[Scipy-tickets] [SciPy] #1465: SciPy output fo mathieu_a and mathieu_b differs from GSL for q < 0

SciPy Trac scipy-tickets@scipy....
Fri Jun 24 14:48:21 CDT 2011


#1465: SciPy output fo mathieu_a and mathieu_b differs from GSL for q < 0
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 Reporter:  Nikolay  |       Owner:  somebody   
     Type:  defect   |      Status:  new        
 Priority:  normal   |   Milestone:  Unscheduled
Component:  Other    |     Version:  0.9.0      
 Keywords:           |  
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 I'm working with Mathieu functions. {{{SciPy}}} is more comfortable for
 me, than [http://www.gnu.org/software/gsl/ GSL].[[BR]]
 I have GSL 1.15, {{{SciPy 0.9.0-r1}}}. Both from gentoo amd64 portage
 tree.[[BR]][[BR]]

 But for negative q (i.e. q=-20) {{{SciPy's}}} output is differ from
 GSL's.[[BR]]
 I wrote 2 simple programs to demonstrate the error.[[BR]][[BR]]

 As we know, there is a relation between '''a''' and '''b'''
 eigenvalues:[[BR]]
 for '''q''' < 0 we have a0 < a1 < b1 < b2 < a2 < a3 < b3 < ...[[BR]][[BR]]

 For {{{SciPy}}} we will have (see ''ar_br_tables.py''):[[BR]]
 a0 = 1.1542828852 '''<''' a1 = -31.3133861669 '''<''' b1 = 15.3958109128
 '''<''' b2 = 15.4939775770 '''<''' a2 = 1.1542828852 '''<''' a3 =
 1.1607056792 '''<''' b3 = 36.6449897341[[BR]]
 as you can see it's false! It's not good.[[BR]][[BR]]

 For GSL we will have (see ''ar_br_tables.c''):[[BR]]
 a0 = -31.3133900703 '''<''' a1 = -31.3133861669 '''<''' b1 =
 -14.4913014252 '''<''' b2 = -14.4910632560 '''<''' a2  = 1.1542828852
 '''<''' a3 = 1.1607056792 '''<''' b3 = 15.3958109128[[BR]]
 as you can see it's true! It's good.[[BR]][[BR]]

 According to {{{WolframAlpha}}}[[BR]]
 [http://www.wolframalpha.com/input/?i=MathieuCharacteristicA%5B0%2C+-20%5D
 MathieuCharacteristicA] a0 = -31.3133900703[[BR]]
 [http://www.wolframalpha.com/input/?i=MathieuCharacteristicB%5B1%2C+-20%5D
 MathieuCharacteristicB] b1 = -14.4913014252.[[BR]][[BR]]

 Please confirm and fix this bug.

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1465>
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