Inverse hyperbolic fit to data

Hi, i'm trying to fit the model (P+a)(V+b)=(Po+a)*b to some data in MATLAB (where a and b are constants and Po is the value of P at V=0), I'm just wondering how you do this.

My data is:

P = [5 7.5 10 12.5 15 17.5 20 25 30 35 40 45 50 55 60 65];

V = [32.89 26.48 22.28 19.16 17.25 14.97 13.40 10.66 9.38 7.88 6.66 5.89 4.79 4.49 2.43 1.37];

Thanks

Answer 1

[Mathieu NOE]

hi

below the code that solve your problem using fminsearch

    P = [5 7.5 10 12.5 15 17.5 20 25 30 35 40 45 50 55 60 65];
    V = [32.89 26.48 22.28 19.16 17.25 14.97 13.40 10.66 9.38 7.88 6.66 5.89 4.79 4.49 2.43 1.37];


% fminsearch optimization loop 
fun = @(x)norm((P+x(1)).*(V+x(2))-(x(3)+x(1))*x(2));  %a = x(1), b=x(2), Po = x(3)
x0 = [0, 0, 0];
X = fminsearch(fun,x0);

a = X(1)
b=X(2) 
Po = X(3)

% check on plot : 
Vfit=((Po+a)*b)./(P+a) - b;

    figure(1), plot(P,V,'b',P,Vfit,'r');grid
    legend('experimental','fit');

Answer 2

[Alan Stevens]

Here's an alternative, with V as the independent variable and P as the dependent one:

% Data 
P = [5 7.5 10 12.5 15 17.5 20 25 30 35 40 45 50 55 60 65]';
V = [32.89 26.48 22.28 19.16 17.25 14.97 13.40 10.66 9.38 7.88 6.66 5.89 4.79 4.49 2.43 1.37]';

% (P + a)(V + b) = (P0 + a)*b
% P*V +a*V + b*P + a*b = P0*b + a*b    
% V*a + P*b - P0b = -P*V
% M*X = C   where  M = [V P -1];  X = [a; b; P0b];  C = -P.*V; 
M = [V  P -ones(size(V))];
C = -P.*V;
X = M\C;
a = X(1);
b = X(2);
P0 = X(3)/b;

disp('a          b          P0')
disp([a b P0])

p = (P0 + a)*b./(V + b) - a;
plot(V,P,'o',V,p,'*-'),grid
xlabel('V'),ylabel('P')
legend('data','curve fit')

This produces

[Alan Stevens]

With V as the independent variable

p = (P0 + a)*b./(V + b) - a;
plot(V,P,'o',V,p,'*-')

should now be replaced by

v = (P0 + a)*b./(P + a) - b;
plot(P,V,'o',P,v,'*-')

with corresponding label changes.

The result should now look like