MATLAB: Fitting an equation with x,y variables and b, d constant.

fitting an equation

Hi,

I have an equation.

x=[10,50,100,300,500,1000,1500,2000,3000];
y=[0.11,0.17,0.2,0.24,0.29,0.3,0.31,0.35,0.38];

I want to fit this equation and get b and d values.

I tried with lsqcurvefit command, but I can not convert this equation to y=function(x).

Anybody has a suggestion.

Best Answer

Use lsqnonlin and define the functions f_i as

f_i = 1/a*(b-ydata(i)).^1.5-log(d./xdata(i))+0.5*log(1-ydata(i)/b)

Best wishes

Torsten.

Related Solutions

MATLAB: Define a variable from an equation

As I posted in your earlier question,

y1 = @(b, d, x) -b .* (exp(-(2/3) .* lambertw(-3 .* (b.^3 ./ a.^2).^(1/2) .* d.^3 ./ x.^3)) .* d.^2 - x.^2) ./ x.^2
y2 = @(b, d, x) -b .* (exp(-(2/3) .* lambertw(3 .* (b.^3 ./ a.^2).^(1/2) .* d.^3 ./ x.^3)) .* d.^2 - x.^2) ./ x.^2;

Now use y1(b, d, 1:10) and y2(b, d, 1:10)

Note: you will need the Symbolic Toolbox for lambertw, but see also https://www.mathworks.com/matlabcentral/fileexchange/43419-the-lambert-w-function

MATLAB: A problem while using lsqnonlin

Use the same random numbers for the same results:

rng('default')
d = linspace(0,3);
y = exp(-1.3*d) + 0.05*randn(size(d)); 
ErrorFunc = @(r)exp(-d*r)-y;
x0 = 4;
x = lsqnonlin(ErrorFunc,x0);
x2 = lsqnonlin(@ErrorFunc2,x0);
figure()
hold on
plot(d,y,'ko')              % DATA

plot(d,exp(-x*d),'b-')      % BEST FIT



plot(d,exp(-x2*d),'r--')      % BEST FIT
legend('Data','x1 fit', 'x2 fit')
xlabel('t')
ylabel('exp(-tx)')
function [error] = ErrorFunc2(x)
  rng('default')
  d = linspace(0,3);
  y = exp(-1.3*d) + 0.05*randn(size(d));  
  error = exp(-d*x) -y;
end

Another approach would be to generate random numbers only one time and use them as input to func2:

d = linspace(0,3);
y = exp(-1.3*d) + 0.05*randn(size(d));
ErrorFunc = @(r)exp(-d*r)-y;
x0 = 4;
x = lsqnonlin(ErrorFunc,x0);
x2 = lsqnonlin(@(x)ErrorFunc2(x,y),x0);
figure()
hold on
plot(d,y,'ko')              % DATA
plot(d,exp(-x*d),'b-')      % BEST FIT
plot(d,exp(-x2*d),'r--')      % BEST FIT
legend('Data','x1 fit', 'x2 fit')
xlabel('t')
ylabel('exp(-tx)')
function [error] = ErrorFunc2(x,y)
d = linspace(0,3);
%   y = exp(-1.3*d) + 0.05*randn(size(d));
error = exp(-d*x) -y;
end

Best Answer

Related Solutions

MATLAB: Define a variable from an equation

MATLAB: A problem while using lsqnonlin

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