calling exponential function to non linear square

2020 9 13
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更新时间：2020 9 14
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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

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Samiu Haque
Samiu Haque 2020-9-13
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
Image Analyst 2020-9-13
Can you put this down in the answer section Samiu? You can even get credit for it down there. Thanks in advance.

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 采纳的回答

Samiu Haque
Samiu Haque 2020-9-13

1 个投票

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;

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Zahra Safari
Zahra Safari 2020-9-13
THANKS A LOT.
i have one more question, how can i calculate R-squared of this method?
what is the code?
Zahra Safari
Zahra Safari 2020-9-13
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
Samiu Haque 2020-9-13
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
Samiu Haque 2020-9-13
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
Zahra Safari 2020-9-14
thank you.
how can i calculate the value of R-squared??

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