MATLAB: Fit of groups of data

curve fitting

Hi,

I have two groups of data. Both of them have the same x-axis but differ in y-axis. I want to to solve an equation that depend on these two groups of data.

The x-axis is representing time x=[1; 2; 3; 4; 5; 10; 15; 30; 45; 60; 90]

and y-axis for the first group is: y1=[56.88; 62.75; 87.07; 114.54; 139.14; 177.24; 216.39; 285.77; 399.99; 357.28; 359.53]

and y-axis for the second group is: y2=[353.64; 343.60; 303.67; 312.73; 328.91; 306.76; 299.97; 259.01; 222.10; 190.04; 228.87]

Here is my equation: y1/(y1+y2)=[k1/(k1+k2)]*{1-exp[-(k1+k2)*t]}

Note: all the equation parameters are known except k1 and k2.

How can I find them by fitting the data please?

Best Answer

If you have the Statistics Toolbox, I think the nlinfit() function will do what you need: http://www.mathworks.com/help/stats/nlinfit.html

Related Solutions

MATLAB: How to solve the two equations numerically in which tabular data is also to be loaded

You can rewrite the interpolation as a polynomial of degree 6; it works out as

- (25*x^6)/12 + (145*x^5)/24 - (359*x^4)/48 + (499*x^3)/96 - (239*x^2)/100 + (10583*x)/12000 + 117/2500

You can then substitute that into your equations, converting all of your floating point values to rationals.

The system you get can then be solved in terms of a value that is the primary root of a degree 15 polynomial,

R = root([512 -15616 222208 -1962496 12118592 -56160800 203296128 -579497504 1277765482 -2115195465 2460287016 -1208021246 11455984710 -86217800113 215987875056 -180007884864])
D = (1/10)*(86016*R^14-2476544*R^13+32687360*R^12-257504256*R^11+1311552000*R^10-4612323392*R^9+12775515552*R^8-33673493056*R^7+86104656976*R^6-190723241666*R^5+393335706409*R^4+1248605641188*R^3-12283484659202*R^2+31089547519966*R-25920766050455)/(136192*R^14-3095552*R^13+19046656*R^12+161221632*R^11-3087622016*R^10+19694850944*R^9-63486597472*R^8+88752422720*R^7+101264091972*R^6-913631183772*R^5-936427888987*R^4+34659208386904*R^3-152565699173910*R^2+279861195719556*R-190086479566579)
c = (1/10)*(15616*R^14-444416*R^13+5887488*R^12-48474368*R^11+280804000*R^10-1219776768*R^9+4056482528*R^8-10222123856*R^7+19036759185*R^6-24602870160*R^5+13288233706*R^4-137471816520*R^3+1120831401469*R^2-3023830250784*R+2700118272960)/(3840*R^14-109312*R^13+1444352*R^12-11774976*R^11+66652256*R^10-280804000*R^9+914832576*R^8-2317990016*R^7+4472179187*R^6-6345586395*R^5+6150717540*R^4-2416042492*R^3+17183977065*R^2-86217800113*R+107993937528)

The values are approximately D = 0.07782594605604250, c = .3715081472598230

MATLAB: How can i call array elements in a plot3 function

s=10;b=8/3; r=28;h=0.003; a=28
x=0;y=1; z=0; f=zeros(1,3); f=[x y z]; 
k=1;
for t=0:h:100 
    k1_x=a*(y(k)-x(k));
    k2_x=a*(y(k)-x(k))+(k1_x*h*0.5);
    k3_x=a*(y(k)-x(k))+(k2_x*h*0.5);
    k4_x=a*(y(k)-x(k))+(k3_x*h);
    x(k+1)=x(k)+(k1_x+2*k2_x+2*k3_x+k4_x)*h/6; 
    k1_y=x(k)*(r-z(k))-y(k);
    k2_y=(x(k)*(r-z(k))-y(k))+k1_y*h*0.5;
    k3_y=(x(k)*(r-z(k))-y(k))+k2_y*h*0.5;
    k4_y=(x(k)*(r-z(k))-y(k))+k3_y*h*0.5;
    y(k+1)=y(k)+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; 
    k1_z=x(k)*y(k)-b*z(k);
    k2_z=(x(k)*y(k)-b*z(k))+k1_z*h*0.5;
    k3_z=(x(k)*y(k)-b*z(k))+k2_z*h*0.5;
    k4_z=(x(k)*y(k)-b*z(k))+k3_z*h*0.5;
    z(k+1)=z(k)+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; 
    k=k+1;
end
    plot3(x,y,z); grid on; xlabel('x'); ylabel('y');
    zlabel('z'); title('Lorenz attractor');

Best Answer

Related Solutions

MATLAB: How to solve the two equations numerically in which tabular data is also to be loaded

MATLAB: How can i call array elements in a plot3 function

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