MATLAB: I want to find coefficients of a equation that gives the relationship between two data sets.

constantsdata setsMATLABsolar radiationtemperature

I have two columns of data. First column is H (solar radiation), second column is T (temperature). And I know the relationship between them. The relationship is H =a*[1-exp{-b*(T)^c}]. a, b and c are emprical coefficients. And these coefficients are constants. I want to find best fitted emprical coefficients in this data set. I have got 3081 {H,T} values in Excel. Thanks.

Best Answer

Use the curve fitting toolbox. Or lacking that, use the optimization toolbox, so lsqnonlin or lsqcurvefit. Or use nlinfit from the stats TB. Or, lacking all of them, use lots of tools you can find on the file exchange.

Expect to have serious numerical problems IF you are not careful. I.e., you will probably want GOOD starting values for those parameters. Exponents are always dangerous to try to estimate. And worse, you have an exponential of an exponentiated parameter.

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I don’t have the Curve Fitting Toolbox, but using the Statistics Toolbox function nlinfit or Optimization Toolbox function lsqcurvefit, it would be relatively easy. Assuming time and temperature are your independent variables, and percentageconversion your dependent variable, combine the first two in one matrix and then regress it against the third using your function.

Example:

TimeTemp = [time temperature];          % Assumes time and temperature are COLUMN vectors
FAMEfcn = (b,X) b(1).*X(:1) + b(2) .* X(:,2);     % FAME = K1*time + K2*temperature
B = nlinfit(TimeTemp, percentageconversion, FAMEfcn, [1 1])

Obviously you would provide the function to fit. I created the very simple example FAMEfcn to illustrate how to refer to the TimeTemp variables within it. The percentageconversion vector is also assumed to be a column vector here.

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How about intersect()?

x = 1:3;
y = 2:5;
[c,Ix,Iy] = intersect(x,y);

intersect() does not give repetitions though.

Wayne

Best Answer

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