Opened 13 years ago
Closed 13 years ago
#6189 closed defect (fixed)
[with patch, positive review] 'integrate' produces incorrect answer
Reported by: | emchristiansen | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-4.2 |
Component: | calculus | Keywords: | integrate, integral, incorrect |
Cc: | Merged in: | sage-4.2.alpha0 | |
Authors: | Karl-Dieter Crisman | Reviewers: | Mike Hansen |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Affects: x64 Ubuntu 9.04 (Jaunty) Sage 4.0, compiled from source, and updated (sage -upgrade) as of this posting
By simply casting a number using 'n()', I can cause integrate to return a vastly different result. See below:
var = sage.calculus.calculus.var def NormalPDF(x,mu,sigma): return 1/sqrt(2*pi*sigma^2)*exp(-1/(2*sigma**2)*(x-mu)^2) x = var('x') mu = var('m') sigma = var('s') assume(sigma>0) child1 = NormalPDF(x,0,1) child2 = NormalPDF(x,n(0),n(1)) parent = NormalPDF(x,mu,sigma) # this expansion helps Sage to do the integral integrand1 = ((parent-child1)^2).expand() integrand2 = ((parent-child2)^2).expand() int1 = integrate(integrand1,x,-infinity,infinity) int2 = integrate(integrand2,x,-infinity,infinity) print "THIS EXPRESSION:" print int1 print "\nSHOULD BE VERY SIMILIAR TO THIS EXPRESSION:" print int2 print "\nMAKING THIS NUMBER:" print int1.subs({mu:0,sigma:1}).n() print "\nVERY SIMILAR TO THIS NUMBER:" print int2.subs({mu:0,sigma:1}).n()
The above produces the output:
THIS EXPRESSION: 1/2*((s + 1)*sqrt(s^2 + 1)*e^(1/2*m^2/(s^2 + 1)) - 2*sqrt(2)*s)*e^(-1/2*m^2/(s^2 + 1))/(sqrt(s^2 + 1)*sqrt(pi)*s) SHOULD BE VERY SIMILIAR TO THIS EXPRESSION: 1/2*(sqrt(0.5*s^2 + 0.5)*e^(1/2*m^2/(s^2 + 1)) - sqrt(2)*s)*e^(-1/2*m^2/(s^2 + 1))/(sqrt(0.5*s^2 + 0.5)*sqrt(pi)*s) MAKING THIS NUMBER: 0.000000000000000 VERY SIMILAR TO THIS NUMBER: -0.116847488627555
Mathematica claims the correct integral is:
\frac{1+\sigma }{2 \sqrt{\pi } \sigma }-\frac{\sqrt{2} e^{-\frac{\mu ^2}{2+2 \sigma ^2}}}{\sqrt{\pi +\pi \sigma ^2}}
Attachments (1)
Change History (5)
comment:1 Changed 13 years ago by
- Summary changed from 'integrate' produces incorrect answer to [with patch, needs review] 'integrate' produces incorrect answer
comment:2 Changed 13 years ago by
Despite what it says, actually based on 4.1.2.alpha4.
comment:3 Changed 13 years ago by
- Merged in set to sage-4.2.alpha0
- Reviewers set to Mike Hansen
- Status changed from needs_review to positive_review
- Summary changed from [with patch, needs review] 'integrate' produces incorrect answer to [with patch, positive review] 'integrate' produces incorrect answer
Looks good to me.
comment:4 Changed 13 years ago by
- Milestone set to sage-4.2
- Resolution set to fixed
- Status changed from positive_review to closed
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This is now fixed, presumably in the Maxima upgrade. Note that the integral in fact computes without expand(), and in that case there is no 'experimental error'! Attached patch verifies this.