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Re: Re: Re: Weird result in Mathematica 6
*To*: mathgroup at smc.vnet.net
*Subject*: [mg76737] Re: [mg76574] Re: [mg76431] Re: [mg76393] Weird result in Mathematica 6
*From*: DrMajorBob <drmajorbob at bigfoot.com>
*Date*: Sat, 26 May 2007 04:45:17 -0400 (EDT)
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*Reply-to*: drmajorbob at bigfoot.com
Oh well. I'll go Mac next time.
Back to the "FindRoot::lstol" error itself, though, I've never seen that
occur when changing precision would actually fix the problem.
Bobby
On Thu, 24 May 2007 09:48:33 -0500, János <janos.lobb at yale.edu> wrote:
> There are function calls in some OS libraries that are not working
> correctly on AMD architecture. A good friend of mine in Hungary worked
> for a software firm and the firm had just AMD machines. The only Intel
> machine was his laptop. When it came to close out a major upgrade of
> the firm software, all AMD machines reported problems and only his Intel
> laptop gave the desired result. All AMDs were changed overnight for
> Intel machines.
>
> János
> On May 24, 2007, at 6:03 AM, DrMajorBob wrote:
>
>> I'm using an AMD 3200+ processor, in case that matters.
>>
>> Bobby
>>
>> On Wed, 23 May 2007 16:37:54 -0500, Andrzej Kozlowski
>> <akoz at mimuw.edu.pl>
>> wrote:
>>
>>> *This message was transferred with a trial version of CommuniGate(tm)
>>> Pro*
>>> That means definitely "platform dependence". It would be interesting if
>>> somone checked this on an Intel Mac. I think it is much more likely to
>>> be the processor than the operating system that makes the difference
>>> here. I don't know much about such things, but some processor specific
>>> libraries could be responsible for this.
>>>
>>> Andrzej
>>>
>>>
>>> On 24 May 2007, at 06:29, DrMajorBob wrote:
>>>
>>>> $Version
>>>>
>>>> "6.0 for Microsoft Windows (32-bit) (April 20, 2007)"
>>>>
>>>> Bobby
>>>>
>>>> On Wed, 23 May 2007 16:17:31 -0500, Andrzej Kozlowski
>>>> <akoz at mimuw.edu.pl> wrote:
>>>>
>>>>> *This message was transferred with a trial version of CommuniGate(tm)
>>>>> Pro*
>>>>> Yes, its curious. It might just be "platform dependence" but is more
>>>>> likely to be "time of release dependence". Mine is:
>>>>>
>>>>>
>>>>> $Version
>>>>>
>>>>> "6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)"
>>>>>
>>>>> Andrzej
>>>>>
>>>>>
>>>>> On 24 May 2007, at 01:37, DrMajorBob wrote:
>>>>>
>>>>>> Interesting. But your results are entirely different from mine, for
>>>>>> the same input.
>>>>>>
>>>>>>> which explains what is wrong (error messages can tell you a lot,
>>>>>>> sometimes).
>>>>>>
>>>>>> And frequently, they don't.
>>>>>>
>>>>>> Here's the error message at THIS machine:
>>>>>>
>>>>>> FindRoot::lstol: The line search decreased the step size to within \
>>>>>> tolerance specified by AccuracyGoal and PrecisionGoal but was
>>>>>> unable \
>>>>>> to find a sufficient decrease in the merit function. You may need \
>>>>>> more than MachinePrecision digits of working precision to meet
>>>>>> these \
>>>>>> tolerances. >>
>>>>>>
>>>>>> Bobby
>>>>>>
>>>>>> On Tue, 22 May 2007 06:28:08 -0500, Andrzej Kozlowski
>>>>>> <akoz at mimuw.edu.pl> wrote:
>>>>>>
>>>>>>> *This message was transferred with a trial version of CommuniGate
>>>>>>> (tm) Pro*
>>>>>>> I don't see any connection between these two issues. Moreover, I
>>>>>>> get:
>>>>>>>
>>>>>>> FindRoot[h == g, {x, 0}]
>>>>>>> FindRoot::njnum:The Jacobian is not a matrix of numbers at {x} =
>>>>>>> {0.}. >>
>>>>>>> {x -> 0.}
>>>>>>>
>>>>>>> which explains what is wrong (error messages can tell you a lot,
>>>>>>> sometimes). Trying a slightly different starting search point:
>>>>>>>
>>>>>>> FindRoot[h == g, {x, 0.1}]
>>>>>>> {x->2.}
>>>>>>>
>>>>>>> {g, h} /. %
>>>>>>> {0., 0.}
>>>>>>>
>>>>>>>
>>>>>>> Andrzej Kozlowski
>>>>>>>
>>>>>>>
>>>>>>> On 22 May 2007, at 15:47, DrMajorBob wrote:
>>>>>>>
>>>>>>>> Even worse, FindRoot returns a wrong answer:
>>>>>>>>
>>>>>>>> g = Piecewise[{{0, x < 0}, {2 x - x^2, 0 <= x < 4}, {16 x - x^2,
>>>>>>>> x³4}}];
>>>>>>>> h = x - 2;
>>>>>>>> FindRoot[h == g, {x, 0}]
>>>>>>>> {g, h} /. %
>>>>>>>>
>>>>>>>> {x->-2.84217*10^-15}
>>>>>>>> {0, -2.}
>>>>>>>>
>>>>>>>> Bobby
>>>>>>>>
>>>>>>>> On Mon, 21 May 2007 05:01:21 -0500, Sebastian Meznaric
>>>>>>>> <meznaric at gmail.com> wrote:
>>>>>>>>
>>>>>>>>> I was playing around with Mathematica 6 a bit and ran this
>>>>>>>>> command
>>>>>>>>> to
>>>>>>>>> solve for the inverse of the Moebius transformation
>>>>>>>>>
>>>>>>>>> FullSimplify[
>>>>>>>>> Reduce[(z - a)/(1 - a\[Conjugate] z) == w && a a\[Conjugate] < 1
>>>>>>>>> &&
>>>>>>>>> w w\[Conjugate] < 1, z]]
>>>>>>>>>
>>>>>>>>> This is what I got as a result:
>>>>>>>>> -1 < w < 1 && -1 < a < 1 && z == (a + w)/(1 + w Conjugate[a])
>>>>>>>>>
>>>>>>>>> Why is Mathematica assuming a and w are real? The Moebius
>>>>>>>>> transformation is invertible in the unit disc regardless of
>>>>>>>>> whether a
>>>>>>>>> and w are real or not. Any thoughts?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --DrMajorBob at bigfoot.com
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> --DrMajorBob at bigfoot.com
>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>> --DrMajorBob at bigfoot.com
>>>
>>>
>>
>>
>>
>> --DrMajorBob at bigfoot.com
>
>
>
> ----------------------------------------------
> Trying to argue with a politician is like lifting up the head of a
> corpse.
> (S. Lem: His Master Voice)
>
>
--
DrMajorBob at bigfoot.com
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