calling exponential function to non linear square

I want to fit data to an exponential function with the nonlinear least squares method, but MATLAB gives an error.

The code that I've written :

clear;
clc;
close all;
%mix code: ref_concrete_T8
tdata = ...
    [1.2560 2.7203 6.0830 10.0306 20.0960 40.9837 80.0923 ];
sdata = ...
    [1.3000 7.2567 23.0167 30.2733 31.9400 43.0667 43.4850 ];
            %fun=x1*exp(-(x2/tdata)^x3)
fun = @(x)x(1)*exp(-(x(2)./tdata)^x(3))-sdata;
x0=[40,0.9,0.1];
options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective');
x = lsqnonlin(fun,x0)
plot(tdata,sdata,'ko')
hold on
tlist = linspace(tdata(1),tdata(end));
plot(tlist,x(1)*exp(-(x(2)./tdata)^x(3)),'b-')
xlabel time(day)
ylabel strength(MPa)
title('exponential Fit to Data ref conc T8')
legend('Data','exponential Fit')
hold off

[Samiu Haque]

In your function you can't raise a matrix to a power. The only thing that is possible is to raise the power of each element in the matrix and for that the line should be

fun = @(x)x(1)*exp(-(x(2)./tdata).^x(3))-sdata;

[Image Analyst]

Can you put this down in the answer section Samiu? You can even get credit for it down there. Thanks in advance.

Answer 1

[Samiu Haque]

In your function you can't raise a matrix to a power. The only thing that is possible is to raise the power of each element in the matrix and for that the line should be

fun = @(x)x(1)*exp(-(x(2)./tdata).^x(3))-sdata;

[Zahra Safari]

THANKS A LOT.

i have one more question, how can i calculate R-squared of this method?

what is the code?

[Zahra Safari]

another problem is that when matlab wants to plot the curvefitting, give bellow error:

Error using plot

Vectors must be the same lengths.

Error in asli (line 16)

plot(tlist,x(1)*exp(-(x(2)./tdata).^x(3)),'b-')

the code that i've written:

clc;

close all;

tdata = ...

[0.43083 0.87792 1.79667 2.59333 6.18667 24.68667 79.39000];

sdata = ...

[2.82 9.05 16.25 18.39 25.21 36.37 38.51];

fun = @(x)x(1)*exp(-(x(2)./tdata).^x(3))-sdata;

x0=[40,0.9,0.1];

options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective');

[x,resnorm, residual] = lsqnonlin(fun,x0)

plot(tdata,sdata,'ko')

hold on

tlist = linspace(tdata(1),tdata(end));

plot(tlist,x(1)*exp(-(x(2)./tdata).^x(3)),'b-')

xlabel tdata

ylabel sdata

title('hyperbolic Fit to Data')

legend('Data','hyperbolic Fit')

hold off

[Samiu Haque]

For plotting the graph, you need equal no. of x and y values. That means two data sets must be equal. But in your code, tlist contains 100 elements whereas your function produces only 7 elements. For that reason, it is showing the error 'Vectors must be the same lengths'.

[Samiu Haque]

Use the following portion to solve the problem

syms tlist
y = x(1)*exp(-(x(2)./tlist).^x(3));
tlist = linspace(tdata(1),tdata(end));
y = subs(y);
plot(tlist,y,'b-')

[Zahra Safari]

thank you.

how can i calculate the value of R-squared??