lsqcurvefit add a constraint

i want to add my constraint, but i doesnt work. how can i put this x0(1).^2+x0(2).^2<RI^2 into my function??

And there is also a error. I cant use the fincom, cause my result is a vector. Someone can fix this two problems? Thank you so much!!

clear all; close all; clc
%%%%%%%%%%%%%%%%%%%%%%Define simulation parameters%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% My = magnetic permeability[H/m]
% Rho = Gain factor
% phi = phase delay [°]
% Theta Sensing directional angle
% r,Theta = Position and angular distance between conductors and sensors
% xs,ys = Coordinate of the sensors
% xi,yi = Coordinate of conductor to be measured
% I = Current of the Cables [A]
% RI = Cable Radius in m
global My Rho phi Theta RI B V Vm xs ys 
My = 4*pi*10^(-7);
Rho = 6.824*10000;
phi = 13.61;
Theta = 0.01;
RI = 21*(1e-3); % in[m]
%------------Calculation of voltage by magnetic flux B in [T]-------------%
%-------------------------------------------------------------------------%
% Define the magetic fields in [T] of sensors
B = [0.17, 0.47, 35.30, 35.32, 6.66, 6.59, 36.28, 35.43, 13.36, 15.04, 42.17, 44.05];
B = B*1e-6;
B
% calculate the output voltage of sensors in [V]
V = (Rho*exp(1i*phi*pi/180))*B; 
V
% % %---------------Define the measured voltage of sensors--------------------%
Vm = [0.0152, 0.03, 2.942, 2.943, 0.5751, 0.6, 3.0238, 2.9529, 1.1235, 1.2535, 3.714, 3.6713];
% Define the positions of each sensor in [m] 
xs = [21;-21;0;0;-14.5;-15;16;15.3;-8.800;-7.900;10.3;9.4];
ys = [0;0;21;-21;14.5;13.8;-12.9;13.9;18.3;-18.8;-17.9;18];
xs = xs.*1e-3;
ys = ys.*1e-3;

%--------------all x-and y-coordinates value of the sensors---------------%
xdata = xs;
xdata(:,2) = ys;
xdata
%---create the initial guess of x-and y-coordinates value of the cables---%
%--------create the initial guess of current value of the cables----------%
%-------------the field x consists of this 3 parameters-------------------%
x0 = [-6.3;-6.3;-6.3]*1e-4;
x0(:,2) = [-6.3;-6.3;-6.3]*1e-4;
x0(:,3) = [-4;-4;-4];
x0
%---------create the Lower(lb) and Upper(ub) bounds of fields x----------%
lb = [-21*1e-4,-21*1e-4,-5];
ub = [21*1e-4,21*1e-4,5];
options=(x0(1).^2+x0(2).^2<RI^2);
%---------solve the NNLS function to find out the fields of x-------------%
[x,resnorm,residual] = lsqcurvefit(@NNLS,x0,xdata,V,lb,ub,options)



function NNLS1 = NNLS(x,xdata)
% x - parameter: positions of the conductors & the current in the conductors
% xdata - array of positions of the sensors
% 
% NNLS - the calculated voltage at each position of each sensor
global My Rho phi Theta
% Create the number of x m and the xdata n
for n=1:1:12
    for m=1:1:3
    % calculate the distance between the sensor and conductor
    dis_array =sqrt((xdata(n,1)).^2+(xdata(n,2)).^2);
    % calculate cos angular distance between conductor and sensor
    cos_delta_a = (xdata(n,1).*cos(Theta)-xdata(n,2).*sin(Theta)).*((xdata(n,1)-x(m,1))+(xdata(n,2).*cos(Theta)+xdata(n,1).*sin(Theta))).*(xdata(n,2)-x(m,2));
    cos_delta_b = (xdata(n,1)-x(m,1)).^2+(xdata(n,2)-x(m,2)).^2;
    a = My*Rho*exp(1i*phi*pi/180)*x(m,3);
    % calculate the Output-voltage
    b(m,n) = (a.*(cos_delta_a)./(2*pi*(dis_array).*cos_delta_b));
    end 
    if n == 12
        NNLS1(:,:) = sum(b);
    end
end
end

error: Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.
<stopping criteria details>

[John D'Errico]

When you remove your question, you insult the person or people who were willing to spend their time to answer your question. You make it less likely they will bother to answer another of your questions. And you reduce the value to the site itself of the answer, because it is now meaningless out of context. So your removal of your question is inappropriate. If you did not want to leave it up, then you should never have posted it in the first place.

[Stephen23]

Original question (from Google Cache):

i want to add my constraint, but i doesnt work. how can i put this x0(1).^2+x0(2).^2<RI^2 into my function??

And there is also a error. I cant use the fincom, cause my result is a vector. Someone can fix this two problems? Thank you so much!!

clear all; close all; clc
%%%%%%%%%%%%%%%%%%%%%%Define simulation parameters%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% My = magnetic permeability[H/m]
% Rho = Gain factor
% phi = phase delay [°]
% Theta Sensing directional angle
% r,Theta = Position and angular distance between conductors and sensors
% xs,ys = Coordinate of the sensors
% xi,yi = Coordinate of conductor to be measured
% I = Current of the Cables [A]
% RI = Cable Radius in m
global My Rho phi Theta RI B V Vm xs ys 
My = 4*pi*10^(-7);
Rho = 6.824*10000;
phi = 13.61;
Theta = 0.01;
RI = 21*(1e-3); % in[m]
%------------Calculation of voltage by magnetic flux B in [T]-------------%
%-------------------------------------------------------------------------%
% Define the magetic fields in [T] of sensors
B = [0.17, 0.47, 35.30, 35.32, 6.66, 6.59, 36.28, 35.43, 13.36, 15.04, 42.17, 44.05];
B = B*1e-6;
B
% calculate the output voltage of sensors in [V]
V = (Rho*exp(1i*phi*pi/180))*B; 
V
% % %---------------Define the measured voltage of sensors--------------------%
Vm = [0.0152, 0.03, 2.942, 2.943, 0.5751, 0.6, 3.0238, 2.9529, 1.1235, 1.2535, 3.714, 3.6713];
% Define the positions of each sensor in [m] 
xs = [21;-21;0;0;-14.5;-15;16;15.3;-8.800;-7.900;10.3;9.4];
ys = [0;0;21;-21;14.5;13.8;-12.9;13.9;18.3;-18.8;-17.9;18];
xs = xs.*1e-3;
ys = ys.*1e-3;
%--------------all x-and y-coordinates value of the sensors---------------%
xdata = xs;
xdata(:,2) = ys;
xdata
%---create the initial guess of x-and y-coordinates value of the cables---%
%--------create the initial guess of current value of the cables----------%
%-------------the field x consists of this 3 parameters-------------------%
x0 = [-6.3;-6.3;-6.3]*1e-4;
x0(:,2) = [-6.3;-6.3;-6.3]*1e-4;
x0(:,3) = [-4;-4;-4];
x0
%---------create the Lower(lb) and Upper(ub) bounds of fields x----------%
lb = [-21*1e-4,-21*1e-4,-5];
ub = [21*1e-4,21*1e-4,5];
options=(x0(1).^2+x0(2).^2<RI^2);
%---------solve the NNLS function to find out the fields of x-------------%
[x,resnorm,residual] = lsqcurvefit(@NNLS,x0,xdata,V,lb,ub,options)
function NNLS1 = NNLS(x,xdata)
% x - parameter: positions of the conductors & the current in the conductors
% xdata - array of positions of the sensors
% 
% NNLS - the calculated voltage at each position of each sensor
global My Rho phi Theta
% Create the number of x m and the xdata n
for n=1:1:12
    for m=1:1:3
    % calculate the distance between the sensor and conductor
    dis_array =sqrt((xdata(n,1)).^2+(xdata(n,2)).^2);
    % calculate cos angular distance between conductor and sensor
    cos_delta_a = (xdata(n,1).*cos(Theta)-xdata(n,2).*sin(Theta)).*((xdata(n,1)-x(m,1))+(xdata(n,2).*cos(Theta)+xdata(n,1).*sin(Theta))).*(xdata(n,2)-x(m,2));
    cos_delta_b = (xdata(n,1)-x(m,1)).^2+(xdata(n,2)-x(m,2)).^2;
    a = My*Rho*exp(1i*phi*pi/180)*x(m,3);
    % calculate the Output-voltage
    b(m,n) = (a.*(cos_delta_a)./(2*pi*(dis_array).*cos_delta_b));
    end 
    if n == 12
        NNLS1(:,:) = sum(b);
    end
end
end
error: Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.
<stopping criteria details>

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Matt J]

No, you cannot supply any constraints except simple bounds with lsqcurvefit. You do need to use fmincon. Write an objective function that returns the scalar quantity that you are trying to minimize. If you are trying to do a least squares fit to your model function F(x,xdata), then this should be

objective=@(x) norm(F(x,xdata)-ydata)^2;