I’m having problems figuring out how to get some MATLAB code from a textbook to run. The code follows. The only original code statements are the first seven lines. I was trying to provide some basic data to get the code to draw a plane. I did have to add some "end" statements to the code, including the end at the bottom. I would like to get this code to draw an image and move it around a screen, but this code is supposed to do that. I need to learn how to get the code to run. I have a number of additional (or perhaps core) questions.
Is "fred" an appropriate handle reference?
Do I need to define a handle reference?
How do I call drawPlaneBody?
Can you help me to get this code (from a textbook) to work?
Thank you most sincerely.

pn = 20;
pe=0;
pd=0;
phi =0;
theta=0;
psi=0;
handle="fred";

function handle = drawPlaneBody(pn,pe,pd,phi,theta,psi,handle)
%define points on plane in local NED coordintates
NED = airplanepoints;
%rotate plane by (phi; theta; psi)
NED = rotate(NED, phi, theta, psi);
%translate plane to [pn; pe; pd]
NED = translate(NED, pn, pe, pd);
%transform vertices from NED to XYZ
R = […
0, 1, 0;…
1, 0 , 0;…
0, 0, -1;…
];
XYZ = R* NED;
%plot plane
if isempty(handle)
handle = plot3(XYZ(1,:),XYZ(2,:),XYZ(3,:),’Erasemode’, mode);
else
set(handle, ‘XData’, XYZ(1,:), ‘YData’,XYZ(2,:), ‘ZData’,XYZ(3,:));
drawnow
end

function XYZ = airplanepoints
%define points on the aircraft in local NED
coordinates
XYZ = […
0 0 0;%point1
-2 1 1;%point2
-2 1 -1;%point3
0 0 0;%point1
-2 -1 1;%point4
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
-2 -1 1;%point4
0 0 0;%point1
-2 1 -1;%point3
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
18 0 0;%point6
-2 1 -1;%point3
18 0 0;%point6
-2 -1 -1;%point5
18 0 0;%point6
-2 -1 1;%point4
18 0 0;%point6
-2 1 1;%point2
0 0 0;%point1
-5 0 0;%point7
-5 -10 0;%point8
-8 -10 0;%point9
-8 10 0;%point10
-5 10 0;%point11
-5 0 0;%point7
-15.5 0 0;%point12
-15.5 2 0;%point13
-17.5 2 0;%point14
-17.5 -2 0;%point15
-15.5 -2 0;%point16
-15.5 0 0;%point12
-18 0 0;%point6
-18 0 2;%point17
-15.5 0 0;%point15
-18 0 0;%point16
];
end

function XYZ=rotate(XYZ,phi,theta,psi)
%define rotation matrix
R_roll = [
1, 0, 0;
0, cos(phi), -sin(phi);
0, sin(phi), cos(phi)];
R_pitch = [
cos(theta), 0, sin(theta);
0, 1, 0;
-sin(theta), 0, cos(theta)];
R_yaw = [
cos(psi), -sin(psi), 0;
sin(psi), cos(psi), 0;
0, 0, 1];
R = R_roll*R_pitch*R_yaw;
%rotate vertices
XYZ =R*XYZ;
end

function XYZ = translate(XYZ, pn, pe, pd)
XYZ = XYZ + repmat([pn;pe;pd],1,size(XYZ,2));
end

endI’m having problems figuring out how to get some MATLAB code from a textbook to run. The code follows. The only original code statements are the first seven lines. I was trying to provide some basic data to get the code to draw a plane. I did have to add some "end" statements to the code, including the end at the bottom. I would like to get this code to draw an image and move it around a screen, but this code is supposed to do that. I need to learn how to get the code to run. I have a number of additional (or perhaps core) questions.
Is "fred" an appropriate handle reference?
Do I need to define a handle reference?
How do I call drawPlaneBody?
Can you help me to get this code (from a textbook) to work?
Thank you most sincerely.

pn = 20;
pe=0;
pd=0;
phi =0;
theta=0;
psi=0;
handle="fred";

function handle = drawPlaneBody(pn,pe,pd,phi,theta,psi,handle)
%define points on plane in local NED coordintates
NED = airplanepoints;
%rotate plane by (phi; theta; psi)
NED = rotate(NED, phi, theta, psi);
%translate plane to [pn; pe; pd]
NED = translate(NED, pn, pe, pd);
%transform vertices from NED to XYZ
R = […
0, 1, 0;…
1, 0 , 0;…
0, 0, -1;…
];
XYZ = R* NED;
%plot plane
if isempty(handle)
handle = plot3(XYZ(1,:),XYZ(2,:),XYZ(3,:),’Erasemode’, mode);
else
set(handle, ‘XData’, XYZ(1,:), ‘YData’,XYZ(2,:), ‘ZData’,XYZ(3,:));
drawnow
end

function XYZ = airplanepoints
%define points on the aircraft in local NED
coordinates
XYZ = […
0 0 0;%point1
-2 1 1;%point2
-2 1 -1;%point3
0 0 0;%point1
-2 -1 1;%point4
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
-2 -1 1;%point4
0 0 0;%point1
-2 1 -1;%point3
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
18 0 0;%point6
-2 1 -1;%point3
18 0 0;%point6
-2 -1 -1;%point5
18 0 0;%point6
-2 -1 1;%point4
18 0 0;%point6
-2 1 1;%point2
0 0 0;%point1
-5 0 0;%point7
-5 -10 0;%point8
-8 -10 0;%point9
-8 10 0;%point10
-5 10 0;%point11
-5 0 0;%point7
-15.5 0 0;%point12
-15.5 2 0;%point13
-17.5 2 0;%point14
-17.5 -2 0;%point15
-15.5 -2 0;%point16
-15.5 0 0;%point12
-18 0 0;%point6
-18 0 2;%point17
-15.5 0 0;%point15
-18 0 0;%point16
];
end

function XYZ=rotate(XYZ,phi,theta,psi)
%define rotation matrix
R_roll = [
1, 0, 0;
0, cos(phi), -sin(phi);
0, sin(phi), cos(phi)];
R_pitch = [
cos(theta), 0, sin(theta);
0, 1, 0;
-sin(theta), 0, cos(theta)];
R_yaw = [
cos(psi), -sin(psi), 0;
sin(psi), cos(psi), 0;
0, 0, 1];
R = R_roll*R_pitch*R_yaw;
%rotate vertices
XYZ =R*XYZ;
end

function XYZ = translate(XYZ, pn, pe, pd)
XYZ = XYZ + repmat([pn;pe;pd],1,size(XYZ,2));
end

end I’m having problems figuring out how to get some MATLAB code from a textbook to run. The code follows. The only original code statements are the first seven lines. I was trying to provide some basic data to get the code to draw a plane. I did have to add some "end" statements to the code, including the end at the bottom. I would like to get this code to draw an image and move it around a screen, but this code is supposed to do that. I need to learn how to get the code to run. I have a number of additional (or perhaps core) questions.
Is "fred" an appropriate handle reference?
Do I need to define a handle reference?
How do I call drawPlaneBody?
Can you help me to get this code (from a textbook) to work?
Thank you most sincerely.

pn = 20;
pe=0;
pd=0;
phi =0;
theta=0;
psi=0;
handle="fred";

function handle = drawPlaneBody(pn,pe,pd,phi,theta,psi,handle)
%define points on plane in local NED coordintates
NED = airplanepoints;
%rotate plane by (phi; theta; psi)
NED = rotate(NED, phi, theta, psi);
%translate plane to [pn; pe; pd]
NED = translate(NED, pn, pe, pd);
%transform vertices from NED to XYZ
R = […
0, 1, 0;…
1, 0 , 0;…
0, 0, -1;…
];
XYZ = R* NED;
%plot plane
if isempty(handle)
handle = plot3(XYZ(1,:),XYZ(2,:),XYZ(3,:),’Erasemode’, mode);
else
set(handle, ‘XData’, XYZ(1,:), ‘YData’,XYZ(2,:), ‘ZData’,XYZ(3,:));
drawnow
end

function XYZ = airplanepoints
%define points on the aircraft in local NED
coordinates
XYZ = […
0 0 0;%point1
-2 1 1;%point2
-2 1 -1;%point3
0 0 0;%point1
-2 -1 1;%point4
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
-2 -1 1;%point4
0 0 0;%point1
-2 1 -1;%point3
-2 -1 -1;%point5
0 0 0;%point1
-2 1 1;%point2
18 0 0;%point6
-2 1 -1;%point3
18 0 0;%point6
-2 -1 -1;%point5
18 0 0;%point6
-2 -1 1;%point4
18 0 0;%point6
-2 1 1;%point2
0 0 0;%point1
-5 0 0;%point7
-5 -10 0;%point8
-8 -10 0;%point9
-8 10 0;%point10
-5 10 0;%point11
-5 0 0;%point7
-15.5 0 0;%point12
-15.5 2 0;%point13
-17.5 2 0;%point14
-17.5 -2 0;%point15
-15.5 -2 0;%point16
-15.5 0 0;%point12
-18 0 0;%point6
-18 0 2;%point17
-15.5 0 0;%point15
-18 0 0;%point16
];
end

function XYZ=rotate(XYZ,phi,theta,psi)
%define rotation matrix
R_roll = [
1, 0, 0;
0, cos(phi), -sin(phi);
0, sin(phi), cos(phi)];
R_pitch = [
cos(theta), 0, sin(theta);
0, 1, 0;
-sin(theta), 0, cos(theta)];
R_yaw = [
cos(psi), -sin(psi), 0;
sin(psi), cos(psi), 0;
0, 0, 1];
R = R_roll*R_pitch*R_yaw;
%rotate vertices
XYZ =R*XYZ;
end

function XYZ = translate(XYZ, pn, pe, pd)
XYZ = XYZ + repmat([pn;pe;pd],1,size(XYZ,2));
end

end handle, matlab function, how to use functions MATLAB Answers — New Questions

​

Hi all,

I have an array of objects that should each have a property _serverDir_ set. Setting this property requires a little bit of effort and computation time (checking folders etc).

When I put this logic inside a "Dependent = True" property of my class, this logic is run on *every* object in my array of objects.

Is there a natural location to store the _serverDir_ information so that it only gets run *once* by the first object that requests this property, and each subsequent object re-uses this result?

Thanks,
Sven.Hi all,

I have an array of objects that should each have a property _serverDir_ set. Setting this property requires a little bit of effort and computation time (checking folders etc).

When I put this logic inside a "Dependent = True" property of my class, this logic is run on *every* object in my array of objects.

Is there a natural location to store the _serverDir_ information so that it only gets run *once* by the first object that requests this property, and each subsequent object re-uses this result?

Thanks,
Sven. Hi all,

I have an array of objects that should each have a property _serverDir_ set. Setting this property requires a little bit of effort and computation time (checking folders etc).

When I put this logic inside a "Dependent = True" property of my class, this logic is run on *every* object in my array of objects.

Is there a natural location to store the _serverDir_ information so that it only gets run *once* by the first object that requests this property, and each subsequent object re-uses this result?

Thanks,
Sven. static property, once MATLAB Answers — New Questions

​

% Define the data
dr_data = [2.5453, 0.042123; 5.0907, 0.075326; 7.636, 0.059506; 10.1813, 0.071553; 12.7267, 0.071365; 15.272, 0.067195; 17.8173, 0.046372; 20.3627, 0.043397; 22.908, 0.017179; 25.4533, -0.0063329; 27.9987, -0.030789; 30.544, -0.047569; 33.0893, -0.089512; 35.6347, -0.080675; 38.18, -0.089138; 40.7253, -0.1102; 43.2707, -0.12061; 45.816, -0.11857; 48.3613, -0.11955; 50.9067, -0.10803; 53.452, -0.10462; 55.9973, -0.099548; 58.5427, -0.097164; 61.088, -0.09994; 63.6333, -0.077017; 66.1787, -0.062839; 68.724, -0.048422; 71.2693, -0.03686; 73.8147, -0.01469; 76.3, 0];
dtheta_data = [2.5453, -0.099251; 5.0907, -0.16064; 7.636, -0.21858; 10.1813, -0.18965; 12.7267, -0.16996; 15.272, -0.18172; 17.8173, -0.15029; 20.3627, -0.12541; 22.908, -0.082786; 25.4533, -0.0071716; 27.9987, 0.03695; 30.544, 0.089002; 33.0893, 0.12873; 35.6347, 0.13092; 38.18, 0.13908; 40.7253, 0.17211; 43.2707, 0.16686; 45.816, 0.15826; 48.3613, 0.14872; 50.9067, 0.15295; 53.452, 0.12677; 55.9973, 0.10964; 58.5427, 0.10223; 61.088, 0.10951; 63.6333, 0.088493; 66.1787, 0.068903; 68.724, 0.054396; 71.2693, 0.035731; 73.8147, 0.030172; 76.3, 0];

% Define the function for the differential equations
function dydr = odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R)
dydr = zeros(4,1);
dydr(1) = y(2);
dydr(2) = -((lambda_init+1)*y(2)+1/r*(kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1)-kappa_init*r*y(3)*sin(theta_k_init)+16*lambda_init*r^2/(c^4*R^2))/(r*(lambda_init+1));
dydr(3) = y(4);
dydr(4) = -(y(4)+1/r*(kappa_init*r^2*cos(theta_k_init)-1)*y(3)+kappa_init*r*y(1)*sin(theta_k_init))/r;
end

% Boundary conditions
function res = bcfun(ya, yb, ya1, ya3, yb1, yb3)
res = [ya(1)-ya1; ya(3)-ya3; yb(1)-yb1; yb(3)-yb3];
end

% Define the function to compute residuals
function residuals = compute_residuals(params, dr_data, dtheta_data, rout, R_init)
lambda_init = params(1);
kappa_init = params(2);
theta_k_init = params(3);
ya1 = params(4); % Boundary condition parameter ya(1)
ya3 = params(5); % Boundary condition parameter ya(3)
yb1 = params(6); % Boundary condition parameter yb(1)
yb3 = params(7); % Boundary condition parameter
c = sqrt(4 – (rout/R_init)^2);

R_init = 2000; % Initial value of R
rout = 76.3; % Max value of r

% Adjust the number of points for interpolation
num_points = size(dr_data, 1);

solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, 0, ya3, 0]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Ensure that arrays have compatible sizes
dr_residuals = dr_data(:, 2) – dr_sol;
dtheta_residuals = dtheta_data(:, 2) – dtheta_sol;

residuals = [dr_residuals; dtheta_residuals];
end

% Initial guess for the parameters
params_init = [2.1, 0.03, 0.004, 0, 0, 0, 0]; % Initial guess for parameters including boundary conditions

% Bounds for parameters
lb = [1, 0.001, 0, -Inf, -Inf, -Inf, -Inf]; % Lower bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3
ub = [3, 0.5, pi/2, Inf, Inf, Inf, Inf]; % Upper bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3

% Perform optimization
params_opt = lsqnonlin(@(params) compute_residuals(params, dr_data, dtheta_data, rout, R_init), params_init, lb, ub);

% Extract optimized parameters
lambda_opt = params_opt(1);
kappa_opt = params_opt(2);
theta_k_opt = params_opt(3);
ya1_opt = params_opt(4);
ya3_opt = params_opt(5);
yb1_opt = params_opt(6);
yb3_opt = params_opt(7);

% Display optimized parameters
disp([‘Optimized lambda: ‘, num2str(lambda_opt)]);
disp([‘Optimized kappa: ‘, num2str(kappa_opt)]);
disp([‘Optimized theta_k: ‘, num2str(theta_k_opt)]);
disp([‘Optimized ya1: ‘, num2str(ya1_opt)]);
disp([‘Optimized ya3: ‘, num2str(ya3_opt)]);
disp([‘Optimized yb1: ‘, num2str(yb1_opt)]);
disp([‘Optimized yb3: ‘, num2str(yb3_opt)]);
% Plot the solutions using optimized parameters
lambda_init = lambda_opt;
kappa_init = kappa_opt;
theta_k_init = theta_k_opt;
ya1 = ya1_opt;
ya3 = ya3_opt;
yb1 = yb1_opt;
yb3 = yb3_opt;
c = sqrt(4 – (rout/R_init)^2);

num_points = size(dr_data, 1);
solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, yb1, ya3, yb3]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r, dr_sol, ‘b-‘, dr_data(:,1), dr_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

subplot(2,1,2);
plot(r, dtheta_sol, ‘b-‘, dtheta_data(:,1), dtheta_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

Now, I want to fit the simulated d_r(r) vs r and d_theta(r) vs r values with the above mentioned coupled differential eqns by usuing the fitting parameters lamda, kappa, theta_k. For the sake of good fitting one can use boundary conditions as parameter. However getting errors. Please help me to solve those errors and fitting those data.% Define the data
dr_data = [2.5453, 0.042123; 5.0907, 0.075326; 7.636, 0.059506; 10.1813, 0.071553; 12.7267, 0.071365; 15.272, 0.067195; 17.8173, 0.046372; 20.3627, 0.043397; 22.908, 0.017179; 25.4533, -0.0063329; 27.9987, -0.030789; 30.544, -0.047569; 33.0893, -0.089512; 35.6347, -0.080675; 38.18, -0.089138; 40.7253, -0.1102; 43.2707, -0.12061; 45.816, -0.11857; 48.3613, -0.11955; 50.9067, -0.10803; 53.452, -0.10462; 55.9973, -0.099548; 58.5427, -0.097164; 61.088, -0.09994; 63.6333, -0.077017; 66.1787, -0.062839; 68.724, -0.048422; 71.2693, -0.03686; 73.8147, -0.01469; 76.3, 0];
dtheta_data = [2.5453, -0.099251; 5.0907, -0.16064; 7.636, -0.21858; 10.1813, -0.18965; 12.7267, -0.16996; 15.272, -0.18172; 17.8173, -0.15029; 20.3627, -0.12541; 22.908, -0.082786; 25.4533, -0.0071716; 27.9987, 0.03695; 30.544, 0.089002; 33.0893, 0.12873; 35.6347, 0.13092; 38.18, 0.13908; 40.7253, 0.17211; 43.2707, 0.16686; 45.816, 0.15826; 48.3613, 0.14872; 50.9067, 0.15295; 53.452, 0.12677; 55.9973, 0.10964; 58.5427, 0.10223; 61.088, 0.10951; 63.6333, 0.088493; 66.1787, 0.068903; 68.724, 0.054396; 71.2693, 0.035731; 73.8147, 0.030172; 76.3, 0];

% Define the function for the differential equations
function dydr = odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R)
dydr = zeros(4,1);
dydr(1) = y(2);
dydr(2) = -((lambda_init+1)*y(2)+1/r*(kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1)-kappa_init*r*y(3)*sin(theta_k_init)+16*lambda_init*r^2/(c^4*R^2))/(r*(lambda_init+1));
dydr(3) = y(4);
dydr(4) = -(y(4)+1/r*(kappa_init*r^2*cos(theta_k_init)-1)*y(3)+kappa_init*r*y(1)*sin(theta_k_init))/r;
end

% Boundary conditions
function res = bcfun(ya, yb, ya1, ya3, yb1, yb3)
res = [ya(1)-ya1; ya(3)-ya3; yb(1)-yb1; yb(3)-yb3];
end

% Define the function to compute residuals
function residuals = compute_residuals(params, dr_data, dtheta_data, rout, R_init)
lambda_init = params(1);
kappa_init = params(2);
theta_k_init = params(3);
ya1 = params(4); % Boundary condition parameter ya(1)
ya3 = params(5); % Boundary condition parameter ya(3)
yb1 = params(6); % Boundary condition parameter yb(1)
yb3 = params(7); % Boundary condition parameter
c = sqrt(4 – (rout/R_init)^2);

R_init = 2000; % Initial value of R
rout = 76.3; % Max value of r

% Adjust the number of points for interpolation
num_points = size(dr_data, 1);

solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, 0, ya3, 0]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Ensure that arrays have compatible sizes
dr_residuals = dr_data(:, 2) – dr_sol;
dtheta_residuals = dtheta_data(:, 2) – dtheta_sol;

residuals = [dr_residuals; dtheta_residuals];
end

% Initial guess for the parameters
params_init = [2.1, 0.03, 0.004, 0, 0, 0, 0]; % Initial guess for parameters including boundary conditions

% Bounds for parameters
lb = [1, 0.001, 0, -Inf, -Inf, -Inf, -Inf]; % Lower bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3
ub = [3, 0.5, pi/2, Inf, Inf, Inf, Inf]; % Upper bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3

% Perform optimization
params_opt = lsqnonlin(@(params) compute_residuals(params, dr_data, dtheta_data, rout, R_init), params_init, lb, ub);

% Extract optimized parameters
lambda_opt = params_opt(1);
kappa_opt = params_opt(2);
theta_k_opt = params_opt(3);
ya1_opt = params_opt(4);
ya3_opt = params_opt(5);
yb1_opt = params_opt(6);
yb3_opt = params_opt(7);

% Display optimized parameters
disp([‘Optimized lambda: ‘, num2str(lambda_opt)]);
disp([‘Optimized kappa: ‘, num2str(kappa_opt)]);
disp([‘Optimized theta_k: ‘, num2str(theta_k_opt)]);
disp([‘Optimized ya1: ‘, num2str(ya1_opt)]);
disp([‘Optimized ya3: ‘, num2str(ya3_opt)]);
disp([‘Optimized yb1: ‘, num2str(yb1_opt)]);
disp([‘Optimized yb3: ‘, num2str(yb3_opt)]);
% Plot the solutions using optimized parameters
lambda_init = lambda_opt;
kappa_init = kappa_opt;
theta_k_init = theta_k_opt;
ya1 = ya1_opt;
ya3 = ya3_opt;
yb1 = yb1_opt;
yb3 = yb3_opt;
c = sqrt(4 – (rout/R_init)^2);

num_points = size(dr_data, 1);
solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, yb1, ya3, yb3]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r, dr_sol, ‘b-‘, dr_data(:,1), dr_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

subplot(2,1,2);
plot(r, dtheta_sol, ‘b-‘, dtheta_data(:,1), dtheta_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

Now, I want to fit the simulated d_r(r) vs r and d_theta(r) vs r values with the above mentioned coupled differential eqns by usuing the fitting parameters lamda, kappa, theta_k. For the sake of good fitting one can use boundary conditions as parameter. However getting errors. Please help me to solve those errors and fitting those data. % Define the data
dr_data = [2.5453, 0.042123; 5.0907, 0.075326; 7.636, 0.059506; 10.1813, 0.071553; 12.7267, 0.071365; 15.272, 0.067195; 17.8173, 0.046372; 20.3627, 0.043397; 22.908, 0.017179; 25.4533, -0.0063329; 27.9987, -0.030789; 30.544, -0.047569; 33.0893, -0.089512; 35.6347, -0.080675; 38.18, -0.089138; 40.7253, -0.1102; 43.2707, -0.12061; 45.816, -0.11857; 48.3613, -0.11955; 50.9067, -0.10803; 53.452, -0.10462; 55.9973, -0.099548; 58.5427, -0.097164; 61.088, -0.09994; 63.6333, -0.077017; 66.1787, -0.062839; 68.724, -0.048422; 71.2693, -0.03686; 73.8147, -0.01469; 76.3, 0];
dtheta_data = [2.5453, -0.099251; 5.0907, -0.16064; 7.636, -0.21858; 10.1813, -0.18965; 12.7267, -0.16996; 15.272, -0.18172; 17.8173, -0.15029; 20.3627, -0.12541; 22.908, -0.082786; 25.4533, -0.0071716; 27.9987, 0.03695; 30.544, 0.089002; 33.0893, 0.12873; 35.6347, 0.13092; 38.18, 0.13908; 40.7253, 0.17211; 43.2707, 0.16686; 45.816, 0.15826; 48.3613, 0.14872; 50.9067, 0.15295; 53.452, 0.12677; 55.9973, 0.10964; 58.5427, 0.10223; 61.088, 0.10951; 63.6333, 0.088493; 66.1787, 0.068903; 68.724, 0.054396; 71.2693, 0.035731; 73.8147, 0.030172; 76.3, 0];

% Define the function for the differential equations
function dydr = odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R)
dydr = zeros(4,1);
dydr(1) = y(2);
dydr(2) = -((lambda_init+1)*y(2)+1/r*(kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1)-kappa_init*r*y(3)*sin(theta_k_init)+16*lambda_init*r^2/(c^4*R^2))/(r*(lambda_init+1));
dydr(3) = y(4);
dydr(4) = -(y(4)+1/r*(kappa_init*r^2*cos(theta_k_init)-1)*y(3)+kappa_init*r*y(1)*sin(theta_k_init))/r;
end

% Boundary conditions
function res = bcfun(ya, yb, ya1, ya3, yb1, yb3)
res = [ya(1)-ya1; ya(3)-ya3; yb(1)-yb1; yb(3)-yb3];
end

% Define the function to compute residuals
function residuals = compute_residuals(params, dr_data, dtheta_data, rout, R_init)
lambda_init = params(1);
kappa_init = params(2);
theta_k_init = params(3);
ya1 = params(4); % Boundary condition parameter ya(1)
ya3 = params(5); % Boundary condition parameter ya(3)
yb1 = params(6); % Boundary condition parameter yb(1)
yb3 = params(7); % Boundary condition parameter
c = sqrt(4 – (rout/R_init)^2);

R_init = 2000; % Initial value of R
rout = 76.3; % Max value of r

% Adjust the number of points for interpolation
num_points = size(dr_data, 1);

solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, 0, ya3, 0]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Ensure that arrays have compatible sizes
dr_residuals = dr_data(:, 2) – dr_sol;
dtheta_residuals = dtheta_data(:, 2) – dtheta_sol;

residuals = [dr_residuals; dtheta_residuals];
end

% Initial guess for the parameters
params_init = [2.1, 0.03, 0.004, 0, 0, 0, 0]; % Initial guess for parameters including boundary conditions

% Bounds for parameters
lb = [1, 0.001, 0, -Inf, -Inf, -Inf, -Inf]; % Lower bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3
ub = [3, 0.5, pi/2, Inf, Inf, Inf, Inf]; % Upper bounds for lambda, kappa, theta_k, ya1, ya3, yb1, yb3

% Perform optimization
params_opt = lsqnonlin(@(params) compute_residuals(params, dr_data, dtheta_data, rout, R_init), params_init, lb, ub);

% Extract optimized parameters
lambda_opt = params_opt(1);
kappa_opt = params_opt(2);
theta_k_opt = params_opt(3);
ya1_opt = params_opt(4);
ya3_opt = params_opt(5);
yb1_opt = params_opt(6);
yb3_opt = params_opt(7);

% Display optimized parameters
disp([‘Optimized lambda: ‘, num2str(lambda_opt)]);
disp([‘Optimized kappa: ‘, num2str(kappa_opt)]);
disp([‘Optimized theta_k: ‘, num2str(theta_k_opt)]);
disp([‘Optimized ya1: ‘, num2str(ya1_opt)]);
disp([‘Optimized ya3: ‘, num2str(ya3_opt)]);
disp([‘Optimized yb1: ‘, num2str(yb1_opt)]);
disp([‘Optimized yb3: ‘, num2str(yb3_opt)]);
% Plot the solutions using optimized parameters
lambda_init = lambda_opt;
kappa_init = kappa_opt;
theta_k_init = theta_k_opt;
ya1 = ya1_opt;
ya3 = ya3_opt;
yb1 = yb1_opt;
yb3 = yb3_opt;
c = sqrt(4 – (rout/R_init)^2);

num_points = size(dr_data, 1);
solinit = bvpinit(linspace(0.0001, rout, num_points), [ya1, yb1, ya3, yb3]);
sol = bvp4c(@(r, y) odefun(r, y, lambda_init, kappa_init, theta_k_init, c, R_init), @(ya, yb) bcfun(ya, yb, ya1, ya3, yb1, yb3), solinit);
r = linspace(0.0001, rout, num_points);
y = deval(sol, r);
dr_sol = y(1,:);
dtheta_sol = y(3,:);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r, dr_sol, ‘b-‘, dr_data(:,1), dr_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

subplot(2,1,2);
plot(r, dtheta_sol, ‘b-‘, dtheta_data(:,1), dtheta_data(:,2), ‘ro’);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);
legend(‘Fitted Solution’, ‘Data’);

Now, I want to fit the simulated d_r(r) vs r and d_theta(r) vs r values with the above mentioned coupled differential eqns by usuing the fitting parameters lamda, kappa, theta_k. For the sake of good fitting one can use boundary conditions as parameter. However getting errors. Please help me to solve those errors and fitting those data. curve fitting MATLAB Answers — New Questions

​

Matlab + yalmip toolbox, when calling cplex or mosek to solve the optimization problem, the result is always wrong: Warning: Solver not applicable (mosek), Warning: Solver not applicable (cplex), I think my software is installed correctly, Now I have several reasons for doubt:
1. Too many constraints, the scale of problem solving is too large
2. The software version does not match?(matlab2014b+mosek 8.0.0.60/cplex 12.6.3)
3. There are some mistakes in the code or there is no feasible solution (I think it is unlikely)
Please help me see what to do，thank you !

Code for solving part：
ops=sdpsettings
ops = sdpsettings(‘verbose’,2,’solver’,’mosek’,’fmincon.MaxFunEvals’,30000);
sol =solvesdp(Constraint,f,ops,’full’);
if sol.problem== 0
value(f)
else
disp(‘求解过程中出错’);

operation result：
ops =

solver: ”
verbose: 1
debug: 0
usex0: 0
warning: 1
cachesolvers: 0
showprogress: 0
saveduals: 1
removeequalities: 0
savesolveroutput: 0
savesolverinput: 0
saveyalmipmodel: 0
convertconvexquad: 1
assertgpnonnegativity: 1
thisisnotagp: 0
radius: Inf
relax: 0
dualize: 0
savedebug: 0
expand: 1
allowmilp: 1
allownonconvex: 1
shift: 0
dimacs: 0
beeponproblem: [-5 -4 -3 -2 -1]
bisection: [1×1 struct]
bilevel: [1×1 struct]
bmibnb: [1×1 struct]
bnb: [1×1 struct]
cutsdp: [1×1 struct]
kkt: [1×1 struct]
moment: [1×1 struct]
mp: [1×1 struct]
mpcvx: [1×1 struct]
plot: [1×1 struct]
robust: [1×1 struct]
sos: [1×1 struct]
refiner: [1×1 struct]
baron: []
bintprog: [1×1 struct]
bonmin: []
cdcs: [1×1 struct]
cdd: [1×1 struct]
cbc: [1×1 struct]
clp: [1×1 struct]
cplex: [1×1 struct]
csdp: [1×1 struct]
dsdp: [1×1 struct]
ecos: []
filtersd: [1×1 struct]
fmincon: [1×1 struct]
fminsearch: [1×1 struct]
frlib: [1×1 struct]
glpk: [1×1 struct]
gurobi: [1×1 struct]
ipopt: [1×1 struct]
intlinprog: [1×1 optim.options.Intlinprog]
knitro: [1×1 struct]
linprog: [1×1 struct]
lmilab: [1×1 struct]
lmirank: [1×1 struct]
logdetppa: [1×1 struct]
lpsolve: [1×1 struct]
lsqnonneg: [1×1 struct]
lsqlin: [1×1 struct]
kypd: [1×1 struct]
nag: [1×1 struct]
mosek: [1×1 struct]
nomad: []
ooqp: []
penbmi: [1×1 struct]
penlab: []
pensdp: [1×1 struct]
pop: [1×1 struct]
qpoases: []
osqp: []
qsopt: [1×1 struct]
quadprog: [1×1 struct]
quadprogbb: [1×1 struct]
scip: []
scs: [1×1 struct]
sdpa: [1×1 struct]
sdplr: [1×1 struct]
sdpt3: [1×1 struct]
sdpnal: [1×1 struct]
sedumi: [1×1 struct]
sparsepop: [1×1 struct]
sparsecolo: [1×1 struct]
vsdp: [1×1 struct]
xpress: []

Warning: Solver not applicable (mosek)
求解过程中出错
>>Matlab + yalmip toolbox, when calling cplex or mosek to solve the optimization problem, the result is always wrong: Warning: Solver not applicable (mosek), Warning: Solver not applicable (cplex), I think my software is installed correctly, Now I have several reasons for doubt:
1. Too many constraints, the scale of problem solving is too large
2. The software version does not match?(matlab2014b+mosek 8.0.0.60/cplex 12.6.3)
3. There are some mistakes in the code or there is no feasible solution (I think it is unlikely)
Please help me see what to do，thank you !

Code for solving part：
ops=sdpsettings
ops = sdpsettings(‘verbose’,2,’solver’,’mosek’,’fmincon.MaxFunEvals’,30000);
sol =solvesdp(Constraint,f,ops,’full’);
if sol.problem== 0
value(f)
else
disp(‘求解过程中出错’);

operation result：
ops =

solver: ”
verbose: 1
debug: 0
usex0: 0
warning: 1
cachesolvers: 0
showprogress: 0
saveduals: 1
removeequalities: 0
savesolveroutput: 0
savesolverinput: 0
saveyalmipmodel: 0
convertconvexquad: 1
assertgpnonnegativity: 1
thisisnotagp: 0
radius: Inf
relax: 0
dualize: 0
savedebug: 0
expand: 1
allowmilp: 1
allownonconvex: 1
shift: 0
dimacs: 0
beeponproblem: [-5 -4 -3 -2 -1]
bisection: [1×1 struct]
bilevel: [1×1 struct]
bmibnb: [1×1 struct]
bnb: [1×1 struct]
cutsdp: [1×1 struct]
kkt: [1×1 struct]
moment: [1×1 struct]
mp: [1×1 struct]
mpcvx: [1×1 struct]
plot: [1×1 struct]
robust: [1×1 struct]
sos: [1×1 struct]
refiner: [1×1 struct]
baron: []
bintprog: [1×1 struct]
bonmin: []
cdcs: [1×1 struct]
cdd: [1×1 struct]
cbc: [1×1 struct]
clp: [1×1 struct]
cplex: [1×1 struct]
csdp: [1×1 struct]
dsdp: [1×1 struct]
ecos: []
filtersd: [1×1 struct]
fmincon: [1×1 struct]
fminsearch: [1×1 struct]
frlib: [1×1 struct]
glpk: [1×1 struct]
gurobi: [1×1 struct]
ipopt: [1×1 struct]
intlinprog: [1×1 optim.options.Intlinprog]
knitro: [1×1 struct]
linprog: [1×1 struct]
lmilab: [1×1 struct]
lmirank: [1×1 struct]
logdetppa: [1×1 struct]
lpsolve: [1×1 struct]
lsqnonneg: [1×1 struct]
lsqlin: [1×1 struct]
kypd: [1×1 struct]
nag: [1×1 struct]
mosek: [1×1 struct]
nomad: []
ooqp: []
penbmi: [1×1 struct]
penlab: []
pensdp: [1×1 struct]
pop: [1×1 struct]
qpoases: []
osqp: []
qsopt: [1×1 struct]
quadprog: [1×1 struct]
quadprogbb: [1×1 struct]
scip: []
scs: [1×1 struct]
sdpa: [1×1 struct]
sdplr: [1×1 struct]
sdpt3: [1×1 struct]
sdpnal: [1×1 struct]
sedumi: [1×1 struct]
sparsepop: [1×1 struct]
sparsecolo: [1×1 struct]
vsdp: [1×1 struct]
xpress: []

Warning: Solver not applicable (mosek)
求解过程中出错
>> Matlab + yalmip toolbox, when calling cplex or mosek to solve the optimization problem, the result is always wrong: Warning: Solver not applicable (mosek), Warning: Solver not applicable (cplex), I think my software is installed correctly, Now I have several reasons for doubt:
1. Too many constraints, the scale of problem solving is too large
2. The software version does not match?(matlab2014b+mosek 8.0.0.60/cplex 12.6.3)
3. There are some mistakes in the code or there is no feasible solution (I think it is unlikely)
Please help me see what to do，thank you !

Code for solving part：
ops=sdpsettings
ops = sdpsettings(‘verbose’,2,’solver’,’mosek’,’fmincon.MaxFunEvals’,30000);
sol =solvesdp(Constraint,f,ops,’full’);
if sol.problem== 0
value(f)
else
disp(‘求解过程中出错’);

operation result：
ops =

solver: ”
verbose: 1
debug: 0
usex0: 0
warning: 1
cachesolvers: 0
showprogress: 0
saveduals: 1
removeequalities: 0
savesolveroutput: 0
savesolverinput: 0
saveyalmipmodel: 0
convertconvexquad: 1
assertgpnonnegativity: 1
thisisnotagp: 0
radius: Inf
relax: 0
dualize: 0
savedebug: 0
expand: 1
allowmilp: 1
allownonconvex: 1
shift: 0
dimacs: 0
beeponproblem: [-5 -4 -3 -2 -1]
bisection: [1×1 struct]
bilevel: [1×1 struct]
bmibnb: [1×1 struct]
bnb: [1×1 struct]
cutsdp: [1×1 struct]
kkt: [1×1 struct]
moment: [1×1 struct]
mp: [1×1 struct]
mpcvx: [1×1 struct]
plot: [1×1 struct]
robust: [1×1 struct]
sos: [1×1 struct]
refiner: [1×1 struct]
baron: []
bintprog: [1×1 struct]
bonmin: []
cdcs: [1×1 struct]
cdd: [1×1 struct]
cbc: [1×1 struct]
clp: [1×1 struct]
cplex: [1×1 struct]
csdp: [1×1 struct]
dsdp: [1×1 struct]
ecos: []
filtersd: [1×1 struct]
fmincon: [1×1 struct]
fminsearch: [1×1 struct]
frlib: [1×1 struct]
glpk: [1×1 struct]
gurobi: [1×1 struct]
ipopt: [1×1 struct]
intlinprog: [1×1 optim.options.Intlinprog]
knitro: [1×1 struct]
linprog: [1×1 struct]
lmilab: [1×1 struct]
lmirank: [1×1 struct]
logdetppa: [1×1 struct]
lpsolve: [1×1 struct]
lsqnonneg: [1×1 struct]
lsqlin: [1×1 struct]
kypd: [1×1 struct]
nag: [1×1 struct]
mosek: [1×1 struct]
nomad: []
ooqp: []
penbmi: [1×1 struct]
penlab: []
pensdp: [1×1 struct]
pop: [1×1 struct]
qpoases: []
osqp: []
qsopt: [1×1 struct]
quadprog: [1×1 struct]
quadprogbb: [1×1 struct]
scip: []
scs: [1×1 struct]
sdpa: [1×1 struct]
sdplr: [1×1 struct]
sdpt3: [1×1 struct]
sdpnal: [1×1 struct]
sedumi: [1×1 struct]
sparsepop: [1×1 struct]
sparsecolo: [1×1 struct]
vsdp: [1×1 struct]
xpress: []

Warning: Solver not applicable (mosek)
求解过程中出错
>> optimization；matlab+mosek；optimization MATLAB Answers — New Questions

​