MATLAB: How initial value of solution can be provided for system solving by fsolve

fsolveinitial value

I am trying to solve the set of equations using commands shown below
x0 = [-1 -1 -1 -1 2 2.5]
options = optimoptions('fsolve','Display','iter');
[x,fval] = fsolve(@calc,x0,options)
function F = cal(x)
F = [x(1)*cos(2*pi*D*q1) + x(3)*sin(2*pi*D*q1) – x(2)*cos(2*pi*D*q2) – x(4)*sin(2*pi*D*q2) + (q2^2*x(5)/(q2^2-1))*sin(2*pi*D+x(6)) – (1/(k+1));
    x(1) - x(2)*cos(2*pi*q2) - x(4)*sin(2*pi*q2) + (q2^2*x(5)/(q2^2-1))*sin(x(6)) - (1/(k+1));
    -q1*x(1)*sin(2*pi*D*q1) + q1*x(3)*cos(2*pi*D*q1) + q2*x(2)*sin(2*pi*D*q2) - q2*x(4)*cos(2*pi*D*q2) + (q2^2*x(5)/(q2^2-1))*cos(2*pi*D+x(6));
    x(3)*q1 + x(2)*q2*sin(2*pi*q2) - x(4)*q2*cos(2*pi*q2) + (q2^2*x(5)/(q2^2-1))*cos(x(6));
    2*pi*(k/(k+1))*(1-D) + x(5)*(cos(2*pi*D+x(6))-cos(x(6)))*((q2^2/(q2^2-1))-(k+1)) + (x(2)/q2)*(sin(2*pi*D*q2)-sin(2*pi*q2)) + (x(4)/q2)*(cos(2*pi*q2)-cos(2*pi*D*q2));
    (k/(k+1)) + x(5)*sin(x(6))*((q2^2/(q2^2-1))-(k+1)) - (x(2)*cos(2*pi*q2)+x(4)*sin(2*pi*q2))];
end
However on running it is showing following error
Attempt to execute SCRIPT calc as a function: C:\Users\PE LAB\Desktop\calc.m
Error in fsolve (line 230) fuser = feval(funfcn{3},x,varargin{:});
Error in calc (line 4) [x,fval] = fsolve(@calc,x0,options)
Caused by: Failure in initial objective function evaluation. FSOLVE cannot continue.
Is there any problem with initialization?
(System is solvable with one case of parameter value q1=2; D=0.375; k=0.867; q2=2.9349; having solution as [−0.94 -0.86 -1.24 -1.23 1.92 2.57])

Best Answer

Hi,
try:
q1=2;
D=0.375; 
k=0.867; 
q2=2.9349;
x0 = [-1 -1 -1 -1 2 2.5]
options = optimoptions('fsolve','Display','iter');
calc = @(x)[x(1)*cos(2*pi*D*q1) + x(3)*sin(2*pi*D*q1) - x(2)*cos(2*pi*D*q2) - x(4)*sin(2*pi*D*q2) + (q2^2*x(5)/(q2^2-1))*sin(2*pi*D+x(6)) - (1/(k+1));
    x(1) - x(2)*cos(2*pi*q2) - x(4)*sin(2*pi*q2) + (q2^2*x(5)/(q2^2-1))*sin(x(6)) - (1/(k+1));
    -q1*x(1)*sin(2*pi*D*q1) + q1*x(3)*cos(2*pi*D*q1) + q2*x(2)*sin(2*pi*D*q2) - q2*x(4)*cos(2*pi*D*q2) + (q2^2*x(5)/(q2^2-1))*cos(2*pi*D+x(6));
    x(3)*q1 + x(2)*q2*sin(2*pi*q2) - x(4)*q2*cos(2*pi*q2) + (q2^2*x(5)/(q2^2-1))*cos(x(6));
    2*pi*(k/(k+1))*(1-D) + x(5)*(cos(2*pi*D+x(6))-cos(x(6)))*((q2^2/(q2^2-1))-(k+1)) + (x(2)/q2)*(sin(2*pi*D*q2)-sin(2*pi*q2)) + (x(4)/q2)*(cos(2*pi*q2)-cos(2*pi*D*q2));
    (k/(k+1)) + x(5)*sin(x(6))*((q2^2/(q2^2-1))-(k+1)) - (x(2)*cos(2*pi*q2)+x(4)*sin(2*pi*q2))];
[x,fval] = fsolve(calc,x0,options)
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