loglikelihood does not involve W anywhere, so the derivative is zero. The reason is that the object Zl and Sl that you introduced have nothing to do with Zk and Sk that were computed earlier, they share the name but are of a different class. Other issues:
Since you are using passive forms Sum, HadamardProduct (instead of summation or hadamard_product), you'll need loglikelihood.doit() to get the computation done before taking the derivative. The summation (t, 0, Tk-1) is out of bounds. Sum ranges include the end value of the index, unlike Python ranges. So you are summing over Tk values of the index but the matrix does not have that many because one column was dropped earlier. Calculus with indexed symbols is still rough around the edges in SymPy. If the above issues are sorted, you'll hit another one, #14216 <https://github.com/sympy/sympy/issues/14216> - differentiating loggamma leads to unpolarify, which doesn't understand indexed matrix elements. A workaround is to fill the matrix with non-indexed symbols, for example generating them with symarray. This is what I do below; the code is modified according to the above remarks. n = 3 T = 5 eta = sympy.Symbol('eta') W = sympy.Matrix(symarray('W', (n, n))) S = sympy.Matrix(symarray('S', (n, T))) def detdyn(s,w): '''Z if a function of S and W''' f = w*s f_average = sympy.HadamardProduct(f, s) f_average = sympy.ones(1,f_average.shape[0]) * f_average #row sum #compute coefficients of Z c=f.as_mutable() for r in range(T): c.col_op(r, lambda i,j: i / f_average[0, r]) z = sympy.HadamardProduct(c,s) return z Tk = S.shape[1] #length of the data Zk = detdyn(S,W)[:,:-1] #compute the deterministic dynamics Sk = S[:,1:] #drop first observation i, t = sympy.symbols('i t', cls=sympy.Idx) loglikelihood=(Tk-1)*sympy.loggamma(eta)+sympy.Sum(sympy.Sum(-sympy.loggamma(eta*Zk[i,t])+(eta*Zk[i,t]-1)*sympy.ln(Sk[i,t]),(i, 0, 2)),(t, 0, Tk-2)) print(loglikelihood.doit().diff(W[0, 0])) -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/0ecc5868-d6dc-4523-98f3-7b1afad53739%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
