Support for Product in SymPy isn't as great as it could be. simplify() doesn't know how to combine two products that are multiplied or divided by each other.
It looks like it works for Sum, so the first step would be to see how it works there and then see if a similar thing can be done for Product. In [10]: simplify(Sum(f(x) + g(x), (x, 0, n)) - Sum(f(x), (x, 0, n))) Out[10]: n ___ ╲ ╲ g(x) ╱ ╱ ‾‾‾ x = 0 Aaron Meurer On Tue, Feb 9, 2016 at 3:45 PM, Jonathan Crall <[email protected]> wrote: > I'm having an issue where an expresion with sympy.tensor.Indexed variables > does not seem to simplify correctly. > It is likely that I'm just doing something incorrect, so I was wondering > if anyone could help me figure this out. > > I'm using sympy to just generate some simple equations based on Bayes > rule. > > N is an event and I'm given a set of observations \set{X} = \{\ldots d_i > \ldots }\. > > I'm using an indexed base to represent the set of observations as an > array. > I'm then using sympy.Product to multiply the probability of these > observations together > (I'm assuming independence), so I create an Idx variable ``i`` and several > sets of varaiables > that are indexed by ``i``. However, at the end of this script. It looks > like ``P(di)[i]`` should be canceled out by a > simplification step, but it is not. > > Here is the script: > > > > import sympy > from sympy.tensor import IndexedBase, Idx # NOQA > from sympy import tensor > from sympy import * # NOQA > cardX = sympy.symbols('|X|', integer=True, positive=True, finite=True) > start, stop = 1, cardX > i = Idx(sympy.symbols('i', integer=True, finite=True)) > > > def psym(expr): > s = symbols(expr, real=True, finite=True, negative=False) > return s > > > def IdxBase(expr): > #s = tensor.IndexedBase(expr, shape=(cardX,))[i] > s = tensor.IndexedBase(expr, shape=(1,))[i] > return s > > > if 1: > def Prod(s): > return sympy.Product(s, (i, start, stop)) > else: > def Prod(s): > return sympy.prod([s.subs(i, i_) for i_ in range(1, 4)]) > > P_N = psym('P(N)') > P_X = psym('P(X)') > P_X_given_N = psym('P(X|N)') > P_N_given_X = psym('P(N|X)') > P_di = IdxBase('P(di)') > P_N_given_di = IdxBase('P(N|di)') > P_di_given_N = IdxBase('P(di|N)') > > pprint = sympy.pretty_print > print(''' > ----------------------- > OUTPUT OF SVM: P(N | di) > ----------------------- > ''') > P_N_given_di_ = (P_di_given_N * P_N) / P_di > pprint(Eq(P_N_given_di, P_N_given_di_)) > > print(''' > ----------------------- > REARANGE USING BAYES P(di | N) > ----------------------- > ''') > P_di_given_N_ = (P_N_given_di * P_di) / P_N > pprint(Eq(P_di_given_N, P_di_given_N_)) > > print(''' > ----------------------- > AGGREGATE USING INDEPENDENCE > ----------------------- > ''') > prod_P_di_given_N = Prod(P_di_given_N) > prod_P_di_given_N_ = Prod(P_di_given_N_) > P_X_given_N__ = prod_P_di_given_N > P_X_given_N_ = prod_P_di_given_N_ > pprint(Eq(P_X_given_N, P_X_given_N__)) > pprint(Eq(P_X_given_N, P_X_given_N_)) > > print(''' > === ALSO === > ''') > prod_P_di = Prod(P_di) > P_X_ = prod_P_di > pprint(Eq(P_X, P_X_)) > > print(''' > ----------------------- > REARANGE TO LIKELIHOOD USING BAYES AGAIN > ----------------------- > ''') > P_N_given_X__ = (P_X_given_N * P_N) / (P_X) > P_N_given_X_ = (P_X_given_N_ * P_N) / (P_X_) > pprint(Eq(P_N_given_X, P_N_given_X__)) > print('---') > pprint(Eq(P_N_given_X, P_N_given_X_)) > print('--- simplify --- ') > P_N_given_X_done = P_N_given_X_.doit(deep=True) > pprint(Eq(P_N_given_X, P_N_given_X_done)) > > # Does not seem to cancel out the P(di)[i] variable > #pprint(Eq(P_N_given_X, sympy.simplify(P_N_given_X_done))) > > > > The output of this script is: > > ----------------------- > OUTPUT OF SVM: P(N | di) > ----------------------- > > P(N)⋅P(di|N)[i] > P(N|di)[i] = ─────────────── > P(di)[i] > > ----------------------- > REARANGE USING BAYES P(di | N) > ----------------------- > > P(N|di)[i]⋅P(di)[i] > P(di|N)[i] = ─────────────────── > P(N) > > ----------------------- > AGGREGATE USING INDEPENDENCE > ----------------------- > > |X| > ┬───┬ > P(X|N) = │ │ P(di|N)[i] > │ │ > i = 1 > |X| > ┬──────┬ > │ │ P(N|di)[i]⋅P(di)[i] > P(X|N) = │ │ ─────────────────── > │ │ P(N) > │ │ > i = 1 > > === ALSO === > > |X| > ┬───┬ > P(X) = │ │ P(di)[i] > │ │ > i = 1 > > ----------------------- > REARANGE TO LIKELIHOOD USING BAYES AGAIN > ----------------------- > > P(N)⋅P(X|N) > P(N|X) = ─────────── > P(X) > --- > |X| > ┬──────┬ > │ │ P(N|di)[i]⋅P(di)[i] > P(N)⋅│ │ ─────────────────── > │ │ P(N) > │ │ > i = 1 > P(N|X) = ───────────────────────────────── > |X| > ┬───┬ > │ │ P(di)[i] > │ │ > i = 1 > --- simplify --- > |X| > -|X| ┬───┬ > P(N)⋅P(N) ⋅│ │ P(N|di)[i]⋅P(di)[i] > │ │ > i = 1 > P(N|X) = ─────────────────────────────────────── > |X| > ┬───┬ > │ │ P(di)[i] > │ │ > i = 1 > > There are no additions in this formula, so the denominator should > completely cancel. > > Any ideas why the bottom term is not canceled by the top term? > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > 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/e7d3ea7d-831e-4236-bd44-a81e22f5468a%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/e7d3ea7d-831e-4236-bd44-a81e22f5468a%40googlegroups.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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