Hi all,
I am trying to generate a dynamic library file by using ‘coder’. When I trying to do it, there is an information said that the function ‘pdepe’ is not supported in code generation. I am wondering if there is any solution to it like a replacement of the ‘pdepe’ function or some other settings?

Thank you in advanceHi all,
I am trying to generate a dynamic library file by using ‘coder’. When I trying to do it, there is an information said that the function ‘pdepe’ is not supported in code generation. I am wondering if there is any solution to it like a replacement of the ‘pdepe’ function or some other settings?

Thank you in advance Hi all,
I am trying to generate a dynamic library file by using ‘coder’. When I trying to do it, there is an information said that the function ‘pdepe’ is not supported in code generation. I am wondering if there is any solution to it like a replacement of the ‘pdepe’ function or some other settings?

Thank you in advance code generation, pdepe, matlab, coder MATLAB Answers — New Questions

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So i have been trying to configure matlab to work with android studio for a project and i came across Simulink Support Package for Android Devices ,but when i try to configure it i get this error message. Does anyone know how to fix this

Build App
A problem occurred configuring root project ‘TestApp’. > Could not open cp_proj generic class cache for build file ‘C:UsersUserAppDataLocalTemptpee9cd55b_8ffa_4e98_82dc_4f945f5ab51cTestAppbuild.gradle’ (C:UsersUser.gradlecaches7.5scripts56lbh5pj36js9453y7f1h6iim). > BUG! exception in phase ‘semantic analysis’ in source unit ‘_BuildScript_’ Unsupported class file major version 65 *So i have been trying to configure matlab to work with android studio for a project and i came across Simulink Support Package for Android Devices ,but when i try to configure it i get this error message. Does anyone know how to fix this

Build App
A problem occurred configuring root project ‘TestApp’. > Could not open cp_proj generic class cache for build file ‘C:UsersUserAppDataLocalTemptpee9cd55b_8ffa_4e98_82dc_4f945f5ab51cTestAppbuild.gradle’ (C:UsersUser.gradlecaches7.5scripts56lbh5pj36js9453y7f1h6iim). > BUG! exception in phase ‘semantic analysis’ in source unit ‘_BuildScript_’ Unsupported class file major version 65 * So i have been trying to configure matlab to work with android studio for a project and i came across Simulink Support Package for Android Devices ,but when i try to configure it i get this error message. Does anyone know how to fix this

Build App
A problem occurred configuring root project ‘TestApp’. > Could not open cp_proj generic class cache for build file ‘C:UsersUserAppDataLocalTemptpee9cd55b_8ffa_4e98_82dc_4f945f5ab51cTestAppbuild.gradle’ (C:UsersUser.gradlecaches7.5scripts56lbh5pj36js9453y7f1h6iim). > BUG! exception in phase ‘semantic analysis’ in source unit ‘_BuildScript_’ Unsupported class file major version 65 * android studio MATLAB Answers — New Questions

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Hello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your helpHello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your help Hello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your help control, pontryagin MATLAB Answers — New Questions

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I want to simulate cloud environment using MATLAB and implement some scheduling algorithms.I want to simulate cloud environment using MATLAB and implement some scheduling algorithms. I want to simulate cloud environment using MATLAB and implement some scheduling algorithms. cloud computing, scheduling algorithms MATLAB Answers — New Questions

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p=polyfit(RANKING,Total,4);
y=polyval(p,Total);
plot(y)p=polyfit(RANKING,Total,4);
y=polyval(p,Total);
plot(y) p=polyfit(RANKING,Total,4);
y=polyval(p,Total);
plot(y) polyfit MATLAB Answers — New Questions

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Hi all
I have three vectors, named X,Y, and Z, related to the coordinates of a structure and also a vector named W showing the displacement of each node. My structure using scatter3 is like this. I’m gonna interpolate it to obtain an 3D image. How should I interpolate such an irregular shape?Hi all
I have three vectors, named X,Y, and Z, related to the coordinates of a structure and also a vector named W showing the displacement of each node. My structure using scatter3 is like this. I’m gonna interpolate it to obtain an 3D image. How should I interpolate such an irregular shape? Hi all
I have three vectors, named X,Y, and Z, related to the coordinates of a structure and also a vector named W showing the displacement of each node. My structure using scatter3 is like this. I’m gonna interpolate it to obtain an 3D image. How should I interpolate such an irregular shape? interpolate MATLAB Answers — New Questions

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I can tell Matlab to make a basic figure such as a plot of ‘x’ versus ‘y’, but when I tell Matlab to make more than one figure in the same script, it will delete my first figure when it makes the next one. Do I need to tell Matlab to save each figure after it creates it and before making the next one? or am I missing something very obvious?I can tell Matlab to make a basic figure such as a plot of ‘x’ versus ‘y’, but when I tell Matlab to make more than one figure in the same script, it will delete my first figure when it makes the next one. Do I need to tell Matlab to save each figure after it creates it and before making the next one? or am I missing something very obvious? I can tell Matlab to make a basic figure such as a plot of ‘x’ versus ‘y’, but when I tell Matlab to make more than one figure in the same script, it will delete my first figure when it makes the next one. Do I need to tell Matlab to save each figure after it creates it and before making the next one? or am I missing something very obvious? figure, subplot MATLAB Answers — New Questions

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I’m currently attempting to get platform or sensor related motion data from my UAV 3d scenario Simulink Model. Attached is the current block diagram:

I have the UAV scenario configuration block, the SImulation 3D scene configuration block, and the UAV Scenario Motion Read block, connected to my workspace as shown above. The UAV scenario block is configured for the singleUAVScenario function, which spawns a single quadrotor. The control part and this configuration were taken from an example in MATLAB’s documentation, so all bus, signal, and data blocks’ names are unchanged. When I run the model, initially the values are updating, as shown:

However, more or less after a single second passes in my simulation, for some reason, my data goes to NaN values for the rest of the simulation, no matter how long it is, as shown here:

Obviously, when I take the data to MATLAB using a To Workspace block, I have the same issue.
I’ve tried running another MATLAB example; quick access for that is this:
openExample(‘uav/SimulateUAVScenarioUsingScenarioBlocksExample’)
In that simulink model, the displays constantly update and there are no nan issues. Can anyone provide any answers? Sorry if it’s an easy fix, I don’t have too much experience in this particular area. Is it the sampling time, some inherent issue? I’m assuming that, according to the matlab documentation for the UAV scenario configuration block…
This block internally stores motion states from platforms and sensors in a global data store memory block as buses within a bus with a name specified in the Scenario motion bus name parameter.
That the motion parameters are automatically stored in this global data store memory block, and by using the read block, I can simply get the motion data. Do let me know if any additional information is needed, I can provide.
Note: Data goes to NaN after an exact second in simulation time has elapsed. No matter what the simulation step size is, the data seems constant except for the Position data for the first second, but instantly after, everything goes to NaN (except platform ID). The constant data also may be wrong, I suspect.I’m currently attempting to get platform or sensor related motion data from my UAV 3d scenario Simulink Model. Attached is the current block diagram:

I have the UAV scenario configuration block, the SImulation 3D scene configuration block, and the UAV Scenario Motion Read block, connected to my workspace as shown above. The UAV scenario block is configured for the singleUAVScenario function, which spawns a single quadrotor. The control part and this configuration were taken from an example in MATLAB’s documentation, so all bus, signal, and data blocks’ names are unchanged. When I run the model, initially the values are updating, as shown:

However, more or less after a single second passes in my simulation, for some reason, my data goes to NaN values for the rest of the simulation, no matter how long it is, as shown here:

Obviously, when I take the data to MATLAB using a To Workspace block, I have the same issue.
I’ve tried running another MATLAB example; quick access for that is this:
openExample(‘uav/SimulateUAVScenarioUsingScenarioBlocksExample’)
In that simulink model, the displays constantly update and there are no nan issues. Can anyone provide any answers? Sorry if it’s an easy fix, I don’t have too much experience in this particular area. Is it the sampling time, some inherent issue? I’m assuming that, according to the matlab documentation for the UAV scenario configuration block…
This block internally stores motion states from platforms and sensors in a global data store memory block as buses within a bus with a name specified in the Scenario motion bus name parameter.
That the motion parameters are automatically stored in this global data store memory block, and by using the read block, I can simply get the motion data. Do let me know if any additional information is needed, I can provide.
Note: Data goes to NaN after an exact second in simulation time has elapsed. No matter what the simulation step size is, the data seems constant except for the Position data for the first second, but instantly after, everything goes to NaN (except platform ID). The constant data also may be wrong, I suspect. I’m currently attempting to get platform or sensor related motion data from my UAV 3d scenario Simulink Model. Attached is the current block diagram:

I have the UAV scenario configuration block, the SImulation 3D scene configuration block, and the UAV Scenario Motion Read block, connected to my workspace as shown above. The UAV scenario block is configured for the singleUAVScenario function, which spawns a single quadrotor. The control part and this configuration were taken from an example in MATLAB’s documentation, so all bus, signal, and data blocks’ names are unchanged. When I run the model, initially the values are updating, as shown:

However, more or less after a single second passes in my simulation, for some reason, my data goes to NaN values for the rest of the simulation, no matter how long it is, as shown here:

Obviously, when I take the data to MATLAB using a To Workspace block, I have the same issue.
I’ve tried running another MATLAB example; quick access for that is this:
openExample(‘uav/SimulateUAVScenarioUsingScenarioBlocksExample’)
In that simulink model, the displays constantly update and there are no nan issues. Can anyone provide any answers? Sorry if it’s an easy fix, I don’t have too much experience in this particular area. Is it the sampling time, some inherent issue? I’m assuming that, according to the matlab documentation for the UAV scenario configuration block…
This block internally stores motion states from platforms and sensors in a global data store memory block as buses within a bus with a name specified in the Scenario motion bus name parameter.
That the motion parameters are automatically stored in this global data store memory block, and by using the read block, I can simply get the motion data. Do let me know if any additional information is needed, I can provide.
Note: Data goes to NaN after an exact second in simulation time has elapsed. No matter what the simulation step size is, the data seems constant except for the Position data for the first second, but instantly after, everything goes to NaN (except platform ID). The constant data also may be wrong, I suspect. uav toolbox, nan values, simulink MATLAB Answers — New Questions

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So, I do research of laser heating metals. We have this code (main code) that separates each hotspot into different qudrants to analyze. Occacsionally, one quadrant nees to be excluded from the calculations (2nd code). So the main code, uses the LT (left top) as the focus for analyzing. The 2nd code, needs to do the analysis with LD (Left down) as the focus instead adn exclude everything that has to do with LT.
So the issue is: the tempeartures calculated from the 2nd code are 300 to 400 K too low. (pics of ffure with each code.). If you have any isight I would greatly appreciate it!
Here is the normal code:
clear;close all;
[filename, pathname, filterindex] = uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname = fullfile(pathname, filename);
mydata = importdata(fullname);
hotspot_ob=double(mydata);
scale= 120; % size of the box 90*90
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
%V_lt=140;H_lt=166;
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
%%find max for hotspot for later T correction Jie add on Mar2216, two ways:
%%neigther seem to work properly
%1st find the strongest point and make it as threshold–find corresponding
%intensities in other quadrants
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [hotspot_lt(mm,nn) hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_lt(countm,countn)-hotspot_lt(m_lt,n_lt)).^2 + (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_lt(mmm,nnn) hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%%
center_LT=[V_lt,H_lt];
center_LD=[V_ld,H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
% Define the bounds of the matrix
k_max = size(hotspot, 1);
l_max = size(hotspot, 2);
% Ensure the indices are within valid bounds
V_lt_start = max(V_lt-hscale, 1);
V_lt_end = min(V_lt+hscale, k_max);
H_lt_start = max(H_lt-hscale, 1);
H_lt_end = min(H_lt+hscale, l_max);
V_ld_start = max(V_ld-hscale, 1);
V_ld_end = min(V_ld+hscale, k_max);
H_ld_start = max(H_ld-hscale, 1);
H_ld_end = min(H_ld+hscale, l_max);
V_rt_start = max(V_rt-hscale, 1);
V_rt_end = min(V_rt+hscale, k_max);
H_rt_start = max(H_rt-hscale, 1);
H_rt_end = min(H_rt+hscale, l_max);
V_rd_start = max(V_rd-hscale, 1);
V_rd_end = min(V_rd+hscale, k_max);
H_rd_start = max(H_rd-hscale, 1);
H_rd_end = min(H_rd+hscale, l_max);
% Now extract the subarrays with valid indices
LT = hotspot(V_lt_start:V_lt_end, H_lt_start:H_lt_end);
LD = hotspot(V_ld_start:V_ld_end, H_ld_start:H_ld_end);
RT = hotspot(V_rt_start:V_rt_end, H_rt_start:H_rt_end);
RD = hotspot(V_rd_start:V_rd_end, H_rd_start:H_rd_end);
% Find New centers and update them
[center_RT_new,Cor_RT] = imagematching (hotspot,LT,center_RT,scale); % use LT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,LT,center_LD,scale);
[center_RD_new,Cor_RD] = imagematching (hotspot,LT,center_RD,scale);
center_LD=center_LD_new;
center_RT=center_RT_new;
center_RD=center_RD_new;
[inter_center_RT,Cor_RT] = intermatching (hotspot,LT,center_RT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,LT,center_LD_new,scale,subpixel);
[inter_center_RD,Cor_RD] = intermatching (hotspot,LT,center_RD_new,scale,subpixel);
center_LD=inter_center_LD;
center_RT=inter_center_RT;
center_RD=inter_center_RD;
Cor=[1 Cor_RT;Cor_LD Cor_RD];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_RT(1,1); H_rt=center_RT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_rt,YI_rt]=meshgrid(H_rt-hscale:H_rt+hscale,V_rt-hscale:V_rt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld); % update images
RT=interp2(hotspot,XI_rt,YI_rt);
RD=interp2(hotspot,XI_rd,YI_rd);
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LT);
for i=1:m
for j=1:n
X=[1/lamda_LT 1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
% X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
Y=[Wien_LT(i,j) Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
% Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg); %% bint is 95% confidence level of T
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1); %% T_inv(1,1) is for T
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb); %% T_inv(2,1) is for emissivity
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2; %% difference between upper limit of T – lower limit of T
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_LT,Indexing] = max(LT(:))
max_RD = max(max(RD));max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [LT(Indexing) RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (LT(countm,countn)-max_LT).^2 + (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [LT(m4,n4) RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [LT(m4,:); RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [LT(:,n4)’; RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
%%
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,1)
imagesc(LT);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

Image result:

2nd code:
clear; close all
[filename, pathname, filterindex]=uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname=fullfile(pathname, filename);
mydata=importdata(fullname);
hotspot_ob=double(mydata);
scale=120;
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
%V_lt=98; H_lt=150;
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [ hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%V_lt=126; H_lt=176;
%V_rt=125; H_rt=565;
%V_ld=398; H_ld=179;
%V_rd=388; H_rd=580;
center_LT=[V_lt,H_lt];
center_LD=[V_ld, H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
LT=hotspot(V_lt-hscale:V_lt+hscale,H_lt-hscale:H_lt+hscale);
LD=hotspot(V_ld-hscale:V_ld+hscale,H_ld-hscale:H_ld+hscale);
RT=hotspot(V_rt-hscale:V_rt+hscale,H_rt-hscale:H_rt+hscale);
RD=hotspot(V_rd-hscale:V_rd+hscale,H_rd-hscale:H_rd+hscale);
% Find New centers and update them
[center_LT_new,Cor_LT] = imagematching (hotspot,RD,center_RT,scale); % use RT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,RD,center_LD,scale);
[center_RT_new,Cor_RT] = imagematching (hotspot,RD,center_RD,scale);
center_LD=center_LD_new;
center_LT=center_LT_new;
center_RT=center_RT_new;
[inter_center_LT,Cor_LT] = intermatching (hotspot,RD,center_LT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,RD,center_LD_new,scale,subpixel);
[inter_center_RT,Cor_RT] = intermatching (hotspot,RD,center_RT_new,scale,subpixel);
center_LD=inter_center_LD;
center_LT=inter_center_LT;
center_RT=inter_center_RT;
Cor=[1 Cor_LT;Cor_LD Cor_RT];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_LT(1,1); H_lt=center_LT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_lt,YI_lt]=meshgrid(H_lt-hscale:H_lt+hscale,V_lt-hscale:V_lt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld,’spline’); % update images
LT=interp2(hotspot,XI_lt,YI_lt,’spline’);
RD=interp2(hotspot,XI_rd,YI_rd,’spline’);
% Assuming you want to exclude 580 nm
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
%Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LD);
for i=1:m
for j=1:n
X=[1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
%X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
%Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
Y=[Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg);
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1);
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb);
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2;
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_RD,Indexing] = max(RD(:))
max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [ RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [ RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [ RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

image result:So, I do research of laser heating metals. We have this code (main code) that separates each hotspot into different qudrants to analyze. Occacsionally, one quadrant nees to be excluded from the calculations (2nd code). So the main code, uses the LT (left top) as the focus for analyzing. The 2nd code, needs to do the analysis with LD (Left down) as the focus instead adn exclude everything that has to do with LT.
So the issue is: the tempeartures calculated from the 2nd code are 300 to 400 K too low. (pics of ffure with each code.). If you have any isight I would greatly appreciate it!
Here is the normal code:
clear;close all;
[filename, pathname, filterindex] = uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname = fullfile(pathname, filename);
mydata = importdata(fullname);
hotspot_ob=double(mydata);
scale= 120; % size of the box 90*90
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
%V_lt=140;H_lt=166;
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
%%find max for hotspot for later T correction Jie add on Mar2216, two ways:
%%neigther seem to work properly
%1st find the strongest point and make it as threshold–find corresponding
%intensities in other quadrants
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [hotspot_lt(mm,nn) hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_lt(countm,countn)-hotspot_lt(m_lt,n_lt)).^2 + (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_lt(mmm,nnn) hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%%
center_LT=[V_lt,H_lt];
center_LD=[V_ld,H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
% Define the bounds of the matrix
k_max = size(hotspot, 1);
l_max = size(hotspot, 2);
% Ensure the indices are within valid bounds
V_lt_start = max(V_lt-hscale, 1);
V_lt_end = min(V_lt+hscale, k_max);
H_lt_start = max(H_lt-hscale, 1);
H_lt_end = min(H_lt+hscale, l_max);
V_ld_start = max(V_ld-hscale, 1);
V_ld_end = min(V_ld+hscale, k_max);
H_ld_start = max(H_ld-hscale, 1);
H_ld_end = min(H_ld+hscale, l_max);
V_rt_start = max(V_rt-hscale, 1);
V_rt_end = min(V_rt+hscale, k_max);
H_rt_start = max(H_rt-hscale, 1);
H_rt_end = min(H_rt+hscale, l_max);
V_rd_start = max(V_rd-hscale, 1);
V_rd_end = min(V_rd+hscale, k_max);
H_rd_start = max(H_rd-hscale, 1);
H_rd_end = min(H_rd+hscale, l_max);
% Now extract the subarrays with valid indices
LT = hotspot(V_lt_start:V_lt_end, H_lt_start:H_lt_end);
LD = hotspot(V_ld_start:V_ld_end, H_ld_start:H_ld_end);
RT = hotspot(V_rt_start:V_rt_end, H_rt_start:H_rt_end);
RD = hotspot(V_rd_start:V_rd_end, H_rd_start:H_rd_end);
% Find New centers and update them
[center_RT_new,Cor_RT] = imagematching (hotspot,LT,center_RT,scale); % use LT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,LT,center_LD,scale);
[center_RD_new,Cor_RD] = imagematching (hotspot,LT,center_RD,scale);
center_LD=center_LD_new;
center_RT=center_RT_new;
center_RD=center_RD_new;
[inter_center_RT,Cor_RT] = intermatching (hotspot,LT,center_RT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,LT,center_LD_new,scale,subpixel);
[inter_center_RD,Cor_RD] = intermatching (hotspot,LT,center_RD_new,scale,subpixel);
center_LD=inter_center_LD;
center_RT=inter_center_RT;
center_RD=inter_center_RD;
Cor=[1 Cor_RT;Cor_LD Cor_RD];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_RT(1,1); H_rt=center_RT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_rt,YI_rt]=meshgrid(H_rt-hscale:H_rt+hscale,V_rt-hscale:V_rt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld); % update images
RT=interp2(hotspot,XI_rt,YI_rt);
RD=interp2(hotspot,XI_rd,YI_rd);
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LT);
for i=1:m
for j=1:n
X=[1/lamda_LT 1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
% X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
Y=[Wien_LT(i,j) Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
% Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg); %% bint is 95% confidence level of T
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1); %% T_inv(1,1) is for T
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb); %% T_inv(2,1) is for emissivity
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2; %% difference between upper limit of T – lower limit of T
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_LT,Indexing] = max(LT(:))
max_RD = max(max(RD));max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [LT(Indexing) RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (LT(countm,countn)-max_LT).^2 + (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [LT(m4,n4) RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [LT(m4,:); RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [LT(:,n4)’; RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
%%
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,1)
imagesc(LT);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

Image result:

2nd code:
clear; close all
[filename, pathname, filterindex]=uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname=fullfile(pathname, filename);
mydata=importdata(fullname);
hotspot_ob=double(mydata);
scale=120;
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
%V_lt=98; H_lt=150;
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [ hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%V_lt=126; H_lt=176;
%V_rt=125; H_rt=565;
%V_ld=398; H_ld=179;
%V_rd=388; H_rd=580;
center_LT=[V_lt,H_lt];
center_LD=[V_ld, H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
LT=hotspot(V_lt-hscale:V_lt+hscale,H_lt-hscale:H_lt+hscale);
LD=hotspot(V_ld-hscale:V_ld+hscale,H_ld-hscale:H_ld+hscale);
RT=hotspot(V_rt-hscale:V_rt+hscale,H_rt-hscale:H_rt+hscale);
RD=hotspot(V_rd-hscale:V_rd+hscale,H_rd-hscale:H_rd+hscale);
% Find New centers and update them
[center_LT_new,Cor_LT] = imagematching (hotspot,RD,center_RT,scale); % use RT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,RD,center_LD,scale);
[center_RT_new,Cor_RT] = imagematching (hotspot,RD,center_RD,scale);
center_LD=center_LD_new;
center_LT=center_LT_new;
center_RT=center_RT_new;
[inter_center_LT,Cor_LT] = intermatching (hotspot,RD,center_LT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,RD,center_LD_new,scale,subpixel);
[inter_center_RT,Cor_RT] = intermatching (hotspot,RD,center_RT_new,scale,subpixel);
center_LD=inter_center_LD;
center_LT=inter_center_LT;
center_RT=inter_center_RT;
Cor=[1 Cor_LT;Cor_LD Cor_RT];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_LT(1,1); H_lt=center_LT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_lt,YI_lt]=meshgrid(H_lt-hscale:H_lt+hscale,V_lt-hscale:V_lt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld,’spline’); % update images
LT=interp2(hotspot,XI_lt,YI_lt,’spline’);
RD=interp2(hotspot,XI_rd,YI_rd,’spline’);
% Assuming you want to exclude 580 nm
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
%Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LD);
for i=1:m
for j=1:n
X=[1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
%X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
%Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
Y=[Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg);
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1);
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb);
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2;
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_RD,Indexing] = max(RD(:))
max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [ RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [ RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [ RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

image result: So, I do research of laser heating metals. We have this code (main code) that separates each hotspot into different qudrants to analyze. Occacsionally, one quadrant nees to be excluded from the calculations (2nd code). So the main code, uses the LT (left top) as the focus for analyzing. The 2nd code, needs to do the analysis with LD (Left down) as the focus instead adn exclude everything that has to do with LT.
So the issue is: the tempeartures calculated from the 2nd code are 300 to 400 K too low. (pics of ffure with each code.). If you have any isight I would greatly appreciate it!
Here is the normal code:
clear;close all;
[filename, pathname, filterindex] = uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname = fullfile(pathname, filename);
mydata = importdata(fullname);
hotspot_ob=double(mydata);
scale= 120; % size of the box 90*90
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
%V_lt=140;H_lt=166;
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
%%find max for hotspot for later T correction Jie add on Mar2216, two ways:
%%neigther seem to work properly
%1st find the strongest point and make it as threshold–find corresponding
%intensities in other quadrants
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [hotspot_lt(mm,nn) hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_lt(countm,countn)-hotspot_lt(m_lt,n_lt)).^2 + (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_lt(mmm,nnn) hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%%
center_LT=[V_lt,H_lt];
center_LD=[V_ld,H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
% Define the bounds of the matrix
k_max = size(hotspot, 1);
l_max = size(hotspot, 2);
% Ensure the indices are within valid bounds
V_lt_start = max(V_lt-hscale, 1);
V_lt_end = min(V_lt+hscale, k_max);
H_lt_start = max(H_lt-hscale, 1);
H_lt_end = min(H_lt+hscale, l_max);
V_ld_start = max(V_ld-hscale, 1);
V_ld_end = min(V_ld+hscale, k_max);
H_ld_start = max(H_ld-hscale, 1);
H_ld_end = min(H_ld+hscale, l_max);
V_rt_start = max(V_rt-hscale, 1);
V_rt_end = min(V_rt+hscale, k_max);
H_rt_start = max(H_rt-hscale, 1);
H_rt_end = min(H_rt+hscale, l_max);
V_rd_start = max(V_rd-hscale, 1);
V_rd_end = min(V_rd+hscale, k_max);
H_rd_start = max(H_rd-hscale, 1);
H_rd_end = min(H_rd+hscale, l_max);
% Now extract the subarrays with valid indices
LT = hotspot(V_lt_start:V_lt_end, H_lt_start:H_lt_end);
LD = hotspot(V_ld_start:V_ld_end, H_ld_start:H_ld_end);
RT = hotspot(V_rt_start:V_rt_end, H_rt_start:H_rt_end);
RD = hotspot(V_rd_start:V_rd_end, H_rd_start:H_rd_end);
% Find New centers and update them
[center_RT_new,Cor_RT] = imagematching (hotspot,LT,center_RT,scale); % use LT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,LT,center_LD,scale);
[center_RD_new,Cor_RD] = imagematching (hotspot,LT,center_RD,scale);
center_LD=center_LD_new;
center_RT=center_RT_new;
center_RD=center_RD_new;
[inter_center_RT,Cor_RT] = intermatching (hotspot,LT,center_RT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,LT,center_LD_new,scale,subpixel);
[inter_center_RD,Cor_RD] = intermatching (hotspot,LT,center_RD_new,scale,subpixel);
center_LD=inter_center_LD;
center_RT=inter_center_RT;
center_RD=inter_center_RD;
Cor=[1 Cor_RT;Cor_LD Cor_RD];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_RT(1,1); H_rt=center_RT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_rt,YI_rt]=meshgrid(H_rt-hscale:H_rt+hscale,V_rt-hscale:V_rt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld); % update images
RT=interp2(hotspot,XI_rt,YI_rt);
RD=interp2(hotspot,XI_rd,YI_rd);
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LT);
for i=1:m
for j=1:n
X=[1/lamda_LT 1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
% X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
Y=[Wien_LT(i,j) Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
% Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg); %% bint is 95% confidence level of T
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1); %% T_inv(1,1) is for T
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb); %% T_inv(2,1) is for emissivity
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2; %% difference between upper limit of T – lower limit of T
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_LT,Indexing] = max(LT(:))
max_RD = max(max(RD));max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [LT(Indexing) RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (LT(countm,countn)-max_LT).^2 + (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [LT(m4,n4) RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [LT(m4,:); RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [LT(:,n4)’; RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
%%
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,1)
imagesc(LT);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

Image result:

2nd code:
clear; close all
[filename, pathname, filterindex]=uigetfile(‘*.txt’, ‘Enter input data file..’);
fullname=fullfile(pathname, filename);
mydata=importdata(fullname);
hotspot_ob=double(mydata);
scale=120;
subpixel=4;
hscale=scale/2;
[k,l]=size(hotspot_ob);
SR=ones(size(hotspot_ob));
box_Num = 1; % box 1 or 2
ND_Num = 0; % 0, .5, 1, 2
switch ND_Num
case 0
ND_col = 1;
case .5
ND_col = 2;
case 1
ND_col = 3;
case 2
ND_col = 4;
end

%LATEST from 08/09/2023
box(1).rs = [ 1.0 1.0 1.0 1.0
1.05 1.101 1.14 1.14
0.803 1.12 1.54 4.17
0.645 0.788 0.929 2.82];
box(2).rs = [1.0 1.0 1.0 1
0.296 0.312 0.325 0.424
0.331 0.457 0.632 1.735
0.245 0.294 0.348 1.077];
SR(1:fix(k/2),1:fix(l/2)) = box(box_Num).rs(1,ND_col);
SR(1:fix(k/2),fix(l/2)+1:l) = box(box_Num).rs(2,ND_col);
SR(fix(k/2)+1:k,1:fix(l/2)) = box(box_Num).rs(3,ND_col);
SR(fix(k/2)+1:k,fix(l/2)+1:l) = box(box_Num).rs(4,ND_col);
hotspot=hotspot_ob./SR;
[V_lt,H_lt]=find_max(hotspot_ob,1,fix(k/2),1,fix(l/2));
[V_rt,H_rt]=find_max(hotspot_ob,1,fix(k/2),fix(l/2)+1,l);
[V_ld,H_ld]=find_max(hotspot_ob,fix(k/2)+1,k,1,fix(l/2));
[V_rd,H_rd]=find_max(hotspot_ob,fix(k/2)+1,k,fix(l/2)+1,l);
hotspot_lt = hotspot(1:fix(k/2),1:fix(l/2)); [k_lt, l_lt] = size(hotspot_lt);
hotspot_rt = hotspot(1:fix(k/2),(fix(l/2)+1):l); [k_rt, l_rt] = size(hotspot_rt);
hotspot_ld = hotspot((fix(k/2)+1):k,1:fix(l/2)); [k_ld, l_ld] = size(hotspot_ld);
hotspot_rd = hotspot((fix(k/2)+1):k,(fix(l/2)+1):l); [k_rd, l_rd] = size(hotspot_rd);
%V_lt=98; H_lt=150;
[m_lt,n_lt]=find_max(hotspot_lt,1,k_lt,1,l_lt);
[m_rt,n_rt]=find_max(hotspot_rt,1,k_rt,1,l_rt);
[m_ld,n_ld]=find_max(hotspot_ld,1,k_ld,1,l_ld);
[m_rd,n_rd]=find_max(hotspot_rd,1,k_rd,1,l_rd);
misfit = zeros(4,1);
misfit(1,1) = (hotspot_rt(m_rt,n_rt)-hotspot_rt(m_lt,n_lt)).^2+(hotspot_ld(m_ld,n_ld)-hotspot_ld(m_lt,n_lt)).^2 …
+(hotspot_rd(m_rd,n_rd)-hotspot_rd(m_lt,n_lt)).^2;
misfit(2,1) = (hotspot_lt(m_rt,n_rt)-hotspot_lt(m_rt,n_rt)).^2+(hotspot_ld(m_rt,n_rt)-hotspot_ld(m_rt,n_rt)).^2 …
+(hotspot_rd(m_rt,n_rt)-hotspot_rd(m_rt,n_rt)).^2;
misfit(3,1) = (hotspot_lt(m_ld,n_ld)-hotspot_lt(m_ld,n_ld)).^2+(hotspot_rt(m_ld,n_ld)-hotspot_rt(m_ld,n_ld)).^2 …
+(hotspot_rd(m_ld,n_ld)-hotspot_rd(m_ld,n_ld)).^2;
misfit(4,1) = (hotspot_lt(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2+(hotspot_rt(m_rd,n_rd)-hotspot_rt(m_rd,n_rd)).^2 …
+(hotspot_ld(m_rd,n_rd)-hotspot_ld(m_rd,n_rd)).^2;
switch min(misfit)
case misfit(1,1)
mm = m_lt; nn = n_lt;
case misfit(2,1)
mm = m_rt; nn = n_rt;
case misfit(3,1)
mm = m_ld; nn = n_ld;
case misfit(4,1)
mm = m_rd; nn = n_rd;
end
Max_color = [ hotspot_rt(mm,nn) hotspot_ld(mm,nn) hotspot_rd(mm,nn)]
m = min([k_lt;k_rt;k_ld;k_rd]); n = min([l_lt;l_rt;l_ld;l_rd]);
misfit2 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit2(countm,countn) = (hotspot_rt(countm,countn)-hotspot_rt(m_rt,n_rt)).^2 …
+(hotspot_ld(countm,countn)-hotspot_ld(m_ld,n_ld)).^2+(hotspot_rd(countm,countn)-hotspot_rd(m_rd,n_rd)).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit2(countm,countn) == min(min(misfit2))
mmm = countm; nnn = countn;
end
end
end
Max_color2 = [hotspot_rt(mmm,nnn) hotspot_ld(mmm,nnn) hotspot_rd(mmm,nnn)]
%V_lt=126; H_lt=176;
%V_rt=125; H_rt=565;
%V_ld=398; H_ld=179;
%V_rd=388; H_rd=580;
center_LT=[V_lt,H_lt];
center_LD=[V_ld, H_ld];
center_RT=[V_rt,H_rt];
center_RD=[V_rd,H_rd];
LT=hotspot(V_lt-hscale:V_lt+hscale,H_lt-hscale:H_lt+hscale);
LD=hotspot(V_ld-hscale:V_ld+hscale,H_ld-hscale:H_ld+hscale);
RT=hotspot(V_rt-hscale:V_rt+hscale,H_rt-hscale:H_rt+hscale);
RD=hotspot(V_rd-hscale:V_rd+hscale,H_rd-hscale:H_rd+hscale);
% Find New centers and update them
[center_LT_new,Cor_LT] = imagematching (hotspot,RD,center_RT,scale); % use RT as target image
[center_LD_new,Cor_LD] = imagematching (hotspot,RD,center_LD,scale);
[center_RT_new,Cor_RT] = imagematching (hotspot,RD,center_RD,scale);
center_LD=center_LD_new;
center_LT=center_LT_new;
center_RT=center_RT_new;
[inter_center_LT,Cor_LT] = intermatching (hotspot,RD,center_LT_new,scale,subpixel);
[inter_center_LD,Cor_LD] = intermatching (hotspot,RD,center_LD_new,scale,subpixel);
[inter_center_RT,Cor_RT] = intermatching (hotspot,RD,center_RT_new,scale,subpixel);
center_LD=inter_center_LD;
center_LT=inter_center_LT;
center_RT=inter_center_RT;
Cor=[1 Cor_LT;Cor_LD Cor_RT];
V_ld=center_LD(1,1); H_ld=center_LD(1,2);
V_rt=center_LT(1,1); H_lt=center_LT(1,2);
V_rd=center_RD(1,1); H_rd=center_RD(1,2);
[XI_ld,YI_ld]=meshgrid(H_ld-hscale:H_ld+hscale,V_ld-hscale:V_ld+hscale);
[XI_lt,YI_lt]=meshgrid(H_lt-hscale:H_lt+hscale,V_lt-hscale:V_lt+hscale);
[XI_rd,YI_rd]=meshgrid(H_rd-hscale:H_rd+hscale,V_rd-hscale:V_rd+hscale);
LD=interp2(hotspot,XI_ld,YI_ld,’spline’); % update images
LT=interp2(hotspot,XI_lt,YI_lt,’spline’);
RD=interp2(hotspot,XI_rd,YI_rd,’spline’);
% Assuming you want to exclude 580 nm
lamda_LT=580*10^(-9);
lamda_RT=640*10^(-9);
lamda_LD=766*10^(-9);
lamda_RD=905*10^(-9);
planck=6.6*10^(-34);
Kb=1.38*10^(-23);
c=3*10^8;
%Wien_LT=Kb/planck/c*log(2*pi*planck*c*c./LT/lamda_LT^5);
Wien_RT=Kb/planck/c*log(2*pi*planck*c*c./RT/lamda_RT^5);
Wien_LD=Kb/planck/c*log(2*pi*planck*c*c./LD/lamda_LD^5);
Wien_RD=Kb/planck/c*log(2*pi*planck*c*c./RD/lamda_RD^5);
[m,n]=size(LD);
for i=1:m
for j=1:n
X=[1/lamda_RT 1/lamda_LD 1/lamda_RD]’;
%X=[1/lamda_650 1/lamda_800 1/lamda_900]’;
X_reg=[X ones(size(X))];
%Y=[Wien_LT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
Y=[Wien_RT(i,j) Wien_LD(i,j) Wien_RD(i,j)]’;
%R(i,j)=corrcoef(X,Y);
[T_inv,bint]=regress(Y,X_reg);
R(i,j)=corr(X,Y);
T(i,j)=1/T_inv(1,1);
Em(i,j)=exp(-T_inv(2,1)*planck*c/Kb);
T_err(i,j)=(1/bint(1,1)-1/bint(1,2))/2;
T_low(i,j)=1/bint(1,2);
T_high(i,j)=1/bint(1,1);

end
end
%% max in four regimes Jie add on Dec 5th 2015
[max_RD,Indexing] = max(RD(:))
max_LD = max(max(LD));max_RT = max(max(RT));
Max_color4 = [RT(Indexing) LD(Indexing) RD(Indexing)]
%% max grid search Jie add on April 1st
[m,n]=size(RD);
misfit3 = zeros(m,n);
for countm = 1:m
for countn = 1:n
misfit3(countm,countn) = (RT(countm,countn)-max_RT).^2 …
+(LD(countm,countn)-max_LD).^2+(RD(countm,countn)-max_RD).^2;
end
end
for countm = 1:m
for countn = 1:n
if misfit3(countm,countn) == min(min(misfit3))
m4 = countm; n4 = countn;
end
end
end
Max_color3 = [ RT(m4,n4) LD(m4,n4) RD(m4,n4)];
Max_Ih = [ RT(m4,:); LD(m4,:); RD(m4,:)];
Max_Iv = [ RT(:,n4)’; LD(:,n4)’; RD(:,n4)’];
figure(‘Name’,’hotspot’);
imagesc(hotspot_ob);
figure(‘Name’,’hot spot in 4 regions’);
subplot(2,2,2)
imagesc(RT);
subplot(2,2,3)
imagesc(LD);
subplot(2,2,4)
imagesc(RD);
figure(‘Name’,’T profile (pixel)’);
imagesc(T);
[Max_T, H]=max(max(T)); % maximum Temperature, horizontal position
[Max_T, V]=max(max(T’)); % maximum Temperature, vertical position
grid=0.48; % each pixel is 0.5um
X_position=(-H+1)*grid: grid: (scale-H+1)*grid;
figure(‘Name’,’Hirizontal T profile throughh highest T point’)
plot (X_position, T(V, :));
title(‘horizotal plot’)
xlabel(‘horizontal positon/um’)
ylabel (‘temperature/K’);
figure(‘Name’,’Vertical T profile throughh highest T point’)
Y_position=(-V+1)*grid: grid: (scale-V+1)*grid;
plot(Y_position,T(:,H));
title(‘Vertical plot’)
xlabel(‘Vertical positon/um’)
ylabel (‘temperature/K’);
[Y_p,X_p]=meshgrid(X_position, Y_position);
figure(‘Name’,’3D T profile’)
surf(X_p,Y_p,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
zlabel(‘Temperature(K)’)
shading interp;
figure(‘Name’,’T profile (pixel)’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
figure(‘Name’,’T profile (pixel) contour’);
imagesc(X_position,Y_position,T);
xlabel(‘Horizontal distance(um)’)
ylabel (‘Vetical distance(um)’);
colormap(‘turbo’)
colorbar;
hold on; % Keep the image displayed while adding contour
contour(X_position, Y_position, T, 10, ‘LineWidth’, 1, ‘LineColor’, ‘w’); % 40 contours, white lines
hold off; % Release the hold on the current figure
figure(‘Name’,’T error’);
imagesc(X_position,Y_position,T_err);
figure(‘Name’,’Emissivity Profile’)
imagesc(X_position,Y_position,log10(Em));
figure(‘Name’,’3D Emissivity profile’)
surf(X_p,Y_p,log10(Em));
H=scale/2; V=scale/2;% give the point needed to plot T cross section
figure(‘Name’,’Vertical Em/Emax vs T trough highest T point’)
plot(T(:,H),Em(:,H)/max(Em(:,H)),’–rs’);
title(‘Vertical plot’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
figure(‘Name’,’horizontal Em/Emax vs T trough highest T point’)
plot(T(V,:),Em(V,:)/max(Em(V,:)),’–rs’);
title(‘horizontal Em/Emax vs T’)
xlabel(‘Temperature’)
ylabel (‘Em/Em_max’);
% figure(12); % 3D image for intensity in 4 regions
% subplot(2,2,1)
% surf(X_p,Y_p,LT);
% subplot(2,2,2)
% surf(X_p,Y_p,RT);
% subplot(2,2,3)
% surf(X_p,Y_p,LD);
% subplot(2,2,4)
% surf(X_p,Y_p,RD)
figure (‘Name’,’Emissivity vs T over whole space’); plot(T,Em);

image result: colormap, contour, image analysis MATLAB Answers — New Questions

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I have been curious to understand the usage of the nohup feature in MATLAB with a Linux-based OS. While I have attempted to find answers to my questions on the internet, the instructions provided by users can be quite confusing to follow. It would be greatly appreciated if someone could assist me in resolving the following queries.
How to execute a MATLAB script file with nohup feature?
How to know if the MATLAB script is being executed on nohup command?
How to stop executing the MATLAB script midway, in case you start it by mistake?
Indeed, the queries and answers provided in this thread form a comprehensive guide for MATLAB users.I have been curious to understand the usage of the nohup feature in MATLAB with a Linux-based OS. While I have attempted to find answers to my questions on the internet, the instructions provided by users can be quite confusing to follow. It would be greatly appreciated if someone could assist me in resolving the following queries.
How to execute a MATLAB script file with nohup feature?
How to know if the MATLAB script is being executed on nohup command?
How to stop executing the MATLAB script midway, in case you start it by mistake?
Indeed, the queries and answers provided in this thread form a comprehensive guide for MATLAB users. I have been curious to understand the usage of the nohup feature in MATLAB with a Linux-based OS. While I have attempted to find answers to my questions on the internet, the instructions provided by users can be quite confusing to follow. It would be greatly appreciated if someone could assist me in resolving the following queries.
How to execute a MATLAB script file with nohup feature?
How to know if the MATLAB script is being executed on nohup command?
How to stop executing the MATLAB script midway, in case you start it by mistake?
Indeed, the queries and answers provided in this thread form a comprehensive guide for MATLAB users. matlab, linux, nohup, gui MATLAB Answers — New Questions

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