I am using classification learner app svm generated code for the classification of multiclass dataset.
Now I wanted to test with the unseen dataset for this I am using yfit.
Now I got the predicted labels for the test data. How to find the test accuracy and from the predicted laebls?
Can someone please help me in this.I am using classification learner app svm generated code for the classification of multiclass dataset.
Now I wanted to test with the unseen dataset for this I am using yfit.
Now I got the predicted labels for the test data. How to find the test accuracy and from the predicted laebls?
Can someone please help me in this. I am using classification learner app svm generated code for the classification of multiclass dataset.
Now I wanted to test with the unseen dataset for this I am using yfit.
Now I got the predicted labels for the test data. How to find the test accuracy and from the predicted laebls?
Can someone please help me in this. calculate test data accuracy MATLAB Answers — New Questions

​

Hey all, I am trying to deploy in a ROS2 device from Simulink. I keep facing this error. FYI, the device being deployed in is Intel Nuc. It is being deployed through Wi-Fi. I also deployed in another ROS2 machine without any error therefore the Simulink model has no error by design. Please don’t hesitate to ask for further information. Glad to provide to solve the issue.Hey all, I am trying to deploy in a ROS2 device from Simulink. I keep facing this error. FYI, the device being deployed in is Intel Nuc. It is being deployed through Wi-Fi. I also deployed in another ROS2 machine without any error therefore the Simulink model has no error by design. Please don’t hesitate to ask for further information. Glad to provide to solve the issue. Hey all, I am trying to deploy in a ROS2 device from Simulink. I keep facing this error. FYI, the device being deployed in is Intel Nuc. It is being deployed through Wi-Fi. I also deployed in another ROS2 machine without any error therefore the Simulink model has no error by design. Please don’t hesitate to ask for further information. Glad to provide to solve the issue. ros2, simulink MATLAB Answers — New Questions

​

Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated!Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated! Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated! definite integration, symbolic toolbox, simplifying MATLAB Answers — New Questions

​

$$
begin{aligned}
& b_{0}^{l}=a_{0}^{l} A_{00}^{l}+sum_{n=a_{n}}^{infty} a_{n}^{l} A_{0} n^{ell}+Z_{0}^{l} \
& b_{m}^{l}=a_{0}^{l} A_{m 0}^{l}+sum_{n=1}^{infty} a_{n}^{l} A_{m n}^{l}+Z_{m}^{l} \
& a_{0}^{l}=b_{0}^{l} B_{00}^{l}+sum_{m=1}^{infty} b_{m}{ }^{l} B_{0 m}^{l}+c_{0}^{l} C_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{0 m}^{l}+Y_{0}^{l} \
& a_{n}^{l}=b_{0}^{l} B_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} B_{n m}^{l}+c_{0}^{l} C_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{n m}^{l}+Y_{n}^{l}
end{aligned}
$$
and:

$$
begin{aligned}
& c_{0}^{l}=d_{0}^{l} D_{00}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{0 n}^{l}+X_{0}^{l} \
& c_{m}^{l}=d_{0}^{l} D_{m 0}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{m n}^{ell}+X_{m}^{ell} \
& d_{0}^{ell} = b_{0}^{l} E_{00}^{ell}+sum_{m=1}^{infty} b_{m}^{ell} E_{0 m}^{l}+c_{0}^{l} F_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{0 m}^{l}+W_{0}^{l} \
& d_{n}^{l}=b_{0}^{l} E_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} E_{n m}^{l}+c_{0}^{l} F_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{n m}^{l}+W_{n}^{l}
end{aligned}
$$
Unknowns are:-

$$
begin{gathered}
left(a_{0}^{l}, a_{n}^{l}right) ;left(b_{0}^{l}, b_{n}^{l}right),left(c_{0}^{l}, c_{n}^{l}right) and \
left(d_{0}^{l}, d_{n}^{l}right) .
end{gathered}
$$
The above system of equations which is linear one is the latex code for these equations and i need to solve it for these unknowns. I am confused that how i can solved this system. how i can write these equations in matrix form to solved it for the unknowns? Help me.$$
begin{aligned}
& b_{0}^{l}=a_{0}^{l} A_{00}^{l}+sum_{n=a_{n}}^{infty} a_{n}^{l} A_{0} n^{ell}+Z_{0}^{l} \
& b_{m}^{l}=a_{0}^{l} A_{m 0}^{l}+sum_{n=1}^{infty} a_{n}^{l} A_{m n}^{l}+Z_{m}^{l} \
& a_{0}^{l}=b_{0}^{l} B_{00}^{l}+sum_{m=1}^{infty} b_{m}{ }^{l} B_{0 m}^{l}+c_{0}^{l} C_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{0 m}^{l}+Y_{0}^{l} \
& a_{n}^{l}=b_{0}^{l} B_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} B_{n m}^{l}+c_{0}^{l} C_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{n m}^{l}+Y_{n}^{l}
end{aligned}
$$
and:

$$
begin{aligned}
& c_{0}^{l}=d_{0}^{l} D_{00}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{0 n}^{l}+X_{0}^{l} \
& c_{m}^{l}=d_{0}^{l} D_{m 0}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{m n}^{ell}+X_{m}^{ell} \
& d_{0}^{ell} = b_{0}^{l} E_{00}^{ell}+sum_{m=1}^{infty} b_{m}^{ell} E_{0 m}^{l}+c_{0}^{l} F_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{0 m}^{l}+W_{0}^{l} \
& d_{n}^{l}=b_{0}^{l} E_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} E_{n m}^{l}+c_{0}^{l} F_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{n m}^{l}+W_{n}^{l}
end{aligned}
$$
Unknowns are:-

$$
begin{gathered}
left(a_{0}^{l}, a_{n}^{l}right) ;left(b_{0}^{l}, b_{n}^{l}right),left(c_{0}^{l}, c_{n}^{l}right) and \
left(d_{0}^{l}, d_{n}^{l}right) .
end{gathered}
$$
The above system of equations which is linear one is the latex code for these equations and i need to solve it for these unknowns. I am confused that how i can solved this system. how i can write these equations in matrix form to solved it for the unknowns? Help me. $$
begin{aligned}
& b_{0}^{l}=a_{0}^{l} A_{00}^{l}+sum_{n=a_{n}}^{infty} a_{n}^{l} A_{0} n^{ell}+Z_{0}^{l} \
& b_{m}^{l}=a_{0}^{l} A_{m 0}^{l}+sum_{n=1}^{infty} a_{n}^{l} A_{m n}^{l}+Z_{m}^{l} \
& a_{0}^{l}=b_{0}^{l} B_{00}^{l}+sum_{m=1}^{infty} b_{m}{ }^{l} B_{0 m}^{l}+c_{0}^{l} C_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{0 m}^{l}+Y_{0}^{l} \
& a_{n}^{l}=b_{0}^{l} B_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} B_{n m}^{l}+c_{0}^{l} C_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} C_{n m}^{l}+Y_{n}^{l}
end{aligned}
$$
and:

$$
begin{aligned}
& c_{0}^{l}=d_{0}^{l} D_{00}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{0 n}^{l}+X_{0}^{l} \
& c_{m}^{l}=d_{0}^{l} D_{m 0}^{ell}+sum_{n=1}^{infty} d_{n}^{l} D_{m n}^{ell}+X_{m}^{ell} \
& d_{0}^{ell} = b_{0}^{l} E_{00}^{ell}+sum_{m=1}^{infty} b_{m}^{ell} E_{0 m}^{l}+c_{0}^{l} F_{00}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{0 m}^{l}+W_{0}^{l} \
& d_{n}^{l}=b_{0}^{l} E_{n 0}^{l}+sum_{m=1}^{infty} b_{m}^{l} E_{n m}^{l}+c_{0}^{l} F_{n 0}^{l}+sum_{m=1}^{infty} c_{m}^{l} F_{n m}^{l}+W_{n}^{l}
end{aligned}
$$
Unknowns are:-

$$
begin{gathered}
left(a_{0}^{l}, a_{n}^{l}right) ;left(b_{0}^{l}, b_{n}^{l}right),left(c_{0}^{l}, c_{n}^{l}right) and \
left(d_{0}^{l}, d_{n}^{l}right) .
end{gathered}
$$
The above system of equations which is linear one is the latex code for these equations and i need to solve it for these unknowns. I am confused that how i can solved this system. how i can write these equations in matrix form to solved it for the unknowns? Help me. system of equations MATLAB Answers — New Questions

​

Rotation axis normally defined axis around Z,I want to rotate my modal around x and y axis how can i change rotation axis of the revolute joint?

ThanksRotation axis normally defined axis around Z,I want to rotate my modal around x and y axis how can i change rotation axis of the revolute joint?

Thanks Rotation axis normally defined axis around Z,I want to rotate my modal around x and y axis how can i change rotation axis of the revolute joint?

Thanks rotation, axis, simmechanics MATLAB Answers — New Questions

​

I am trying to create some graphs, and I am struggling to put the legend where I want it in my graph. I would like my graph to look like this:

However, the code that i have wrtiien:
%%% plot mean and SD:
s = sprintf(‘[%c]’, char(176)); % degree angle symbol
figure
title(‘Mean and SD’)
ax1=subplot(4,1,1);
fontsize=get(ax1, ‘FontSize’);
title(‘Start’)
hold on
[m,n] = size(DATA1start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1start’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2start’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3start’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1start’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2start’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3start’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

% Create fake points for the legend
hFakeDATA1 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#228b22", ‘MarkerEdgeColor’, "#228b22", ‘MarkerSize’, 5);
hFakeDATA2 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#395dc7", ‘MarkerEdgeColor’, "#395dc7", ‘MarkerSize’, 5);
hFakeDATA3 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#f88f09", ‘MarkerEdgeColor’, "#f88f09", ‘MarkerSize’, 5);

% Create fake entry for the shaded region
hShadedRegion = plot(NaN, NaN, ‘s’, ‘MarkerFaceColor’, [0.7 0.7 0.7], ‘MarkerEdgeColor’, ‘none’, ‘MarkerSize’, 8);
% Create custom legend with the fake points
legend([hFakeDATA1, hFakeDATA2, hFakeDATA3, hShadedRegion], …
{‘DATA1’, ‘DATA2’, ‘DATA3’, ‘Main effect of group’}, ‘Location’, ‘bestoutside’);

subplot(4,1,2)
title(‘Middle’)
hold on
[m,n] = size(DATA1middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1middle’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2middle’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3middle’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1middle’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2middle’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3middle’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

subplot(4,1,3)
title(‘End’)
hold on
[m,n] = size(DATA1last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1last’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2last’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3last’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1last’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2last’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3last’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])
Provides me with the graph shown here. I can’t seem to put the legend in the correct place ( I have moved the block of code around to create the legend before and after each graph, but with no success). I would like the legend to be outside of all the tiles! Any advice would be much appreciated :)I am trying to create some graphs, and I am struggling to put the legend where I want it in my graph. I would like my graph to look like this:

However, the code that i have wrtiien:
%%% plot mean and SD:
s = sprintf(‘[%c]’, char(176)); % degree angle symbol
figure
title(‘Mean and SD’)
ax1=subplot(4,1,1);
fontsize=get(ax1, ‘FontSize’);
title(‘Start’)
hold on
[m,n] = size(DATA1start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1start’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2start’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3start’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1start’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2start’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3start’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

% Create fake points for the legend
hFakeDATA1 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#228b22", ‘MarkerEdgeColor’, "#228b22", ‘MarkerSize’, 5);
hFakeDATA2 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#395dc7", ‘MarkerEdgeColor’, "#395dc7", ‘MarkerSize’, 5);
hFakeDATA3 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#f88f09", ‘MarkerEdgeColor’, "#f88f09", ‘MarkerSize’, 5);

% Create fake entry for the shaded region
hShadedRegion = plot(NaN, NaN, ‘s’, ‘MarkerFaceColor’, [0.7 0.7 0.7], ‘MarkerEdgeColor’, ‘none’, ‘MarkerSize’, 8);
% Create custom legend with the fake points
legend([hFakeDATA1, hFakeDATA2, hFakeDATA3, hShadedRegion], …
{‘DATA1’, ‘DATA2’, ‘DATA3’, ‘Main effect of group’}, ‘Location’, ‘bestoutside’);

subplot(4,1,2)
title(‘Middle’)
hold on
[m,n] = size(DATA1middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1middle’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2middle’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3middle’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1middle’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2middle’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3middle’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

subplot(4,1,3)
title(‘End’)
hold on
[m,n] = size(DATA1last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1last’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2last’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3last’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1last’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2last’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3last’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])
Provides me with the graph shown here. I can’t seem to put the legend in the correct place ( I have moved the block of code around to create the legend before and after each graph, but with no success). I would like the legend to be outside of all the tiles! Any advice would be much appreciated  I am trying to create some graphs, and I am struggling to put the legend where I want it in my graph. I would like my graph to look like this:

However, the code that i have wrtiien:
%%% plot mean and SD:
s = sprintf(‘[%c]’, char(176)); % degree angle symbol
figure
title(‘Mean and SD’)
ax1=subplot(4,1,1);
fontsize=get(ax1, ‘FontSize’);
title(‘Start’)
hold on
[m,n] = size(DATA1start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1start’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2start’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3start);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3start’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1start’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2start’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3start’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

% Create fake points for the legend
hFakeDATA1 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#228b22", ‘MarkerEdgeColor’, "#228b22", ‘MarkerSize’, 5);
hFakeDATA2 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#395dc7", ‘MarkerEdgeColor’, "#395dc7", ‘MarkerSize’, 5);
hFakeDATA3 = plot(NaN, NaN, ‘o’, ‘MarkerFaceColor’, "#f88f09", ‘MarkerEdgeColor’, "#f88f09", ‘MarkerSize’, 5);

% Create fake entry for the shaded region
hShadedRegion = plot(NaN, NaN, ‘s’, ‘MarkerFaceColor’, [0.7 0.7 0.7], ‘MarkerEdgeColor’, ‘none’, ‘MarkerSize’, 8);
% Create custom legend with the fake points
legend([hFakeDATA1, hFakeDATA2, hFakeDATA3, hShadedRegion], …
{‘DATA1’, ‘DATA2’, ‘DATA3’, ‘Main effect of group’}, ‘Location’, ‘bestoutside’);

subplot(4,1,2)
title(‘Middle’)
hold on
[m,n] = size(DATA1middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1middle’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2middle’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3middle);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3middle’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1middle’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2middle’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3middle’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])

subplot(4,1,3)
title(‘End’)
hold on
[m,n] = size(DATA1last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA1last’,2,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
[m,n] = size(DATA2last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA2last’,2,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)%stdshade(DATA2start’,’0.3′,’b’)
hold on
[m,n] = size(DATA3last);
xaxis=repmat(1:101, n, 1);
scatter(xaxis,DATA3last’,2,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09", ‘MarkerFaceAlpha’,.3,’MarkerEdgeAlpha’,.3)
hold on
scatter(1:101,mean(DATA1last’,’omitnan’),10,’MarkerFaceColor’,"#228b22",’MarkerEdgeColor’,"#228b22")
hold on
scatter(1:101,mean(DATA2last’,’omitnan’),10,’MarkerFaceColor’,"#395dc7",’MarkerEdgeColor’,"#395dc7")
hold on
scatter(1:101,mean(DATA3last’,’omitnan’),10,’MarkerFaceColor’,"#f88f09",’MarkerEdgeColor’,"#f88f09")

ylabel([‘Angular Difference’, s])
xlabel([‘Percentage of gait cycle (%)’])
xlim([0 100])
ylim([0 60])
Provides me with the graph shown here. I can’t seem to put the legend in the correct place ( I have moved the block of code around to create the legend before and after each graph, but with no success). I would like the legend to be outside of all the tiles! Any advice would be much appreciated  scatter, legend, tiledlayout, location, bestoutside MATLAB Answers — New Questions

​

Hi there,
I am currently working on a Matlab code for my task (optimization task), and I tried two different methods;

Method A: the fmincon was used to minimize the objective function in which different algorithms, such as interior-point, sqp, sqp-legacy, interior-point, and active-set, were applied.
Method B: Nonlinear least squares optimization was combined with three algorithms, levenberg-marquardt, and trust-region-reflective.

The best results I got now are (from the Nonlinear least squares optimization + ‘interior-point’):
RMSE for X, Y, Z Direction(mm) : [1.18, 0.16, 1.33] mm; however, I want to reduce it as far as it is possible.
@ A quick guide for the code, and how it works.
1. I do have 3D data sets, and I used some mathematical methods to convert these 3D data into 2D data (Step 3).
2. The goal is to use some inverse method to get the same 3D datasets; therefore, after defining the objective function, I applied different optimization methods to address this task.

Any assistance or alternative approaches would be greatly appreciated.
Thank you in advance!
% @ Payam Samadi (2025.3.15) NLSP (Nonlinear least squares optimization)

% In step 3, the 2D projection data was extracted from the 3D data at
% different projections.

% In step4, the objective function is defined.

% In step 5, the Nonlinear least squares optimization is used to minimize
% the objective function.

% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Note: It is important to carefully consider the initial guesses for
% target locations, as well as the lower bounds (lb) and upper bounds (ub).

tic;
clc;
clear;
close all;

%% Step 1: Load xls file (3D Tumor position)

Load_Data = xlsread(‘Sample 1.xlsx’); % Data include 12 (sec)
% Load_Data = xlsread(‘Sample 2.xlsx’); % Data include 60 (sec)

Time = Load_Data(:,1); % Time (s)
xt=Load_Data(:,2); % xt for targets
yt=Load_Data(:,3); % yt for targets
zt=Load_Data(:,4); % zt for targets

true_T=[xt,yt,zt]; % target locations
[~,numT]=size(true_T); % number of targets

%% Step 2: Define imaging system parameters
SAD = 100; % source-axis distance (cm)
SID = 150; % source-image plane distance (cm)

num_projections = length(Time); % number of different views

% Generate projection angles
alpha = linspace(0, 360, num_projections);
% alpha=30;
theta_rad = deg2rad(alpha); % view angles (radians)

%% Step 3: Projection Model: Compute 2D projections

Xp=zeros(1,num_projections); % allocate array
Yp=zeros(1,num_projections);

for i=1:num_projections
f_theta = (SAD – (true_T(i,1) .* sin(theta_rad(i)) + true_T(i,3) .* cos(theta_rad(i)))) ./ SID;
Xp(1, i) = (true_T(i,1) .* cos(theta_rad(i)) – true_T(i,3) .* sin(theta_rad(i))) ./ f_theta;
Yp(1, i) = true_T(i,2) ./ f_theta;
end

xp = Xp’;
yp = Yp’;

%% Step 4: Define the objective function

% Define the objective function
objFun = @(T) computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections);

%% Step 5: Minimize the objective function using lsqnonlin
% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Define bounds
lb = []; % Lower bounds
ub = []; % Upper bounds

% Define optimization options
options = optimoptions(‘lsqnonlin’, …
‘Algorithm’, ‘interior-point’, …
‘Display’, ‘iter’, …
‘MaxIterations’, 300, …
‘MaxFunctionEvaluations’, 20000, …
‘TolFun’, 1e-10, …
‘TolX’, 1e-10, …
‘StepTolerance’, 1e-8, …
‘FiniteDifferenceStepSize’, 1e-3, …
‘UseParallel’, true);

% Generate a better initial guess
T0 = ones(3, num_projections);

% Run optimization for each projection
estimated_T = zeros(3, num_projections);
for i = 1:num_projections
objFun_i = @(T) computeProjectionError(T, xp(i), yp(i), theta_rad(i), SAD, SID, 1);
estimated_T(:, i) = lsqnonlin(objFun_i, T0(:, i), lb, ub, options);
end

%% Step 6: Calculate RMSE value

% Estimated Tumor Position in X, Y, and Z Direction
Estimate_3D_X = estimated_T(1,:);
Estimate_3D_Y = estimated_T(2,:);
Estimate_3D_Z = estimated_T(3,:);

RMSE_x = Calculate_RMSR (xt,Estimate_3D_X);
RMSE_y = Calculate_RMSR (yt,Estimate_3D_Y);
RMSE_z = Calculate_RMSR (zt,Estimate_3D_Z);

fprintf([‘RMSE for X, Y, Z Direction(mm): ‘ …
‘[%.2f, %.2f, %.2f] mmn’], RMSE_x, RMSE_y, RMSE_z);

%% Step 7: Plot Estimated vs Real Data

Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z);
toc;

%% Objective function: Computes error between observed and estimated projections
function error = computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections)
for i=1:num_projections
x_est = T(1,:);
y_est = T(2,:);
z_est = T(3,:);

% Compute estimated projection using the perspective transformation
f_theta = (SAD – (x_est(i) .* sin(theta_rad(i)) + z_est(i) .* cos(theta_rad(i))))./ SID;

xp_est(i) = (x_est(i) .* cos(theta_rad(i)) – z_est(i) .* sin(theta_rad(i))) ./ f_theta;
yp_est(i) = y_est(i) ./ f_theta;

end

%% Compute residual error (Method 1)
% Compute the residual error
error_x = xp – xp_est;
error_y = yp – yp_est;

% Return residuals for least squares minimization
error = [error_x; error_y];

end
function RMSE = Calculate_RMSR (True_value,Estimated_value)

% Calculate RMSE
e1 = (True_value(:)-Estimated_value(:)).^2;
RMSE = sqrt(mean(e1,’omitnan’));

end
function Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z)

figure(‘WindowState’, ‘maximized’)
subplot(3,1,1);
plot(Time, Estimate_3D_X,’r’);
hold on;
plot(Time, xt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘X Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,2);
plot(Time, Estimate_3D_Y,’r’);
hold on;
plot(Time, yt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Y Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,3);
plot(Time, Estimate_3D_Z,’r’);
hold on;
plot(Time, zt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Z Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

endHi there,
I am currently working on a Matlab code for my task (optimization task), and I tried two different methods;

Method A: the fmincon was used to minimize the objective function in which different algorithms, such as interior-point, sqp, sqp-legacy, interior-point, and active-set, were applied.
Method B: Nonlinear least squares optimization was combined with three algorithms, levenberg-marquardt, and trust-region-reflective.

The best results I got now are (from the Nonlinear least squares optimization + ‘interior-point’):
RMSE for X, Y, Z Direction(mm) : [1.18, 0.16, 1.33] mm; however, I want to reduce it as far as it is possible.
@ A quick guide for the code, and how it works.
1. I do have 3D data sets, and I used some mathematical methods to convert these 3D data into 2D data (Step 3).
2. The goal is to use some inverse method to get the same 3D datasets; therefore, after defining the objective function, I applied different optimization methods to address this task.

Any assistance or alternative approaches would be greatly appreciated.
Thank you in advance!
% @ Payam Samadi (2025.3.15) NLSP (Nonlinear least squares optimization)

% In step 3, the 2D projection data was extracted from the 3D data at
% different projections.

% In step4, the objective function is defined.

% In step 5, the Nonlinear least squares optimization is used to minimize
% the objective function.

% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Note: It is important to carefully consider the initial guesses for
% target locations, as well as the lower bounds (lb) and upper bounds (ub).

tic;
clc;
clear;
close all;

%% Step 1: Load xls file (3D Tumor position)

Load_Data = xlsread(‘Sample 1.xlsx’); % Data include 12 (sec)
% Load_Data = xlsread(‘Sample 2.xlsx’); % Data include 60 (sec)

Time = Load_Data(:,1); % Time (s)
xt=Load_Data(:,2); % xt for targets
yt=Load_Data(:,3); % yt for targets
zt=Load_Data(:,4); % zt for targets

true_T=[xt,yt,zt]; % target locations
[~,numT]=size(true_T); % number of targets

%% Step 2: Define imaging system parameters
SAD = 100; % source-axis distance (cm)
SID = 150; % source-image plane distance (cm)

num_projections = length(Time); % number of different views

% Generate projection angles
alpha = linspace(0, 360, num_projections);
% alpha=30;
theta_rad = deg2rad(alpha); % view angles (radians)

%% Step 3: Projection Model: Compute 2D projections

Xp=zeros(1,num_projections); % allocate array
Yp=zeros(1,num_projections);

for i=1:num_projections
f_theta = (SAD – (true_T(i,1) .* sin(theta_rad(i)) + true_T(i,3) .* cos(theta_rad(i)))) ./ SID;
Xp(1, i) = (true_T(i,1) .* cos(theta_rad(i)) – true_T(i,3) .* sin(theta_rad(i))) ./ f_theta;
Yp(1, i) = true_T(i,2) ./ f_theta;
end

xp = Xp’;
yp = Yp’;

%% Step 4: Define the objective function

% Define the objective function
objFun = @(T) computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections);

%% Step 5: Minimize the objective function using lsqnonlin
% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Define bounds
lb = []; % Lower bounds
ub = []; % Upper bounds

% Define optimization options
options = optimoptions(‘lsqnonlin’, …
‘Algorithm’, ‘interior-point’, …
‘Display’, ‘iter’, …
‘MaxIterations’, 300, …
‘MaxFunctionEvaluations’, 20000, …
‘TolFun’, 1e-10, …
‘TolX’, 1e-10, …
‘StepTolerance’, 1e-8, …
‘FiniteDifferenceStepSize’, 1e-3, …
‘UseParallel’, true);

% Generate a better initial guess
T0 = ones(3, num_projections);

% Run optimization for each projection
estimated_T = zeros(3, num_projections);
for i = 1:num_projections
objFun_i = @(T) computeProjectionError(T, xp(i), yp(i), theta_rad(i), SAD, SID, 1);
estimated_T(:, i) = lsqnonlin(objFun_i, T0(:, i), lb, ub, options);
end

%% Step 6: Calculate RMSE value

% Estimated Tumor Position in X, Y, and Z Direction
Estimate_3D_X = estimated_T(1,:);
Estimate_3D_Y = estimated_T(2,:);
Estimate_3D_Z = estimated_T(3,:);

RMSE_x = Calculate_RMSR (xt,Estimate_3D_X);
RMSE_y = Calculate_RMSR (yt,Estimate_3D_Y);
RMSE_z = Calculate_RMSR (zt,Estimate_3D_Z);

fprintf([‘RMSE for X, Y, Z Direction(mm): ‘ …
‘[%.2f, %.2f, %.2f] mmn’], RMSE_x, RMSE_y, RMSE_z);

%% Step 7: Plot Estimated vs Real Data

Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z);
toc;

%% Objective function: Computes error between observed and estimated projections
function error = computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections)
for i=1:num_projections
x_est = T(1,:);
y_est = T(2,:);
z_est = T(3,:);

% Compute estimated projection using the perspective transformation
f_theta = (SAD – (x_est(i) .* sin(theta_rad(i)) + z_est(i) .* cos(theta_rad(i))))./ SID;

xp_est(i) = (x_est(i) .* cos(theta_rad(i)) – z_est(i) .* sin(theta_rad(i))) ./ f_theta;
yp_est(i) = y_est(i) ./ f_theta;

end

%% Compute residual error (Method 1)
% Compute the residual error
error_x = xp – xp_est;
error_y = yp – yp_est;

% Return residuals for least squares minimization
error = [error_x; error_y];

end
function RMSE = Calculate_RMSR (True_value,Estimated_value)

% Calculate RMSE
e1 = (True_value(:)-Estimated_value(:)).^2;
RMSE = sqrt(mean(e1,’omitnan’));

end
function Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z)

figure(‘WindowState’, ‘maximized’)
subplot(3,1,1);
plot(Time, Estimate_3D_X,’r’);
hold on;
plot(Time, xt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘X Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,2);
plot(Time, Estimate_3D_Y,’r’);
hold on;
plot(Time, yt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Y Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,3);
plot(Time, Estimate_3D_Z,’r’);
hold on;
plot(Time, zt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Z Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

end Hi there,
I am currently working on a Matlab code for my task (optimization task), and I tried two different methods;

Method A: the fmincon was used to minimize the objective function in which different algorithms, such as interior-point, sqp, sqp-legacy, interior-point, and active-set, were applied.
Method B: Nonlinear least squares optimization was combined with three algorithms, levenberg-marquardt, and trust-region-reflective.

The best results I got now are (from the Nonlinear least squares optimization + ‘interior-point’):
RMSE for X, Y, Z Direction(mm) : [1.18, 0.16, 1.33] mm; however, I want to reduce it as far as it is possible.
@ A quick guide for the code, and how it works.
1. I do have 3D data sets, and I used some mathematical methods to convert these 3D data into 2D data (Step 3).
2. The goal is to use some inverse method to get the same 3D datasets; therefore, after defining the objective function, I applied different optimization methods to address this task.

Any assistance or alternative approaches would be greatly appreciated.
Thank you in advance!
% @ Payam Samadi (2025.3.15) NLSP (Nonlinear least squares optimization)

% In step 3, the 2D projection data was extracted from the 3D data at
% different projections.

% In step4, the objective function is defined.

% In step 5, the Nonlinear least squares optimization is used to minimize
% the objective function.

% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Note: It is important to carefully consider the initial guesses for
% target locations, as well as the lower bounds (lb) and upper bounds (ub).

tic;
clc;
clear;
close all;

%% Step 1: Load xls file (3D Tumor position)

Load_Data = xlsread(‘Sample 1.xlsx’); % Data include 12 (sec)
% Load_Data = xlsread(‘Sample 2.xlsx’); % Data include 60 (sec)

Time = Load_Data(:,1); % Time (s)
xt=Load_Data(:,2); % xt for targets
yt=Load_Data(:,3); % yt for targets
zt=Load_Data(:,4); % zt for targets

true_T=[xt,yt,zt]; % target locations
[~,numT]=size(true_T); % number of targets

%% Step 2: Define imaging system parameters
SAD = 100; % source-axis distance (cm)
SID = 150; % source-image plane distance (cm)

num_projections = length(Time); % number of different views

% Generate projection angles
alpha = linspace(0, 360, num_projections);
% alpha=30;
theta_rad = deg2rad(alpha); % view angles (radians)

%% Step 3: Projection Model: Compute 2D projections

Xp=zeros(1,num_projections); % allocate array
Yp=zeros(1,num_projections);

for i=1:num_projections
f_theta = (SAD – (true_T(i,1) .* sin(theta_rad(i)) + true_T(i,3) .* cos(theta_rad(i)))) ./ SID;
Xp(1, i) = (true_T(i,1) .* cos(theta_rad(i)) – true_T(i,3) .* sin(theta_rad(i))) ./ f_theta;
Yp(1, i) = true_T(i,2) ./ f_theta;
end

xp = Xp’;
yp = Yp’;

%% Step 4: Define the objective function

% Define the objective function
objFun = @(T) computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections);

%% Step 5: Minimize the objective function using lsqnonlin
% Algorithm:
% 1. ‘levenberg-marquardt’ : [1.21, 0.17, 1.39] mm,
% 2. ‘trust-region-reflective’ : [1.21, 0.17, 1.39] mm,
% 3. ‘interior-point’ : [1.18, 0.16, 1.33] mm

% Define bounds
lb = []; % Lower bounds
ub = []; % Upper bounds

% Define optimization options
options = optimoptions(‘lsqnonlin’, …
‘Algorithm’, ‘interior-point’, …
‘Display’, ‘iter’, …
‘MaxIterations’, 300, …
‘MaxFunctionEvaluations’, 20000, …
‘TolFun’, 1e-10, …
‘TolX’, 1e-10, …
‘StepTolerance’, 1e-8, …
‘FiniteDifferenceStepSize’, 1e-3, …
‘UseParallel’, true);

% Generate a better initial guess
T0 = ones(3, num_projections);

% Run optimization for each projection
estimated_T = zeros(3, num_projections);
for i = 1:num_projections
objFun_i = @(T) computeProjectionError(T, xp(i), yp(i), theta_rad(i), SAD, SID, 1);
estimated_T(:, i) = lsqnonlin(objFun_i, T0(:, i), lb, ub, options);
end

%% Step 6: Calculate RMSE value

% Estimated Tumor Position in X, Y, and Z Direction
Estimate_3D_X = estimated_T(1,:);
Estimate_3D_Y = estimated_T(2,:);
Estimate_3D_Z = estimated_T(3,:);

RMSE_x = Calculate_RMSR (xt,Estimate_3D_X);
RMSE_y = Calculate_RMSR (yt,Estimate_3D_Y);
RMSE_z = Calculate_RMSR (zt,Estimate_3D_Z);

fprintf([‘RMSE for X, Y, Z Direction(mm): ‘ …
‘[%.2f, %.2f, %.2f] mmn’], RMSE_x, RMSE_y, RMSE_z);

%% Step 7: Plot Estimated vs Real Data

Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z);
toc;

%% Objective function: Computes error between observed and estimated projections
function error = computeProjectionError(T, xp, yp, theta_rad, SAD, SID, num_projections)
for i=1:num_projections
x_est = T(1,:);
y_est = T(2,:);
z_est = T(3,:);

% Compute estimated projection using the perspective transformation
f_theta = (SAD – (x_est(i) .* sin(theta_rad(i)) + z_est(i) .* cos(theta_rad(i))))./ SID;

xp_est(i) = (x_est(i) .* cos(theta_rad(i)) – z_est(i) .* sin(theta_rad(i))) ./ f_theta;
yp_est(i) = y_est(i) ./ f_theta;

end

%% Compute residual error (Method 1)
% Compute the residual error
error_x = xp – xp_est;
error_y = yp – yp_est;

% Return residuals for least squares minimization
error = [error_x; error_y];

end
function RMSE = Calculate_RMSR (True_value,Estimated_value)

% Calculate RMSE
e1 = (True_value(:)-Estimated_value(:)).^2;
RMSE = sqrt(mean(e1,’omitnan’));

end
function Plot_results (Time, xt, yt, zt, Estimate_3D_X, Estimate_3D_Y, Estimate_3D_Z)

figure(‘WindowState’, ‘maximized’)
subplot(3,1,1);
plot(Time, Estimate_3D_X,’r’);
hold on;
plot(Time, xt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘X Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,2);
plot(Time, Estimate_3D_Y,’r’);
hold on;
plot(Time, yt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Y Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

subplot(3,1,3);
plot(Time, Estimate_3D_Z,’r’);
hold on;
plot(Time, zt,’b’);
legend (‘Estimate’, ‘Real’);
title (‘Z Dierction’)
xlabel (‘Time (s)’);
ylabel (‘Motion (mm)’)
hold off;

end optimization, fmincon, nonlinear least squares, objective function MATLAB Answers — New Questions

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Bonjour, j’ai un probleme avec ma conception d’un projet de cours j’aimerais calculé l’angle adequat pour mon projectile avec un x0 et y0 en fonction de x mais matlab me donne aucune reponse. voici ce que je recois comme resultat. merciBonjour, j’ai un probleme avec ma conception d’un projet de cours j’aimerais calculé l’angle adequat pour mon projectile avec un x0 et y0 en fonction de x mais matlab me donne aucune reponse. voici ce que je recois comme resultat. merci Bonjour, j’ai un probleme avec ma conception d’un projet de cours j’aimerais calculé l’angle adequat pour mon projectile avec un x0 et y0 en fonction de x mais matlab me donne aucune reponse. voici ce que je recois comme resultat. merci symbolic, trigonometric MATLAB Answers — New Questions

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