Analytical Jacobian Use

In the previous post I mentioned the issue of user provided analytical derivative not giving correct results. With the help of Josef, the issue is resolved now. It turned out that, before passing on to leastsq the jacobian values had to transformed into those of "whitened" exogenous data. Here is an example of a typical Nonlinear Model Class:

class Myfunc(NonlinearLS):

    def expr(self, params, exog=None):
        if exog is None:
            x = self.exog
        else:
            x = exog

        x0, x1 = x[:,0], x[:,1]
        a, b, c = params
        return a + b*x0 + c*x1

    def jacobian(self,params, exog=None):
        if exog is None:
            x = self.exog
        else:
            x = exog

        x0, x1 = x[:,0], x[:,1]
        a, b, c = params
        a1 = np.ones(len(x0),)
        b1 = x0
        c1 = x1
        jacob = np.column_stack((a1,b1,c1))
        return jacob
 

Some points to note:

• The above class is for linear model y = a + b*x0 + c*x1 + e, where a,b and c are the parameters to be estimated.
• The expr is the 'expression' of the function of exogenous variable. Simply, it is 'f' in y = f(x) + e. Here f is a + b*x0 + c*x1.
• The jacobian is the analytical derivative matrix of 'f' given above with respect to the parameters to estimated.
• The jacobian function is optional. If it is not provided, jacobian is calculated using numerical derivative.

A test has been included in test_nonlinearls.py for above class. The results obtained after nonlinear least squares fitting were:

Next we move on inlcude the result statistics for NonLinearLS class.