Matthew... what do you think of the union of intervals as an alternative to
the usual ranges in integrate/Integral?
I suppose that you wrote the code outputting that integral, which currently
does not work, and I want to make it work.
I am undecided on whether to edit sympy.stats in order to give *Integral(
... , (x, -oo, -1)) + Integral( ... , (x, 1, oo)) *instead of *Integral(
... , (x, Union(Interval(-oo, -1), Interval(1, oo))))*.
On the other hand, this alternative notation may be useful. Unfortunately
it would require some algorithmic changes and I am a bit wary about a
substantial edit of the integration algorithm.
On Thursday, March 26, 2015 at 9:12:37 PM UTC+1, Matthew wrote:
>
> You don't need to square the random variable to compute the result. You
> just need to integrate the pdf over x < -1 and x > 1
>
> On Thu, Mar 26, 2015 at 5:42 AM, Francesco Bonazzi <franz....@gmail.com
> <javascript:>> wrote:
>
>>
>> Well, I was a bit surprised too, but the stats module apparently does so,
>> as shown in this example:
>>
>> In [1]: from sympy.stats import *
>>
>> In [2]: var('sigma', positive=True)
>> Out[2]: σ
>>
>> In [3]: N = Normal('X', mu, sigma)
>>
>> In [6]: P(N**2>1, evaluate=False)
>> Out[6]:
>> (-∞, -1) ∪ (1, ∞)
>> ⌠
>> ⎮ 2
>> ⎮ -(z - μ)
>> ⎮ ──────────
>> ⎮ 2
>> ⎮ ___ 2⋅σ
>> ⎮ ╲╱ 2 ⋅ℯ
>> ⎮ ───────────────── dz
>> ⎮ ___
>> ⎮ 2⋅╲╱ π ⋅σ
>> ⌡
>>
>>
>> In [7]: srepr(P(N**2>1, evaluate=False))
>> Out[7]: "Integral(Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)),
>> Pow(pi, Rational(-1, 2)), Pow(Symbol('sigma'), Integer(-1)),
>> exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('sigma'), Integer(-2)),
>> Pow(Add(Dummy('z'), Mul(Integer(-1), Symbol('mu'))), Integer(2))))),
>> Tuple(Dummy('z'), Union(Interval(-oo, Integer(-1), S.true, S.true),
>> Interval(Integer(1), oo, S.true, S.true))))"
>>
>>
>> Apart the fact that such an integral looks wrong to me, i.e. there is no
>> account for the random variable being squared (or am I missing something?),
>> it looks like SymPy is OK with intervals, but not with unions of intervals:
>>
>>
>> https://github.com/sympy/sympy/blob/9242d31f6d31a1d9c3464264a5a6e61eab8acfb8/sympy/concrete/expr_with_limits.py#L37
>>
>> That's the point where an Interval gets parsed by the integration
>> algorithm.
>>
>> I think it's an easy fix to add the processing for unions of intervals.
>>
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