Re: Re: Derivative of function with indexed variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg84026] Re: [mg83988] Re: Derivative of function with indexed variables*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Fri, 7 Dec 2007 03:02:45 -0500 (EST)*References*: <33430946.1196931596825.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

D[expr, y[i]] is zero here for several reasons: 1) y[i] is no specific symbol, since i is undefined. 2) expr is no specific Sum, since n, y, and p are undefined. (Especially n.) 3) The i in y[i] doesn't have the same scope (isn't the same variable) as the i in expr. The last is especially important. 0 This is fairly general, but not too general to "work": Clear[num, den, expr] n = 5; num[i_] = Exp[-(y[i] - y[j])^2]; den[y_] = Sum[Exp[-(y[k] - y[h])^2], {h, k + 1, n}, {k, 1, n}]; expr[y_, p_] = Sum[p[i, j] Log[p[i, j] den[y]/num[i]], {j, 1, n}]; dExpr[i_] := D[expr[y, p], y[i]] dExpr[3] 2 p[3, 1] (-y[1] + y[3]) + 2 p[3, 2] (-y[2] + y[3]) + 2 p[3, 4] (y[3] - y[4]) + 2 p[3, 5] (y[3] - y[5]) Bobby On Thu, 06 Dec 2007 01:44:18 -0600, Laurens van der Maaten <l.vandermaaten at micc.unimaas.nl> wrote: > Here is the same in proper Mathematica-style: > > num = Exp[- (y[i] - y[j])^2] > den = Sum[Sum[Exp[-(y[k] - y[h])^2], {h, k + 1, n}], {k, 1, n}] > expr = Sum[p[i, j]Log[p[i, j]/(num / den)], {j, 1, n}] > D[expr, y[i]] > > The resulting derivative is incorrect, because Mathematica does not seem > to notice that y[k] and y[h] are sometimes equal to y[i] (over which we > compute the derivative). Any ideas? > > -- DrMajorBob at bigfoot.com