MATLAB: How to fit inverse proportional function

curve fittinginverse proportional function

x,y is a vectors. How to get a fitting function like y'=a/(x+b)+c

Best Answer

Your function could be difficult to fit. You can use the fminsearch function to estimate the parameters:

% Define ‘x’ and ‘y’ here
% Parameter Vector: b(1) = a,  b(2) = b,  b(3) = c
yfit = @(b,x) b(1)./(x + b(2)) + b(3);  % Objective Function
CF = @(b) sum((y-yfit(b,x)).^2);        % Cost Function
b0 = rand(1,3)*10;                      % Initial Parameter Estimates
[B, fv] = fminsearch(CF, b0);           % Estimate Parameters

Note that ‘x’ and ‘y’ have to be defined in your workspace

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You can use core MATLAB functions to do the regression:

x = ...;                                                    % Independent Variable
y = ...;                                                    % Dependent Variable
fcn1 = @(b,x) b(1)./(b(2).*x + b(3));                       % Objective Function #1
fcn2 = @(b,x) b(1)./(b(2).*x);                              % Objective Function #2
SSECF = @(b) sum((y - fcn2(b,x)).^2);                       % Sum-Squared-Error Cost Function (Use ‘fcn2’ Here)
B0 = [1; 1];                                                % Initial Parameter Estimates
[B,SSE] = fminsearch(SSECF, [1; 1]);                        % Estimate Parameters
xv = linspace(min(x), max(x));
figure(1)
plot(x, y, 'bp')
hold on
plot(xv, fcn2(B,xv), '-r')
hold off
grid

I tested this with random vectors and it ran without error.

EDIT — Note that the two-parameter model you want requires only one parameter. A simple ratio (or product) of parameters will not uniquely identify either of them, only the ratio (or product). The three-parameter model actually makes sense.

MATLAB: Wich is the good soulution My vs. School – curve fitting

Don’t linearise! It distorts the errors and results in inaccurate parameter estimates.

Using fminsearch gives a decent fit to the data:

x = [1 2 4 7]; 
y = [2 1 0.4 0.1];
fy = @(b,x) x./(b(1) + b(2).*x);
CF = @(b) sum((y-fy(b,x)).^2);
[b, fv] = fminsearch(CF, [1;1])
figure(1)
plot(x, y, '*r')
hold on
plot(x, fy(b,x), '-b')
hold off

producing the parameter estimates:

b =
      -2.0553e+000
       2.5517e+000

where a=b(1) and b=b(2).

Best Answer

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