lsqcurvefit requires all values returned by functions to be of data type double.

I am having this error :

"Error using lsqncommon

lsqcurvefit requires all values returned by functions to be of data type double.

Error in lsqcurvefit (line 295)

lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,optimgetFlag,caller,..."

Here's my code.

syms a b c d e f theta

ydata=[10 12 5 65 32 12 25 30 15 26];
theta_Val=0:5:45;

y = (a+445)*c*cos(theta)+e/f*sin(theta)+d;

%Variable equal to 0
Var_Zero=[a b c d];
%Variable to search
Var_Search=[e f];
%Initial value
Init=[0,0];
%I replace my variable equal to 0 by 0
y_reduce = eval(subs(y,Var_Zero,zeros(size(Var_Zero))));

%I declare my function
Fonction = @(Var_Cherche,theta) y_reduce;

%I do a test to see if the size are corresponding
size(ydata) %1x10
size(Fonction(Init,theta_Val)) %1x1
%They are not
%I replace my theta with the values that I want
y_reduce=(subs(y_reduce,theta,theta_Val));
%I recreate the function
Fonction = @(Var_Search,theta) y_reduce;

%Size Test
size(ydata) %1x10
size(Fonction(Init,theta_Val)) %1x10
%They are the same size


%Then I try to fit
x = lsqcurvefit(Fonction,Init,theta_Val,ydata)

The problem comes with how I handle theta in my function but I don't know what to change.

Answer 1

[Torsten]

Setting y = e/f*sind(theta) makes no sense because this setup will have infinitely many solutions.

Use a single parameter e instead.

syms a b c d e theta

ydata=[10 12 5 65 32 12 25 30 15 26];
theta_Val=0:5:45;

y = (a+445)*c*cosd(theta)+e*sind(theta)+d;

%Variable equal to 0
Var_Zero=[a b c d];
%Variable to search
Var_Search=[e];
%Initial value
Init=[1];
%I replace my variable equal to 0 by 0
y_reduce = eval(subs(y,Var_Zero,zeros(size(Var_Zero))));

%I declare my function
Fonction = @(Var_Cherche,theta) y_reduce;

%I do a test to see if the size are corresponding
%size(ydata) %1x10
%size(Fonction(Init,theta_Val)) %1x1
%They are not
%I replace my theta with the values that I want
y_reduce=(subs(y_reduce,theta,theta_Val));
%I recreate the function
%Fonction = @(Var_Search,theta) y_reduce
Fonction = matlabFunction(y_reduce)

Fonction = function_handle with value:
    @(e)[0.0,e.*sin(pi./3.6e+1),e.*sin(pi./1.8e+1),-e.*(sqrt(2.0)./4.0-sqrt(6.0)./4.0),e.*sin(pi./9.0),e.*sin(pi.*(5.0./3.6e+1)),e./2.0,e.*sin(pi.*(7.0./3.6e+1)),e.*sin(pi.*(2.0./9.0)),(sqrt(2.0).*e)./2.0]

Fonction = @(x,theta_Val)Fonction(x);

%Size Test
%size(ydata) %1x10
%size(Fonction(Init,theta_Val)) %1x10
%They are the same size


%Then I try to fit
x = lsqcurvefit(Fonction,Init,theta_Val,ydata)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

x = 48.8708

Fonction(x,theta_Val)-ydata

ans = 1×10

-10.0000 -7.7406 3.4863 -52.3513 -15.2852 8.6537 -0.5646 -1.9689 16.4135 8.5569

[Quentin Javey]

Thank you very much. The equation doesn't really make sense because the original equation and how to obtain it is way to long, but the egxemple is similar to my problem.

[Quentin Javey]

Hi, I changed my program so that e/f doesn't appear and there is more than one parameter.

However, I still have a problem and I don't understand why.

"Arrays have incompatible sizes for this operation.".

syms a b c d e theta

ydata=[10 12 5 65 32 12 25 30 15 26];
theta_Val=0:5:45;

y = (a+445)*c*cos(theta)+e*sin(theta)+d;

%Variable equal to 0
Var_Zero=[a b c];
%Variable to search
Var_Search=[e d];
%Initial value
Init=[0,0];
%I replace my variable equal to 0 by 0
y_reduce = eval(subs(y,Var_Zero,zeros(size(Var_Zero))));

y_reduce=(subs(y_reduce,theta,theta_Val));
Fonction = matlabFunction(y_reduce);

%Size Test
% size(ydata) %1x10
% size(Fonction(Init,theta_Val)) %1x10


%Then I try to fit
lsqcurvefit(Fonction,Init,theta_Val,ydata)

Arrays have incompatible sizes for this operation.

Error in symengine>@(d,e)[d,d+e.*sin(5.0),d+e.*sin(1.0e+1),d+e.*sin(1.5e+1),d+e.*sin(2.0e+1),d+e.*sin(2.5e+1),d+e.*sin(3.0e+1),d+e.*sin(3.5e+1),d+e.*sin(4.0e+1),d+e.*sin(4.5e+1)]

Error in lsqcurvefit (line 225)
initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

It seem that calling the function doesn't even works.

Fonction(Init)

[Torsten]

syms a b c d e theta
ydata=[10 12 5 65 32 12 25 30 15 26];
theta_Val=0:5:45;
y = (a+445)*c*cos(theta)+e*sin(theta)+d;
%Variable equal to 0
Var_Zero=[a b c];
%Variable to search
Var_Search=[e d];
%Initial value
Init=[0,0];
%I replace my variable equal to 0 by 0
y_reduce = eval(subs(y,Var_Zero,zeros(size(Var_Zero))));
y_reduce=(subs(y_reduce,theta,theta_Val));
Fonction = matlabFunction(y_reduce)

Fonction = function_handle with value:
    @(d,e)[d,d+e.*sin(5.0),d+e.*sin(1.0e+1),d+e.*sin(1.5e+1),d+e.*sin(2.0e+1),d+e.*sin(2.5e+1),d+e.*sin(3.0e+1),d+e.*sin(3.5e+1),d+e.*sin(4.0e+1),d+e.*sin(4.5e+1)]

Fonction = @(x,theta_Val)Fonction(x(1),x(2));
%Size Test
% size(ydata) %1x10
% size(Fonction(Init,theta_Val)) %1x10
%Then I try to fit
sol = lsqcurvefit(Fonction,Init,theta_Val,ydata);

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

d = sol(1)

d = 23.0930

e = sol(2)

e = 9.9294

[Quentin Javey]

Thank you, I can make it work with 2+ variable on this program but it doesn't seem to work on my original problem with 2+ variable. It's okay with 2 but no more than that: "Failure in initial objective function evaluation. LSQCURVEFIT cannot continue."

Here's the original work.

At first, it's just symbolic calcul.Nothing wrong here.

clear all; clc;

%% Main

%défauts
syms x_l_M_TR y_l_M_TR z_l_M_TR a_l_M_TR b_l_M_TR c_l_M_TR
syms x_m_M_TR y_m_M_TR z_m_M_TR a_m_M_TR b_m_M_TR c_m_M_TR
syms x_l_TR_RX y_l_TR_RX z_l_TR_RX a_l_TR_RX b_l_TR_RX c_l_TR_RX
syms x_m_TR_RX y_m_TR_RX z_m_TR_RX a_m_TR_RX b_m_TR_RX c_m_TR_RX
syms x_l_RX_P y_l_RX_P z_l_RX_P a_l_RX_P b_l_RX_P c_l_RX_P
Var=[x_l_M_TR y_l_M_TR z_l_M_TR a_l_M_TR b_l_M_TR c_l_M_TR x_m_M_TR y_m_M_TR z_m_M_TR a_m_M_TR...
    b_m_M_TR c_m_M_TR x_l_TR_RX y_l_TR_RX z_l_TR_RX a_l_TR_RX b_l_TR_RX c_l_TR_RX x_m_TR_RX y_m_TR_RX... 
    z_m_TR_RX a_m_TR_RX b_m_TR_RX c_m_TR_RX x_l_RX_P y_l_RX_P z_l_RX_P a_l_RX_P b_l_RX_P c_l_RX_P];


%mouvement
syms theta

%constantes
dist_z_TR_RX = 185.0;
dist_z_RX_P = 71.11;
dist_z_P_M1 = 16.77;
dist_z_P_M2 = 50.31;

%matrices de passage
%lock nominal
T_ln_M_TR = eye(4);
T_ln_TR_RX = eye(4); T_ln_TR_RX(3,4)=dist_z_TR_RX;
T_ln_RX_P = eye(4);  T_ln_RX_P(3,4)=dist_z_RX_P;

%lock error
T_le_M_TR = MTH(x_l_M_TR,y_l_M_TR,z_l_M_TR,a_l_M_TR,b_l_M_TR,c_l_M_TR);
T_le_TR_RX = MTH(x_l_TR_RX,y_l_TR_RX,z_l_TR_RX,a_l_TR_RX,b_l_TR_RX,c_l_TR_RX);
T_le_RX_P = MTH(x_l_RX_P,y_l_RX_P,z_l_RX_P,a_l_RX_P,b_l_RX_P,c_l_RX_P);

%mouvement nominal
T_mn_M_TR = MTH(0,0,0,0,0,theta);
T_mn_TR_RX = MTH(0,0,0,0,0,-theta);

%mouvement error
T_me_M_TR = MTH(x_m_M_TR,y_m_M_TR,z_m_M_TR,a_m_M_TR,b_m_M_TR,c_m_M_TR);
T_me_TR_RX = MTH(x_m_TR_RX,y_m_TR_RX,z_m_TR_RX,a_m_TR_RX,b_m_TR_RX,c_m_TR_RX);

%changement de repère
T_M_TR = T_ln_M_TR*T_le_M_TR*T_mn_M_TR*T_me_M_TR;
T_TR_RX = T_ln_TR_RX*T_le_TR_RX*T_mn_TR_RX*T_me_TR_RX;
T_RX_P = T_ln_RX_P*T_le_RX_P;
%global symbolique
T_sym= T_M_TR*T_TR_RX*T_RX_P;

%Tri
% clear T_ln_M_TR T_le_M_TR T_mn_M_TR T_me_M_TR T_ln_TR_RX T_le_TR_RX T_mn_TR_RX T_me_TR_RX...
%     T_ln_RX_P T_le_RX_P T_M_TR T_TR_RX T_RX_P...
%     x_l_M_TR y_l_M_TR z_l_M_TR a_l_M_TR b_l_M_TR c_l_M_TR x_m_M_TR y_m_M_TR z_m_M_TR a_m_M_TR b_m_M_TR...
%     c_m_M_TR x_l_TR_RX y_l_TR_RX z_l_TR_RX a_l_TR_RX b_l_TR_RX c_l_TR_RX x_m_TR_RX y_m_TR_RX z_m_TR_RX...
%     a_m_TR_RX b_m_TR_RX c_m_TR_RX x_l_RX_P y_l_RX_P z_l_RX_P a_l_RX_P b_l_RX_P c_l_RX_P

Then i get the expression of my function (Angle).

%transformation de la mesure
load('Mesure_7_6_RX10.mat')
Y_Val=Val*1.e-5*3600;

theta_Val=0:5:360;
theta_Val_rad = theta_Val/180*pi;

%Variables à 0
Var_Zero=[z_l_M_TR c_l_M_TR x_m_M_TR y_m_M_TR z_m_M_TR a_m_M_TR...
    b_m_M_TR c_m_M_TR z_l_TR_RX c_l_TR_RX x_m_TR_RX y_m_TR_RX... 
    z_m_TR_RX a_m_TR_RX b_m_TR_RX c_m_TR_RX z_l_RX_P  c_l_RX_P...
    x_l_M_TR y_l_M_TR a_l_M_TR b_l_M_TR x_l_TR_RX y_l_TR_RX  a_l_TR_RX...
    b_l_TR_RX x_l_RX_P ];
%Varibles à déterminer
Var_Cherche=[y_l_RX_P a_l_RX_P b_l_RX_P];

%départ:
Depart=zeros(1,size(Var_Cherche,2));

M1 = T_sym* [0;0;dist_z_P_M1;1];
M2 = T_sym* [0;0;dist_z_P_M2;1];

Angle = atan2(M1(2,:)-M2(2,:),M2(3,:)-M1(3,:))/pi*180;

Then I change the value of theta and those that are equal to zero.

Angle = eval(subs(Angle,Var_Zero,zeros(size(Var_Zero))));
Angle = subs(Angle,theta,theta_Val);

Fonction = matlabFunction(Angle);
Fonction = @(x,theta_Val)Fonction(x(1),x(2),x(3));

And I try to do my fit.

x = lsqcurvefit(Fonction,Depart,theta_Val,Y_Val);

Error using symengine>@(a_l_RX_P,b_l_RX_P)[(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./3.6e+1).^2+sin(pi./3.6e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./1.8e+1).^2+sin(pi./1.8e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./9.0).^2+sin(pi./9.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./3.6e+1)).^2+sin(pi.*(5.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./3.6e+1)).^2+sin(pi.*(7.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(2.0./9.0)).^2+sin(pi.*(2.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./1.8e+1)).^2+sin(pi.*(5.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.1e+1./3.6e+1)).^2+sin(pi.*(1.1e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.3e+1./3.6e+1)).^2+sin(pi.*(1.3e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./1.8e+1)).^2+sin(pi.*(7.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(4.0./9.0)).^2+sin(pi.*(4.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.7e+1./3.6e+1)).^2+sin(pi.*(1.7e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.7e+1./3.6e+1)).^2+sin(pi.*(1.7e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(4.0./9.0)).^2+sin(pi.*(4.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./1.8e+1)).^2+sin(pi.*(7.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.3e+1./3.6e+1)).^2+sin(pi.*(1.3e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.1e+1./3.6e+1)).^2+sin(pi.*(1.1e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./1.8e+1)).^2+sin(pi.*(5.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(2.0./9.0)).^2+sin(pi.*(2.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./3.6e+1)).^2+sin(pi.*(7.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./3.6e+1)).^2+sin(pi.*(5.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./9.0).^2+sin(pi./9.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./1.8e+1).^2+sin(pi./1.8e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./3.6e+1).^2+sin(pi./3.6e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./3.6e+1).^2+sin(pi./3.6e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./1.8e+1).^2+sin(pi./1.8e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./9.0).^2+sin(pi./9.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./3.6e+1)).^2+sin(pi.*(5.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./3.6e+1)).^2+sin(pi.*(7.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(2.0./9.0)).^2+sin(pi.*(2.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./1.8e+1)).^2+sin(pi.*(5.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.1e+1./3.6e+1)).^2+sin(pi.*(1.1e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.3e+1./3.6e+1)).^2+sin(pi.*(1.3e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./1.8e+1)).^2+sin(pi.*(7.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(4.0./9.0)).^2+sin(pi.*(4.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.7e+1./3.6e+1)).^2+sin(pi.*(1.7e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.7e+1./3.6e+1)).^2+sin(pi.*(1.7e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(4.0./9.0)).^2+sin(pi.*(4.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./1.8e+1)).^2+sin(pi.*(7.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.3e+1./3.6e+1)).^2+sin(pi.*(1.3e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(1.1e+1./3.6e+1)).^2+sin(pi.*(1.1e+1./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./1.8e+1)).^2+sin(pi.*(5.0./1.8e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(2.0./9.0)).^2+sin(pi.*(2.0./9.0)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(7.0./3.6e+1)).^2+sin(pi.*(7.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi.*(5.0./3.6e+1)).^2+sin(pi.*(5.0./3.6e+1)).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./9.0).^2+sin(pi./9.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*((sqrt(2.0)./4.0-sqrt(6.0)./4.0).^2+(sqrt(2.0)./4.0+sqrt(6.0)./4.0).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./1.8e+1).^2+sin(pi./1.8e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2).*(cos(pi./3.6e+1).^2+sin(pi./3.6e+1).^2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi,(atan2(sin((a_l_RX_P.*pi)./1.8e+2),cos((a_l_RX_P.*pi)./1.8e+2).*cos((b_l_RX_P.*pi)./1.8e+2)).*1.8e+2)./pi]
Too many input arguments.

Error in solution (line 84)
Fonction = @(x,theta_Val)Fonction(x(1),x(2),x(3));

Error in lsqcurvefit (line 225)
initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

I don't know why it's not working with 2+ while it's working with 2.

At the end, I want to have 12 variables to search.

Var_Zero=[z_l_M_TR c_l_M_TR x_m_M_TR y_m_M_TR z_m_M_TR a_m_M_TR...
    b_m_M_TR c_m_M_TR z_l_TR_RX c_l_TR_RX x_m_TR_RX y_m_TR_RX... 
    z_m_TR_RX a_m_TR_RX b_m_TR_RX c_m_TR_RX z_l_RX_P  c_l_RX_P];
%Varibles à déterminer
Var_Cherche=[x_l_M_TR y_l_M_TR a_l_M_TR b_l_M_TR x_l_TR_RX y_l_TR_RX  a_l_TR_RX...
    b_l_TR_RX x_l_RX_Py_l_RX_P a_l_RX_P b_l_RX_P];

[Torsten]

According to the error message, your function "Angle" does not depend on y_l_RX_P.

Thus you'll have to define

Fonction = @(x,theta_Val)Fonction(x(1),x(2));

instead of

Fonction = @(x,theta_Val)Fonction(x(1),x(2),x(3));

Since the source error is always the same in your requests:

After defining

Fonction = matlabFunction(something);

look at the list of input parameters to the function and count them. If the total number is N, redefine Fonction as

Fonction = @(x,theta_Val)Fonction(x(1),x(2),x(3),...,x(N))