k});

Error in SolveEcu (line 19) uTemp = S.ucTemp;% Lo uso para evaluar

>>

Answer 1

[Roger Stafford]

In the equation

 Dist(i)^2 == (ucTemp-ug)^2+(vcTemp-vg)^2

when the right side of the equation

 vcTemp == -0.1209*ucTemp + 0.4827

is substituted for vcTemp, it can be shown by completing the square that the smallest possible real value of the resulting quadratic in ucTemp is about 6.54e-8. Eventually your while-loop will reduce Dist(i)^2 to the point where Dist(i) is still positive but Dist(i)^2 is below 6.54e-8. At this point your equations will have no real solutions. I suspect it is at this time that the 'solve' function issues its error message that no explicit solution could be found since you are requiring a real result. You can find out if this is true by running your code while using the debugger.

Whether or not this is the source of the error message, it is a definite coding mistake which should be corrected. You should make sure that for every value of Dist(i) you present to 'solve' there is a real solution to avoid error messages. Either that or you should not require the solutions to be real.