Why do I receive "Error using lsqcurvefit (line 251) Function value and YDATA sizes are not equal."

f = ...

[15 25 35 50 65 80];

s = ...

[1070 1602 1931 2100 2041 1876];

plot(f,s,'ro')

title('Data points')

F1 = @(x,xdata)x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)));

x0 = [1000 0.01];

x1 = lsqcurvefit(F1,x0,f,s)

plot(f,F1(x1,f))

F2 = @(x,xdata)(x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)))/(1-cos(xdata*pi/180)*exp(-50*x(2))));

x0 = [1000 0.01];

x2 = lsqcurvefit(F2,x0,f,s)

plot(f,F2(x2,f))

%The program works with function F1 but not function F2

[Wingchi Kwok]

Hi, Star,

It works. Thank you very much for your help.

Wing

[Star Strider]

As always, my pleasure!

.

Answer 1

[Star Strider]

Do element-wise division

F2 = @(x,xdata)(x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)))./(1-cos(xdata*pi/180)*exp(-50*x(2))));

↑ ← HERE

and it works!

f = ...
[15 25 35 50 65 80];  
s = ...
[1070 1602 1931 2100 2041 1876];

figure
plot(f,s,'ro')
hold on
title('Data points')
F1 = @(x,xdata)x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)));
x0 = [1000 0.01];
x1 = lsqcurvefit(F1,x0,f,s)

Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.

x1 = 1×2

1.0e+03 * 2.4952 0.0016

plot(f,F1(x1,f))
F2 = @(x,xdata)(x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)))./(1-cos(xdata*pi/180)*exp(-50*x(2))));
x0 = [1000 0.01];
x2 = lsqcurvefit(F2,x0,f,s)

Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.

x2 = 1×2

1.0e+03 * 2.4952 0.0014

plot(f,F2(x2,f),'--')
hold off
legend('Data','F_1','F_2', 'Location','best')

.

.

[Alex Sha]

F1 = @(x,xdata)x(1)*sin(xdata*pi/180)*(1-exp(-50*x(2)));

The above F1 function can be simplified to "F1 = @(x,xdata)x(1)*sin(xdata*pi/180);", with the exactly same result, but avoiding multiple solutions.

For F2 function, the best result should be:

Root of Mean Square Error (RMSE): 14.9218445307446
Sum of Squared Residual: 1335.96866519828
Correlation Coef. (R): 0.999332922291571
R-Square: 0.998666289575811

Parameter	Best Estimate
----------	-------------
x1	4323.03442875393
x2	0.00984518829719931