How to debug this? Not getting into it. Need help

% Data
rData = [5.3571429, 0.096854535; 10.714286, 0.055104186; 16.071429, 0.042811499; 21.428571, 0.024825886; 26.785714, 0.023279183; 32.142857, 0.016328542; 37.5, 0.0092185037; 42.857143, 0.0075624777; 48.214286, 0.0023514323; 53.571429, 0.001637045; 58.928571, -0.0024887011; 64.285714, -0.0034741333; 69.642857, -0.0056340032; 75, -0.0040906991; 80.357143, -0.0039738424; 85.714286, -0.0044593789; 91.071429, -0.0054884315; 96.428571, -0.0037277341; 101.78571, -0.0041691748; 107.14286, -0.0039292558; 112.5, -0.0037408923; 117.85714, -0.0040700255; 123.21429, -0.0028904555; 128.57143, -0.0022557232; 133.92857, -0.0020756487; 139.28571, -0.0020739949; 144.64286, -0.0015149035; 150, -0.0019796368; 155.35714, -0.00068430865; 160.71429, -0.00060721168; 166.07143, -0.00055972397; 171.42857, -0.0011788755; 176.78571, -0.00090675531; 182.14286, -0.00060012026; 187.5, 7.6071311e-6];
tData = [5.3571429, 0.081473653; 10.714286, -0.0076210718; 16.071429, -0.038565046; 21.428571, -0.014000405; 26.785714, -0.042161254; 32.142857, -0.071404281; 37.5, -0.066992712; 42.857143, -0.031355057; 48.214286, -0.02043848; 53.571429, -0.025259291; 58.928571, -0.019615094; 64.285714, -0.015185751; 69.642857, -0.012213914; 75, -0.0047624032; 80.357143, -0.00041652762; 85.714286, 0.0028162852; 91.071429, 0.00979253; 96.428571, 0.0080315783; 101.78571, 0.0034739882; 107.14286, 0.0021786814; 112.5, 0.0043349925; 117.85714, 0.0053397331; 123.21429, 0.0061087654; 128.57143, 0.0028425693; 133.92857, 0.002129577; 139.28571, 0.0068534431; 144.64286, 0.0071201038; 150, 0.0099290536; 155.35714, 0.0089545127; 160.71429, 0.0079282308; 166.07143, 0.0075533041; 171.42857, 0.01092774; 176.78571, 0.012219652; 182.14286, 0.01013098; 187.5, 0.0096622622];

% Define equations
Alpha = @(mu, lambda) 1/(2*mu + lambda);

% Define equations
eqns = @(x, y, mu, lambda, ke, ko) [y(2); -y(1) + Alpha(mu, lambda)^-1 * ke^2 * x.^2 .* y(1) - Alpha(mu, lambda)^-1 * ko^2 * x.^2 .* y(2)];

% Define the model
funr = @(params, x) deval(ode45(@(x, y) eqns(x, y, params(1), params(2), params(3), params(4)), [0.75, 187.5], [0.1625, 0]), x, 1);

% Fit the data with initial guess values
initialGuess = [15, 50, 0.01, 0.01];
fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1), rData(:,2));

Error using lsqcurvefit
Function value and YDATA sizes are not equal.

fit2 = lsqcurvefit(@(params, x) funr(params, x), initialGuess, tData(:,1), tData(:,2));

% Plot the fitted functions
x_values = linspace(1, 187.5, 1000);
r_fit = funr(fit, x_values);
theta_fit = funr(fit2, x_values);

figure;
plot(x_values, r_fit, 'r', 'LineWidth', 2);
hold on;
scatter(rData(:,1), rData(:,2), 'b');
xlabel('x');
ylabel('r(x)');
title('Fitted r(x)');
legend('Fitted r(x)', 'rData');

figure;
plot(x_values, theta_fit, 'r', 'LineWidth', 2);
hold on;
scatter(tData(:,1), tData(:,2), 'b');
xlabel('x');
ylabel('\theta(x)');
title('Fitted \theta(x)');
legend('Fitted \theta(x)', 'tData');

~

Getting the following Errors: using lsqcurvefit Function value and YDATA sizes are not equal. Error in test (line 16) fit = lsqcurvefit(@(params, x) deval(funr(params(1), params(2), params(3), params(4), x), x, 1), initialGuess, rData(:,1), rData(:,2));

Answer 1

[Torsten]

Use

fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');
fit2 = lsqcurvefit(@(params, x) funr(params, x), initialGuess, tData(:,1).', tData(:,2).');

instead of

fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1), rData(:,2));
fit2 = lsqcurvefit(@(params, x) funr(params, x), initialGuess, tData(:,1), tData(:,2));

[tuhin]

% Data

rData = [5.3571429, 0.096854535; 10.714286, 0.055104186; 16.071429, 0.042811499; 21.428571, 0.024825886; 26.785714, 0.023279183; 32.142857, 0.016328542; 37.5, 0.0092185037; 42.857143, 0.0075624777; 48.214286, 0.0023514323; 53.571429, 0.001637045; 58.928571, -0.0024887011; 64.285714, -0.0034741333; 69.642857, -0.0056340032; 75, -0.0040906991; 80.357143, -0.0039738424; 85.714286, -0.0044593789; 91.071429, -0.0054884315; 96.428571, -0.0037277341; 101.78571, -0.0041691748; 107.14286, -0.0039292558; 112.5, -0.0037408923; 117.85714, -0.0040700255; 123.21429, -0.0028904555; 128.57143, -0.0022557232; 133.92857, -0.0020756487; 139.28571, -0.0020739949; 144.64286, -0.0015149035; 150, -0.0019796368; 155.35714, -0.00068430865; 160.71429, -0.00060721168; 166.07143, -0.00055972397; 171.42857, -0.0011788755; 176.78571, -0.00090675531; 182.14286, -0.00060012026; 187.5, 7.6071311e-6];

tData = [5.3571429, 0.081473653; 10.714286, -0.0076210718; 16.071429, -0.038565046; 21.428571, -0.014000405; 26.785714, -0.042161254; 32.142857, -0.071404281; 37.5, -0.066992712; 42.857143, -0.031355057; 48.214286, -0.02043848; 53.571429, -0.025259291; 58.928571, -0.019615094; 64.285714, -0.015185751; 69.642857, -0.012213914; 75, -0.0047624032; 80.357143, -0.00041652762; 85.714286, 0.0028162852; 91.071429, 0.00979253; 96.428571, 0.0080315783; 101.78571, 0.0034739882; 107.14286, 0.0021786814; 112.5, 0.0043349925; 117.85714, 0.0053397331; 123.21429, 0.0061087654; 128.57143, 0.0028425693; 133.92857, 0.002129577; 139.28571, 0.0068534431; 144.64286, 0.0071201038; 150, 0.0099290536; 155.35714, 0.0089545127; 160.71429, 0.0079282308; 166.07143, 0.0075533041; 171.42857, 0.01092774; 176.78571, 0.012219652; 182.14286, 0.01013098; 187.5, 0.0096622622];

% Define equations

syms x;

mu = sym('mu'); lambda = sym('lambda'); ke = sym('ke'); ko = sym('ko');

Alpha = @(mu, lambda) 1/(2*mu + lambda);

r = @(x) x;

theta = @(x) x;

% Define equations

eqn1 = x^2*diff(r(x), x, x) + x*diff(r(x), x) - r(x) + Alpha(mu, lambda)^-1*ke^2*x^2*r(x) - Alpha(mu, lambda)^-1*ko^2*x^2*theta(x) == 0;

eqn2 = x^2*diff(theta(x), x, x) + x*diff(theta(x), x) - theta(x) + mu^-1*ko^2*x^2*r(x) + mu^-1*ke^2*x^2*theta(x) == 0;

% Convert symbolic equations to function handles

eqn1_func = matlabFunction(eqn1);

eqn2_func = matlabFunction(eqn2);

% Define the model

funr = @(params, x) deval(ode45(@(x, y) [eqn1_func(params(1), params(2), params(3), params(4), x); eqn2_func(params(1), params(2), params(3), params(4), x)], [0.75, 187.5], [0.1625, 0]), x, 1);

% Fit the data with initial guess values

initialGuess = [15, 50, 0.01, 0.01];

fit = lsqcurvefit(@(params, x) funr(params, x), initialGuess, rData(:,1).', rData(:,2).');

fit2 = lsqcurvefit(@(params, x) funr(params, x), initialGuess, tData(:,1).', tData(:,2).');

% Plot the fitted functions

x_values = linspace(1, 187.5, 1000);

r_fit = funr(fit, x_values);

theta_fit = funr(fit2, x_values);

figure;

plot(x_values, r_fit, 'r', 'LineWidth', 2);

hold on;

scatter(rData(:,1), rData(:,2), 'b');

xlabel('x');

ylabel('r(x)');

title('Fitted r(x) vs. Data');

legend('Fitted r(x)', 'Data');

figure;

plot(x_values, theta_fit, 'g', 'LineWidth', 2);

hold on;

scatter(tData(:,1), tData(:,2), 'b');

xlabel('x');

ylabel('theta(x)');

title('Fitted theta(x) vs. Data');

legend('Fitted theta(x)', 'Data');

Changed it and explained it elaborately. However getting eror. Help me with the possible eror corrections. Thanks in advance!

[Torsten]

Your initial code works with the changes I suggested. Why do you present a new problem now ?

[tuhin]

There were something wrong in the eqns. That I corrected now. The actual form of two coupled differential eqns are:

(*Define the equations*)

\[Alpha][\[Mu]_, \[Lambda]_] := 1/(2*\[Mu] + \[Lambda]);

eqns[\[Mu]_, \[Lambda]_, ke_, ko_] := {

x^2*r''[x] + x*r'[x] - r[x] + \[Alpha][\[Mu], \[Lambda]]^-1*ke^2*x^2*r[x] - \[Alpha][\[Mu], \[Lambda]]^-1*ko^2*x^2*\[Theta][x] == 0,

x^2*\[Theta]''[x] + x*\[Theta]'[x] - \[Theta][x] + \[Mu]^-1*ko^2*x^2*r[x] + \[Mu]^-1*ke^2*x^2*\[Theta][x] == 0};

I want to use and solve this two coupled differential eqns (with four boundary conditions) and fit it with the experimental data of r(x) vs x and \theta(x) vs x. For this I want to tune those four parameters mu; lambda; ke; ko. Please let me know if you need more clarifications. I want to get an estimate of these parameters.