My situation is
1. external ADC samples from one channel and transmit to Serial port Via Uart and then switches over to second channel to do same and then third.
2. I manage to view data in Hterm and it looked quite fine.
3. I want to plot it live in matlab- I know there are ways to do it but can someone here explain me a basic step by step to achieve my objective?
I have basic idea of what i should be doing
setup serial communication.
create array to store uart values
calculate voltage values
plot live values
It would be nice if someone points out me for where to look for point 2 and 4 specifically.My situation is
1. external ADC samples from one channel and transmit to Serial port Via Uart and then switches over to second channel to do same and then third.
2. I manage to view data in Hterm and it looked quite fine.
3. I want to plot it live in matlab- I know there are ways to do it but can someone here explain me a basic step by step to achieve my objective?
I have basic idea of what i should be doing
setup serial communication.
create array to store uart values
calculate voltage values
plot live values
It would be nice if someone points out me for where to look for point 2 and 4 specifically. My situation is
1. external ADC samples from one channel and transmit to Serial port Via Uart and then switches over to second channel to do same and then third.
2. I manage to view data in Hterm and it looked quite fine.
3. I want to plot it live in matlab- I know there are ways to do it but can someone here explain me a basic step by step to achieve my objective?
I have basic idea of what i should be doing
setup serial communication.
create array to store uart values
calculate voltage values
plot live values
It would be nice if someone points out me for where to look for point 2 and 4 specifically. msp430, adc, uart, serial MATLAB Answers — New Questions

​

Hello,
i have a problem at the calculation / estimation of a transfer function when using frequency-domain data.
My task is to get the continious transfer function for further simulation from measured magnitude and phase response by an impedance analyser.
The quality of the estimated curve is ok, but the problem is that the curve is shifted in omega and i cannot observe the problem.
The frequency limits of the measured data are 20 Hz to 5000 Hz with the units (freq. [Hz], magn [-], phase [°]).
Figure 1 and Figrue 2 shows the magnitude and phase of the measured data.
In Figure 3 shows the bode plot with idfrd() / frd() and the estimated TF.
Here the values are shiftet.
What ist the problem in this case?

format short g
clear
matt = readmatrix(‘data.CSV’);
fre = matt(1:300,1);
frerad = fre.*(pi/180);

abso = matt(1:300,2);
absdb = 20*log10(abso);

phdeg = matt(1:300,3);
phrad = phdeg.*(pi/180);

% options = bodeoptions;
% options.FreqUnits = ‘Hz’;

figure(1)
semilogx(fre,absdb)
legend()
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
grid()
figure(2)
semilogx(fre,phdeg)
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
legend()
grid()

complexVector = abso.* exp(1j*phrad);
vect_mess = idfrd(complexVector,frerad,0);
% vect_mess = frd(complexVector,frerad);
tf_estimated = tfest(vect_mess,3)
figure(3)
bode(vect_mess,tf_estimated )
legend()
grid()Hello,
i have a problem at the calculation / estimation of a transfer function when using frequency-domain data.
My task is to get the continious transfer function for further simulation from measured magnitude and phase response by an impedance analyser.
The quality of the estimated curve is ok, but the problem is that the curve is shifted in omega and i cannot observe the problem.
The frequency limits of the measured data are 20 Hz to 5000 Hz with the units (freq. [Hz], magn [-], phase [°]).
Figure 1 and Figrue 2 shows the magnitude and phase of the measured data.
In Figure 3 shows the bode plot with idfrd() / frd() and the estimated TF.
Here the values are shiftet.
What ist the problem in this case?

format short g
clear
matt = readmatrix(‘data.CSV’);
fre = matt(1:300,1);
frerad = fre.*(pi/180);

abso = matt(1:300,2);
absdb = 20*log10(abso);

phdeg = matt(1:300,3);
phrad = phdeg.*(pi/180);

% options = bodeoptions;
% options.FreqUnits = ‘Hz’;

figure(1)
semilogx(fre,absdb)
legend()
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
grid()
figure(2)
semilogx(fre,phdeg)
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
legend()
grid()

complexVector = abso.* exp(1j*phrad);
vect_mess = idfrd(complexVector,frerad,0);
% vect_mess = frd(complexVector,frerad);
tf_estimated = tfest(vect_mess,3)
figure(3)
bode(vect_mess,tf_estimated )
legend()
grid() Hello,
i have a problem at the calculation / estimation of a transfer function when using frequency-domain data.
My task is to get the continious transfer function for further simulation from measured magnitude and phase response by an impedance analyser.
The quality of the estimated curve is ok, but the problem is that the curve is shifted in omega and i cannot observe the problem.
The frequency limits of the measured data are 20 Hz to 5000 Hz with the units (freq. [Hz], magn [-], phase [°]).
Figure 1 and Figrue 2 shows the magnitude and phase of the measured data.
In Figure 3 shows the bode plot with idfrd() / frd() and the estimated TF.
Here the values are shiftet.
What ist the problem in this case?

format short g
clear
matt = readmatrix(‘data.CSV’);
fre = matt(1:300,1);
frerad = fre.*(pi/180);

abso = matt(1:300,2);
absdb = 20*log10(abso);

phdeg = matt(1:300,3);
phrad = phdeg.*(pi/180);

% options = bodeoptions;
% options.FreqUnits = ‘Hz’;

figure(1)
semilogx(fre,absdb)
legend()
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
grid()
figure(2)
semilogx(fre,phdeg)
ylabel(‘magn. [dB]’)
xlabel(‘freq. [Hz]’)
legend()
grid()

complexVector = abso.* exp(1j*phrad);
vect_mess = idfrd(complexVector,frerad,0);
% vect_mess = frd(complexVector,frerad);
tf_estimated = tfest(vect_mess,3)
figure(3)
bode(vect_mess,tf_estimated )
legend()
grid() transfer function, estimation tfest MATLAB Answers — New Questions

​

Hello there I am trying to train a ML model with leave-out-one trial cross validation. Right now I have input data stored in the 1×10 cell array: "XTrain" with each cell containing the prediction inputs for all 10 trials and another 1×10 cell array: "YTrain" that contains the correposding continous variable we are trying to predict/output.

net = connectLayers(net,outputName,"fc");

% Specify training options
options = trainingOptions(‘adam’, …
‘MaxEpochs’, 60, …
‘MiniBatchSize’, 1, …
‘SequenceLength’, ‘longest’, …
‘InputDataFormats’, ‘CTB’, …
‘Plots’, ‘training-progress’, …
‘Metrics’, ‘rmse’, …
‘Verbose’, 0 …
‘Validation);

% Train the network
net = trainnet(XTrain,YTrain,net,"mse",options)
I have built my model’s network architecture stored in "net", but I am unsure of how to incorporte "leave out one trial" validation during training and then test my model’s performance. I want the model to pull out one trial at a time and then train the model and continue to do this for all 10 trials so that I end up with one final network trained and validated on all the trials. But I also want to have data to test the model’s performance? Do I need to create a loop for this? or is there a way I can specify this in the training options? Any help would be greatly appreciated!Hello there I am trying to train a ML model with leave-out-one trial cross validation. Right now I have input data stored in the 1×10 cell array: "XTrain" with each cell containing the prediction inputs for all 10 trials and another 1×10 cell array: "YTrain" that contains the correposding continous variable we are trying to predict/output.

net = connectLayers(net,outputName,"fc");

% Specify training options
options = trainingOptions(‘adam’, …
‘MaxEpochs’, 60, …
‘MiniBatchSize’, 1, …
‘SequenceLength’, ‘longest’, …
‘InputDataFormats’, ‘CTB’, …
‘Plots’, ‘training-progress’, …
‘Metrics’, ‘rmse’, …
‘Verbose’, 0 …
‘Validation);

% Train the network
net = trainnet(XTrain,YTrain,net,"mse",options)
I have built my model’s network architecture stored in "net", but I am unsure of how to incorporte "leave out one trial" validation during training and then test my model’s performance. I want the model to pull out one trial at a time and then train the model and continue to do this for all 10 trials so that I end up with one final network trained and validated on all the trials. But I also want to have data to test the model’s performance? Do I need to create a loop for this? or is there a way I can specify this in the training options? Any help would be greatly appreciated! Hello there I am trying to train a ML model with leave-out-one trial cross validation. Right now I have input data stored in the 1×10 cell array: "XTrain" with each cell containing the prediction inputs for all 10 trials and another 1×10 cell array: "YTrain" that contains the correposding continous variable we are trying to predict/output.

net = connectLayers(net,outputName,"fc");

% Specify training options
options = trainingOptions(‘adam’, …
‘MaxEpochs’, 60, …
‘MiniBatchSize’, 1, …
‘SequenceLength’, ‘longest’, …
‘InputDataFormats’, ‘CTB’, …
‘Plots’, ‘training-progress’, …
‘Metrics’, ‘rmse’, …
‘Verbose’, 0 …
‘Validation);

% Train the network
net = trainnet(XTrain,YTrain,net,"mse",options)
I have built my model’s network architecture stored in "net", but I am unsure of how to incorporte "leave out one trial" validation during training and then test my model’s performance. I want the model to pull out one trial at a time and then train the model and continue to do this for all 10 trials so that I end up with one final network trained and validated on all the trials. But I also want to have data to test the model’s performance? Do I need to create a loop for this? or is there a way I can specify this in the training options? Any help would be greatly appreciated! machine learning, validation, neural network, trainnet MATLAB Answers — New Questions

​

Hi, I would like to have to automatize a procedure to extract data from different URLs, One example of one URL link is the following:
% Generating the URL link
url=’https://earthquake.usgs.gov/fdsnws/event/1/query?format=quakeml&eventid=us6000n8tq’;
% Reading the data
data=webread(url);
The variable “data” contains huge amount of information that I would like to structure in order to access and retrieve data easily without the need of creating a xml file.
I would appreciate the help.Hi, I would like to have to automatize a procedure to extract data from different URLs, One example of one URL link is the following:
% Generating the URL link
url=’https://earthquake.usgs.gov/fdsnws/event/1/query?format=quakeml&eventid=us6000n8tq’;
% Reading the data
data=webread(url);
The variable “data” contains huge amount of information that I would like to structure in order to access and retrieve data easily without the need of creating a xml file.
I would appreciate the help. Hi, I would like to have to automatize a procedure to extract data from different URLs, One example of one URL link is the following:
% Generating the URL link
url=’https://earthquake.usgs.gov/fdsnws/event/1/query?format=quakeml&eventid=us6000n8tq’;
% Reading the data
data=webread(url);
The variable “data” contains huge amount of information that I would like to structure in order to access and retrieve data easily without the need of creating a xml file.
I would appreciate the help. structuring data from webread MATLAB Answers — New Questions

​

what the error (Error using Untitled18 (line 12)
Conversion to cell from double is not possible.)
% Ensure all columns except the last one are numeric
for i = 1:(width(data) – 1)
if iscell(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
elseif ischar(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
end
endwhat the error (Error using Untitled18 (line 12)
Conversion to cell from double is not possible.)
% Ensure all columns except the last one are numeric
for i = 1:(width(data) – 1)
if iscell(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
elseif ischar(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
end
end what the error (Error using Untitled18 (line 12)
Conversion to cell from double is not possible.)
% Ensure all columns except the last one are numeric
for i = 1:(width(data) – 1)
if iscell(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
elseif ischar(data{:, i})
data{:, i} = grp2idx(categorical(data{:, i}));
end
end axes, optimization MATLAB Answers — New Questions

​

Good day,
I have a challenge launching MATLAB2024a. I get an error message of "Why do I get an error of "You do not have a valid license file. How can I resolve this issue?
Your help will be much appreciated.
Kind regards,Good day,
I have a challenge launching MATLAB2024a. I get an error message of "Why do I get an error of "You do not have a valid license file. How can I resolve this issue?
Your help will be much appreciated.
Kind regards, Good day,
I have a challenge launching MATLAB2024a. I get an error message of "Why do I get an error of "You do not have a valid license file. How can I resolve this issue?
Your help will be much appreciated.
Kind regards, matlab, matlab2024a MATLAB Answers — New Questions

​

I am trying to include a field value in a ThingHTTP GET request but have not been successful.
For example, I have have successfully used
https://myurl.com/site?value=12.34
to send a specifice value to an external site, but was unsuccessful when I tried to send a ThingSpeak channel field value in a similar way. I used the %% method, which works for ThingTweet, but that didn’t seem to work here. e.g.
https://myurl.com/site?value=%%channel_1234567_field_1%%
Am I doing something wrong, or is there an alternative method for doing this?I am trying to include a field value in a ThingHTTP GET request but have not been successful.
For example, I have have successfully used
https://myurl.com/site?value=12.34
to send a specifice value to an external site, but was unsuccessful when I tried to send a ThingSpeak channel field value in a similar way. I used the %% method, which works for ThingTweet, but that didn’t seem to work here. e.g.
https://myurl.com/site?value=%%channel_1234567_field_1%%
Am I doing something wrong, or is there an alternative method for doing this? I am trying to include a field value in a ThingHTTP GET request but have not been successful.
For example, I have have successfully used
https://myurl.com/site?value=12.34
to send a specifice value to an external site, but was unsuccessful when I tried to send a ThingSpeak channel field value in a similar way. I used the %% method, which works for ThingTweet, but that didn’t seem to work here. e.g.
https://myurl.com/site?value=%%channel_1234567_field_1%%
Am I doing something wrong, or is there an alternative method for doing this? thinghttp MATLAB Answers — New Questions

​

% Example5_5.m
% Solution to Example 5.5. This program calculates and plots
% the concentration of cell mass, concentration of penicillin,
% optimal temperature profile, and adjoint variable of a batch
% penicillin fermentor. It uses the function COLLOCATION to
% solve the set of system and adjoint equations.
clear
clc
clf
% Input data
w = input(‘ Enter w”s as a vector : ‘);
y0 = input(‘ Vector of known initial conditions = ‘);
yf = input(‘ Vector of final conditions = ‘);
guess = input(‘ Vector of guessed initial conditions = ‘);
fname = input(‘n M-file containing the set of differential equations : ‘);
fth = input(‘ M-file containing the necessary condition function : ‘);
n = input(‘ Number of internal collocation points = ‘);
rho = input(‘ Relaxation factor = ‘);
% Solution of the set of differential equations
[t,y] = collocation(fname,0,1,y0,yf,guess,n,rho,[],w,fth);
% Temperature changes
for k = 1:n+2
options=optimset;
theta(k) = fzero(fth,30,options,y(:,k),w);
end
% Plotting the results
subplot(2,2,1), plot(t,y(1,:))
xlabel(‘Time’)
ylabel(‘Cell’)
title(‘(a)’)
subplot(2,2,2), plot(t,y(2,:))
xlabel(‘Time’)
ylabel(‘Penicillin’)
title(‘(b)’)
subplot(2,2,3), plot(t,y(3,:))
xlabel(‘Time’)
ylabel(‘First Adjoint’)
title(‘(c)’)
subplot(2,2,4), plot(t,theta)
xlabel(‘Time’)
ylabel(‘Temperature (deg C)’)
title(‘(d)’)

function f = Ex5_5_func(t,y,w,fth)
% Function Ex5_5_func.M
% This function introduces the set of ordinary differential
% equations used in Example 5.5.
% Temperature
options=optimset;
theta = fzero(fth,30,options,y,w);
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b1<0, b1=0; end
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b2<0, b2=1e-6; end
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
if b3<0, b3=0; end
% Evaluating the function values
f(1) = b1*y(1) – b1/b2*y(1)^2;
f(2) = b3*y(1);
f(3) = -b1*y(3) + 2*b1/b2*y(1)*y(3) – b3;
f = f’; % Make it a column vector

function ftheta = Ex5_5_theta(theta,y,w)
% Function Ex5_5_theta.M
% This function calculates the value of the necessary condition
% as a function of the temperature (theta). It is used in solving
% Example 5.5.
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db1 = w(1)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db2 = w(4)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
db3 = w(5)*(-w(2))*2*(theta-w(6)) / (1-w(2)*(25-w(6))^2);
% The function
ftheta = y(3)*(y(1)*db1-y(1)^2*(db1*b2-db2*b1)/b2^2)+y(1)*db3;

function [x,y] = collocation(ODEfile,x0,xf,y0,yf,guess,n,rho,tol,varargin)
%COLLOCATION Solves a boundary value set of ordinary differential
% equations by the orthogonal collocation method.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N) integrates the set of
% ordinary differential equations from X0 to XF by the Nth-degree
% orthogonal collocation method. The equations are contained in
% the M-file F.M. Y0, YF, and GAMMA are the vectors of initial
% conditions, final conditions, and starting guesses respectively.
% The function returns the independent variable in the vector X
% and the set of dependent variables in the matrix Y.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N,RHO,TOL,P1,P2,…)
% uses relaxation factor RHO and tolerance TOL for convergence
% test. Additional parameters P1, P2, … are passed directly to
% the function F. Pass an empty matrix for RHO or TOL to use the
% default value.
%
% See also SHOOTING
% (c) N. Mostoufi & A. Constantinides
% January 1, 1999
% Initialization
if nargin < 7 | isempty(n)
n = 1;
end
if nargin < 8 | isempty(rho)
rho = 1;
end
if nargin < 9 | isempty(tol)
tol = 1e-6;
end
y0 = (y0(:).’)’; % Make sure it’s a column vector
yf = (yf(:).’)’; % Make sure it’s a column vector
guess = (guess(:).’)’; % Make sure it’s a column vector
% Checking the number of guesses
if length(yf) ~= length(guess)
error(‘ The number of guessed conditions is not equal to the number of final conditions.’)
end
r = length(y0); % Number of initial conditions
m = r + length(yf); % Number of boundary conditions
% Checking the number of equations
ftest = feval(ODEfile,x0,[y0 ; guess],varargin{:});
if length(ftest) ~= m
error(‘ The number of equations is not equal to the number of boundary conditions.’)
end
fprintf(‘n Integrating. Please wait.nn’)
% Coefficients of the Legendre polynomial
for k = 0 : n/2
cl(2*k+1) = (-1)^k * gamma(2*n-2*k+1) / …
(2^n * gamma(k+1) * gamma(n-k+1) * gamma(n-2*k+1));
if k < n/2
cl(2*k+2) = 0;
end
end
zl = roots(cl); % Roots of the Legendre polynomial
z = [-1; sort(zl); 1]; % Collocation points (z)
x = (xf-x0)*z/2+(xf+x0)/2; % Collocation points (x)
% Bulding the vector of starting values of the dependent variables
[p,q] = RK(ODEfile,x0,xf,(xf-x0)/20,[y0 ; guess],2,varargin{:});
for k = 1:m
y(k,:) = spline(p,q(k,:),x’);
end
y(r+1:m,end) = yf(1:m-r);
% Building the matrix A
Q(:,1) = ones(n+2,1);
C(:,1) = zeros(n+2,1);
for i = 1:n+1
Q(:,i+1) = x.^i;
C(:,i+1) = i*x.^(i-1);
end
A = C*inv(Q);
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
Am(k1:k2,k1:k2) = A; % Building the matrix Am
Y(k1:k2) = y(k,:); % Building the vector Y
end
Y = Y’; % Make it a column vector
Y1 = Y * 1.1;
iter = 0;
maxiter = 100;
F = zeros(m*(n+2),1);
Fa = zeros(m*(n+2),1);
dY = zeros(m*(n+2),1);
position = []; % Collocation points excluding boundary conditions
for k = 1:m
if k <= r
position = [position, (k-1)*(n+2)+[2:n+2] ];
else
position = [position, (k-1)*(n+2)+[1:n+1] ];
end
end
% Newton’s method
while max(abs(Y1 – Y)) > tol & iter < maxiter
iter = iter + 1;
fprintf(‘ Iteration %3dn’,iter)
Y1 = Y;
% Building the vector F
for k = 1:n+2
F(k : n+2 : (m-1)*(n+2)+k) = …
feval(ODEfile,x(k),Y(k : n+2 : (m-1)*(n+2)+k),varargin{:});
end
fnk = Am * Y – F;

% Set dY for derivation
for k = 1:m*(n+1)
if Y(position(k)) ~= 0
dY(position(k)) = Y(position(k)) / 100;
else
dY(position(k)) = 0.01;
end
end

% Calculation of the Jacobian matrix
for k = 1:m
for kk = 1:n+1
a = Y;
nc = (k-1)*(n+1)+kk;
a(position(nc)) = Y(position(nc)) + dY(position(nc));
for kkk = 1:n+2
Fa(kkk : n+2 : (m-1)*(n+2)+kkk) = …
feval(ODEfile,x(kkk),a(kkk:n+2:(m-1)*(n+2)+kkk),varargin{:});
end
fnka = Am * a – Fa;
jacob(:,nc) = (fnka(position) – fnk(position))…
/ dY(position(nc));
end
end
% Next approximation of the roots
if det(jacob) == 0
Y(position) = Y(position) + max([abs(dY(position)); 1.1*tol]);
else
Y(position) = Y(position) – rho * inv(jacob) * fnk(position);
end
end
% Rearranging the y’s
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
y(k,:) = Y(k1:k2)’;
end
x = x’;
if iter >= maxiter
disp(‘Warning : Maximum iterations reached.’)
end% Example5_5.m
% Solution to Example 5.5. This program calculates and plots
% the concentration of cell mass, concentration of penicillin,
% optimal temperature profile, and adjoint variable of a batch
% penicillin fermentor. It uses the function COLLOCATION to
% solve the set of system and adjoint equations.
clear
clc
clf
% Input data
w = input(‘ Enter w”s as a vector : ‘);
y0 = input(‘ Vector of known initial conditions = ‘);
yf = input(‘ Vector of final conditions = ‘);
guess = input(‘ Vector of guessed initial conditions = ‘);
fname = input(‘n M-file containing the set of differential equations : ‘);
fth = input(‘ M-file containing the necessary condition function : ‘);
n = input(‘ Number of internal collocation points = ‘);
rho = input(‘ Relaxation factor = ‘);
% Solution of the set of differential equations
[t,y] = collocation(fname,0,1,y0,yf,guess,n,rho,[],w,fth);
% Temperature changes
for k = 1:n+2
options=optimset;
theta(k) = fzero(fth,30,options,y(:,k),w);
end
% Plotting the results
subplot(2,2,1), plot(t,y(1,:))
xlabel(‘Time’)
ylabel(‘Cell’)
title(‘(a)’)
subplot(2,2,2), plot(t,y(2,:))
xlabel(‘Time’)
ylabel(‘Penicillin’)
title(‘(b)’)
subplot(2,2,3), plot(t,y(3,:))
xlabel(‘Time’)
ylabel(‘First Adjoint’)
title(‘(c)’)
subplot(2,2,4), plot(t,theta)
xlabel(‘Time’)
ylabel(‘Temperature (deg C)’)
title(‘(d)’)

function f = Ex5_5_func(t,y,w,fth)
% Function Ex5_5_func.M
% This function introduces the set of ordinary differential
% equations used in Example 5.5.
% Temperature
options=optimset;
theta = fzero(fth,30,options,y,w);
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b1<0, b1=0; end
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b2<0, b2=1e-6; end
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
if b3<0, b3=0; end
% Evaluating the function values
f(1) = b1*y(1) – b1/b2*y(1)^2;
f(2) = b3*y(1);
f(3) = -b1*y(3) + 2*b1/b2*y(1)*y(3) – b3;
f = f’; % Make it a column vector

function ftheta = Ex5_5_theta(theta,y,w)
% Function Ex5_5_theta.M
% This function calculates the value of the necessary condition
% as a function of the temperature (theta). It is used in solving
% Example 5.5.
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db1 = w(1)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db2 = w(4)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
db3 = w(5)*(-w(2))*2*(theta-w(6)) / (1-w(2)*(25-w(6))^2);
% The function
ftheta = y(3)*(y(1)*db1-y(1)^2*(db1*b2-db2*b1)/b2^2)+y(1)*db3;

function [x,y] = collocation(ODEfile,x0,xf,y0,yf,guess,n,rho,tol,varargin)
%COLLOCATION Solves a boundary value set of ordinary differential
% equations by the orthogonal collocation method.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N) integrates the set of
% ordinary differential equations from X0 to XF by the Nth-degree
% orthogonal collocation method. The equations are contained in
% the M-file F.M. Y0, YF, and GAMMA are the vectors of initial
% conditions, final conditions, and starting guesses respectively.
% The function returns the independent variable in the vector X
% and the set of dependent variables in the matrix Y.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N,RHO,TOL,P1,P2,…)
% uses relaxation factor RHO and tolerance TOL for convergence
% test. Additional parameters P1, P2, … are passed directly to
% the function F. Pass an empty matrix for RHO or TOL to use the
% default value.
%
% See also SHOOTING
% (c) N. Mostoufi & A. Constantinides
% January 1, 1999
% Initialization
if nargin < 7 | isempty(n)
n = 1;
end
if nargin < 8 | isempty(rho)
rho = 1;
end
if nargin < 9 | isempty(tol)
tol = 1e-6;
end
y0 = (y0(:).’)’; % Make sure it’s a column vector
yf = (yf(:).’)’; % Make sure it’s a column vector
guess = (guess(:).’)’; % Make sure it’s a column vector
% Checking the number of guesses
if length(yf) ~= length(guess)
error(‘ The number of guessed conditions is not equal to the number of final conditions.’)
end
r = length(y0); % Number of initial conditions
m = r + length(yf); % Number of boundary conditions
% Checking the number of equations
ftest = feval(ODEfile,x0,[y0 ; guess],varargin{:});
if length(ftest) ~= m
error(‘ The number of equations is not equal to the number of boundary conditions.’)
end
fprintf(‘n Integrating. Please wait.nn’)
% Coefficients of the Legendre polynomial
for k = 0 : n/2
cl(2*k+1) = (-1)^k * gamma(2*n-2*k+1) / …
(2^n * gamma(k+1) * gamma(n-k+1) * gamma(n-2*k+1));
if k < n/2
cl(2*k+2) = 0;
end
end
zl = roots(cl); % Roots of the Legendre polynomial
z = [-1; sort(zl); 1]; % Collocation points (z)
x = (xf-x0)*z/2+(xf+x0)/2; % Collocation points (x)
% Bulding the vector of starting values of the dependent variables
[p,q] = RK(ODEfile,x0,xf,(xf-x0)/20,[y0 ; guess],2,varargin{:});
for k = 1:m
y(k,:) = spline(p,q(k,:),x’);
end
y(r+1:m,end) = yf(1:m-r);
% Building the matrix A
Q(:,1) = ones(n+2,1);
C(:,1) = zeros(n+2,1);
for i = 1:n+1
Q(:,i+1) = x.^i;
C(:,i+1) = i*x.^(i-1);
end
A = C*inv(Q);
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
Am(k1:k2,k1:k2) = A; % Building the matrix Am
Y(k1:k2) = y(k,:); % Building the vector Y
end
Y = Y’; % Make it a column vector
Y1 = Y * 1.1;
iter = 0;
maxiter = 100;
F = zeros(m*(n+2),1);
Fa = zeros(m*(n+2),1);
dY = zeros(m*(n+2),1);
position = []; % Collocation points excluding boundary conditions
for k = 1:m
if k <= r
position = [position, (k-1)*(n+2)+[2:n+2] ];
else
position = [position, (k-1)*(n+2)+[1:n+1] ];
end
end
% Newton’s method
while max(abs(Y1 – Y)) > tol & iter < maxiter
iter = iter + 1;
fprintf(‘ Iteration %3dn’,iter)
Y1 = Y;
% Building the vector F
for k = 1:n+2
F(k : n+2 : (m-1)*(n+2)+k) = …
feval(ODEfile,x(k),Y(k : n+2 : (m-1)*(n+2)+k),varargin{:});
end
fnk = Am * Y – F;

% Set dY for derivation
for k = 1:m*(n+1)
if Y(position(k)) ~= 0
dY(position(k)) = Y(position(k)) / 100;
else
dY(position(k)) = 0.01;
end
end

% Calculation of the Jacobian matrix
for k = 1:m
for kk = 1:n+1
a = Y;
nc = (k-1)*(n+1)+kk;
a(position(nc)) = Y(position(nc)) + dY(position(nc));
for kkk = 1:n+2
Fa(kkk : n+2 : (m-1)*(n+2)+kkk) = …
feval(ODEfile,x(kkk),a(kkk:n+2:(m-1)*(n+2)+kkk),varargin{:});
end
fnka = Am * a – Fa;
jacob(:,nc) = (fnka(position) – fnk(position))…
/ dY(position(nc));
end
end
% Next approximation of the roots
if det(jacob) == 0
Y(position) = Y(position) + max([abs(dY(position)); 1.1*tol]);
else
Y(position) = Y(position) – rho * inv(jacob) * fnk(position);
end
end
% Rearranging the y’s
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
y(k,:) = Y(k1:k2)’;
end
x = x’;
if iter >= maxiter
disp(‘Warning : Maximum iterations reached.’)
end % Example5_5.m
% Solution to Example 5.5. This program calculates and plots
% the concentration of cell mass, concentration of penicillin,
% optimal temperature profile, and adjoint variable of a batch
% penicillin fermentor. It uses the function COLLOCATION to
% solve the set of system and adjoint equations.
clear
clc
clf
% Input data
w = input(‘ Enter w”s as a vector : ‘);
y0 = input(‘ Vector of known initial conditions = ‘);
yf = input(‘ Vector of final conditions = ‘);
guess = input(‘ Vector of guessed initial conditions = ‘);
fname = input(‘n M-file containing the set of differential equations : ‘);
fth = input(‘ M-file containing the necessary condition function : ‘);
n = input(‘ Number of internal collocation points = ‘);
rho = input(‘ Relaxation factor = ‘);
% Solution of the set of differential equations
[t,y] = collocation(fname,0,1,y0,yf,guess,n,rho,[],w,fth);
% Temperature changes
for k = 1:n+2
options=optimset;
theta(k) = fzero(fth,30,options,y(:,k),w);
end
% Plotting the results
subplot(2,2,1), plot(t,y(1,:))
xlabel(‘Time’)
ylabel(‘Cell’)
title(‘(a)’)
subplot(2,2,2), plot(t,y(2,:))
xlabel(‘Time’)
ylabel(‘Penicillin’)
title(‘(b)’)
subplot(2,2,3), plot(t,y(3,:))
xlabel(‘Time’)
ylabel(‘First Adjoint’)
title(‘(c)’)
subplot(2,2,4), plot(t,theta)
xlabel(‘Time’)
ylabel(‘Temperature (deg C)’)
title(‘(d)’)

function f = Ex5_5_func(t,y,w,fth)
% Function Ex5_5_func.M
% This function introduces the set of ordinary differential
% equations used in Example 5.5.
% Temperature
options=optimset;
theta = fzero(fth,30,options,y,w);
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b1<0, b1=0; end
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
if b2<0, b2=1e-6; end
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
if b3<0, b3=0; end
% Evaluating the function values
f(1) = b1*y(1) – b1/b2*y(1)^2;
f(2) = b3*y(1);
f(3) = -b1*y(3) + 2*b1/b2*y(1)*y(3) – b3;
f = f’; % Make it a column vector

function ftheta = Ex5_5_theta(theta,y,w)
% Function Ex5_5_theta.M
% This function calculates the value of the necessary condition
% as a function of the temperature (theta). It is used in solving
% Example 5.5.
% Calculating the b’s
b1 = w(1) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db1 = w(1)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b2 = w(4) * (1-w(2)*(theta-w(3))^2) / (1-w(2)*(25-w(3))^2);
db2 = w(4)*(-w(2))*2*(theta-w(3)) / (1-w(2)*(25-w(3))^2);
b3 = w(5) * (1-w(2)*(theta-w(6))^2) / (1-w(2)*(25-w(6))^2);
db3 = w(5)*(-w(2))*2*(theta-w(6)) / (1-w(2)*(25-w(6))^2);
% The function
ftheta = y(3)*(y(1)*db1-y(1)^2*(db1*b2-db2*b1)/b2^2)+y(1)*db3;

function [x,y] = collocation(ODEfile,x0,xf,y0,yf,guess,n,rho,tol,varargin)
%COLLOCATION Solves a boundary value set of ordinary differential
% equations by the orthogonal collocation method.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N) integrates the set of
% ordinary differential equations from X0 to XF by the Nth-degree
% orthogonal collocation method. The equations are contained in
% the M-file F.M. Y0, YF, and GAMMA are the vectors of initial
% conditions, final conditions, and starting guesses respectively.
% The function returns the independent variable in the vector X
% and the set of dependent variables in the matrix Y.
%
% [X,Y]=COLLOCATION(‘F’,X0,XF,Y0,YF,GAMMA,N,RHO,TOL,P1,P2,…)
% uses relaxation factor RHO and tolerance TOL for convergence
% test. Additional parameters P1, P2, … are passed directly to
% the function F. Pass an empty matrix for RHO or TOL to use the
% default value.
%
% See also SHOOTING
% (c) N. Mostoufi & A. Constantinides
% January 1, 1999
% Initialization
if nargin < 7 | isempty(n)
n = 1;
end
if nargin < 8 | isempty(rho)
rho = 1;
end
if nargin < 9 | isempty(tol)
tol = 1e-6;
end
y0 = (y0(:).’)’; % Make sure it’s a column vector
yf = (yf(:).’)’; % Make sure it’s a column vector
guess = (guess(:).’)’; % Make sure it’s a column vector
% Checking the number of guesses
if length(yf) ~= length(guess)
error(‘ The number of guessed conditions is not equal to the number of final conditions.’)
end
r = length(y0); % Number of initial conditions
m = r + length(yf); % Number of boundary conditions
% Checking the number of equations
ftest = feval(ODEfile,x0,[y0 ; guess],varargin{:});
if length(ftest) ~= m
error(‘ The number of equations is not equal to the number of boundary conditions.’)
end
fprintf(‘n Integrating. Please wait.nn’)
% Coefficients of the Legendre polynomial
for k = 0 : n/2
cl(2*k+1) = (-1)^k * gamma(2*n-2*k+1) / …
(2^n * gamma(k+1) * gamma(n-k+1) * gamma(n-2*k+1));
if k < n/2
cl(2*k+2) = 0;
end
end
zl = roots(cl); % Roots of the Legendre polynomial
z = [-1; sort(zl); 1]; % Collocation points (z)
x = (xf-x0)*z/2+(xf+x0)/2; % Collocation points (x)
% Bulding the vector of starting values of the dependent variables
[p,q] = RK(ODEfile,x0,xf,(xf-x0)/20,[y0 ; guess],2,varargin{:});
for k = 1:m
y(k,:) = spline(p,q(k,:),x’);
end
y(r+1:m,end) = yf(1:m-r);
% Building the matrix A
Q(:,1) = ones(n+2,1);
C(:,1) = zeros(n+2,1);
for i = 1:n+1
Q(:,i+1) = x.^i;
C(:,i+1) = i*x.^(i-1);
end
A = C*inv(Q);
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
Am(k1:k2,k1:k2) = A; % Building the matrix Am
Y(k1:k2) = y(k,:); % Building the vector Y
end
Y = Y’; % Make it a column vector
Y1 = Y * 1.1;
iter = 0;
maxiter = 100;
F = zeros(m*(n+2),1);
Fa = zeros(m*(n+2),1);
dY = zeros(m*(n+2),1);
position = []; % Collocation points excluding boundary conditions
for k = 1:m
if k <= r
position = [position, (k-1)*(n+2)+[2:n+2] ];
else
position = [position, (k-1)*(n+2)+[1:n+1] ];
end
end
% Newton’s method
while max(abs(Y1 – Y)) > tol & iter < maxiter
iter = iter + 1;
fprintf(‘ Iteration %3dn’,iter)
Y1 = Y;
% Building the vector F
for k = 1:n+2
F(k : n+2 : (m-1)*(n+2)+k) = …
feval(ODEfile,x(k),Y(k : n+2 : (m-1)*(n+2)+k),varargin{:});
end
fnk = Am * Y – F;

% Set dY for derivation
for k = 1:m*(n+1)
if Y(position(k)) ~= 0
dY(position(k)) = Y(position(k)) / 100;
else
dY(position(k)) = 0.01;
end
end

% Calculation of the Jacobian matrix
for k = 1:m
for kk = 1:n+1
a = Y;
nc = (k-1)*(n+1)+kk;
a(position(nc)) = Y(position(nc)) + dY(position(nc));
for kkk = 1:n+2
Fa(kkk : n+2 : (m-1)*(n+2)+kkk) = …
feval(ODEfile,x(kkk),a(kkk:n+2:(m-1)*(n+2)+kkk),varargin{:});
end
fnka = Am * a – Fa;
jacob(:,nc) = (fnka(position) – fnk(position))…
/ dY(position(nc));
end
end
% Next approximation of the roots
if det(jacob) == 0
Y(position) = Y(position) + max([abs(dY(position)); 1.1*tol]);
else
Y(position) = Y(position) – rho * inv(jacob) * fnk(position);
end
end
% Rearranging the y’s
for k = 1:m
k1 = (k-1)*(n+2)+1;
k2 = k1 + n+1;
y(k,:) = Y(k1:k2)’;
end
x = x’;
if iter >= maxiter
disp(‘Warning : Maximum iterations reached.’)
end collocation MATLAB Answers — New Questions

​

Hello. Im working on color image encryption and need to plot the histogram for each color channels. I can plot the individual color channel histogram in three 2D plot with this code.
close all;
image = imread(‘peppers.png’);
R = image(:,:,1);
G = image(:,:,2);
B = image(:,:,3);
[Width,Length] = size(image);
subplot(2,2,1); imshow(image);
title(‘Plain Image’)
subplot(2,2,2);
imhist(R);
myHist1 = findobj(gca, ‘Type’, ‘Stem’);
myHist1.Color = [1 0 0];
title(‘Red Channel Plain Histogram’)
subplot(2,2,3);
imhist(G);
myHist2 = findobj(gca, ‘Type’, ‘Stem’);
myHist2.Color = [0 1 0];
title(‘Green Channel Plain Histogram’)
subplot(2,2,4);
imhist(B);
myHist3 = findobj(gca, ‘Type’, ‘Stem’);
myHist3.Color = [0 0 1];
xlim([0 256]);
title(‘Blue Channel Plain Histogram’)
But, i tried to plot them together in a 3D plot like this below (picture from an article i found), but i cant. I tried to find any forum that talks about this, but i can only found slice plots of meshgrid, not from histogram.
If anyone could help, I would appreciate it so much.
Thank you!Hello. Im working on color image encryption and need to plot the histogram for each color channels. I can plot the individual color channel histogram in three 2D plot with this code.
close all;
image = imread(‘peppers.png’);
R = image(:,:,1);
G = image(:,:,2);
B = image(:,:,3);
[Width,Length] = size(image);
subplot(2,2,1); imshow(image);
title(‘Plain Image’)
subplot(2,2,2);
imhist(R);
myHist1 = findobj(gca, ‘Type’, ‘Stem’);
myHist1.Color = [1 0 0];
title(‘Red Channel Plain Histogram’)
subplot(2,2,3);
imhist(G);
myHist2 = findobj(gca, ‘Type’, ‘Stem’);
myHist2.Color = [0 1 0];
title(‘Green Channel Plain Histogram’)
subplot(2,2,4);
imhist(B);
myHist3 = findobj(gca, ‘Type’, ‘Stem’);
myHist3.Color = [0 0 1];
xlim([0 256]);
title(‘Blue Channel Plain Histogram’)
But, i tried to plot them together in a 3D plot like this below (picture from an article i found), but i cant. I tried to find any forum that talks about this, but i can only found slice plots of meshgrid, not from histogram.
If anyone could help, I would appreciate it so much.
Thank you! Hello. Im working on color image encryption and need to plot the histogram for each color channels. I can plot the individual color channel histogram in three 2D plot with this code.
close all;
image = imread(‘peppers.png’);
R = image(:,:,1);
G = image(:,:,2);
B = image(:,:,3);
[Width,Length] = size(image);
subplot(2,2,1); imshow(image);
title(‘Plain Image’)
subplot(2,2,2);
imhist(R);
myHist1 = findobj(gca, ‘Type’, ‘Stem’);
myHist1.Color = [1 0 0];
title(‘Red Channel Plain Histogram’)
subplot(2,2,3);
imhist(G);
myHist2 = findobj(gca, ‘Type’, ‘Stem’);
myHist2.Color = [0 1 0];
title(‘Green Channel Plain Histogram’)
subplot(2,2,4);
imhist(B);
myHist3 = findobj(gca, ‘Type’, ‘Stem’);
myHist3.Color = [0 0 1];
xlim([0 256]);
title(‘Blue Channel Plain Histogram’)
But, i tried to plot them together in a 3D plot like this below (picture from an article i found), but i cant. I tried to find any forum that talks about this, but i can only found slice plots of meshgrid, not from histogram.
If anyone could help, I would appreciate it so much.
Thank you! image processing, histogram, 3d plots MATLAB Answers — New Questions

​

In Simulink (Aerospace Blockset) there is a Spacecraft Dynamics block. How does he work? I can’t look inside it (Look Under Mask option is inactive). The description page shows the equations that are used in the block, but the numbers given are clearly not given in full (it seems to me). https://www.mathworks.com/help/aeroblks/getting-started-with-the-spacecraft-dynamics-block.html
In addition, the equations themselves raise some questions, for example, the PDEs are given. Simulink can now solve PDEs in real time?
I want to understand how this block works in order to learn how to write my own to suit my own needs.In Simulink (Aerospace Blockset) there is a Spacecraft Dynamics block. How does he work? I can’t look inside it (Look Under Mask option is inactive). The description page shows the equations that are used in the block, but the numbers given are clearly not given in full (it seems to me). https://www.mathworks.com/help/aeroblks/getting-started-with-the-spacecraft-dynamics-block.html
In addition, the equations themselves raise some questions, for example, the PDEs are given. Simulink can now solve PDEs in real time?
I want to understand how this block works in order to learn how to write my own to suit my own needs. In Simulink (Aerospace Blockset) there is a Spacecraft Dynamics block. How does he work? I can’t look inside it (Look Under Mask option is inactive). The description page shows the equations that are used in the block, but the numbers given are clearly not given in full (it seems to me). https://www.mathworks.com/help/aeroblks/getting-started-with-the-spacecraft-dynamics-block.html
In addition, the equations themselves raise some questions, for example, the PDEs are given. Simulink can now solve PDEs in real time?
I want to understand how this block works in order to learn how to write my own to suit my own needs. aerospace blockset, spacecraft dynamics, simulink MATLAB Answers — New Questions

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