numpy-discussion — Discussion list for all users of Numerical Python

[Numpy-discussion] how to compute a Gamma function with Numpy?

[Charles G W. <cg...@fn...>]

Jean-Bernard Addor writes:
 > Hey Numpy people!
 > 
 > I need to compute the Gamma function (the one related to factorial) with
 > Numpy. It seems no to be included in the module, Am I right? 

Yes, but it is present in Travis Oliphant's "cephes" module which is
an addon to stock NumPy.  See

http://oliphant.netpedia.net/packages/included_functions.html

for the list of functions, and go to 

http://oliphant.netpedia.net/

to download the package itself.

[Numpy-discussion] how to compute a Gamma function with Numpy?

[Jean-Bernard A. <jb...@ph...>]

Hey Numpy people!

I need to compute the Gamma function (the one related to factorial) with
Numpy. It seems no to be included in the module, Am I right? Is any code
for computing it available? Where could I find an algorythme to adapt ?

Jean-Bernard

RE: [Numpy-discussion] Documentation

[Hassan A. <au...@cr...>]

 This is not totally related, but I'd love to see a docbook based doc 
for numpy.

 See, I am writing GmatH (http://gmath.sourceforge.net) and among 
otherb things it provides a nice GUI (I hope) to NumPy.

 Now I'd love to see a docbook based thinggy that could be added to 
the app using a gtkhtml widget (duh!).

 It'd be nice to also have a Quick help file that I could incorporate 
into the app. 



>>>>>>>>>>>>>>>>>> Original Message <<<<<<<<<<<<<<<<<<

On 3/13/00, 6:54:22 PM, Janko Hauser <jh...@if...> wrote 
regarding RE: [Numpy-discussion] Documentation:


> I'm currently build a reference for NumPy and some of the other
> modules in the format of the standard python library reference. At the
> moment this is more a personal effort to get an overview which
> functions are there. I do not really write stuff myself, but bring
> information of various sources together and reformat it.

> Than I want to test some approaches to extract info for a function
> from the HTML source at the interactive commandline.

> I see this not as a replacement for the excellent PDF documentation,
> which has far more information and many examples.

> The standard latex documentation package for Python has currently a
> bug with the index generation. If this is solved I will put a HTML
> tree online, so it can be examined and criticized.

> Yust for information,

> __Janko

> _______________________________________________
> Numpy-discussion mailing list
> Num...@li...
> http://lists.sourceforge.net/mailman/listinfo/numpy-discussion

[Numpy-discussion] single precision version of interp

[Janko H. <jh...@if...>]

Shouldn't this be handled in the function and decided by the typecode
of the parameters. Or put a typcode keyword parameter in the function
signature of interp. To derive functions for different types and put
these into the public namespace is not so good IMHO.

This could also be handled by a wrapper, which calls different the
compiled _functions.

__Janko

RE: [Numpy-discussion] Documentation

[Janko H. <jh...@if...>]

I'm currently build a reference for NumPy and some of the other
modules in the format of the standard python library reference. At the
moment this is more a personal effort to get an overview which
functions are there. I do not really write stuff myself, but bring
information of various sources together and reformat it.

Than I want to test some approaches to extract info for a function
from the HTML source at the interactive commandline. 

I see this not as a replacement for the excellent PDF documentation,
which has far more information and many examples. 

The standard latex documentation package for Python has currently a
bug with the index generation. If this is solved I will put a HTML
tree online, so it can be examined and criticized.

Yust for information,

__Janko

[Numpy-discussion] single precision version of interp

[Joe V. A. <van...@at...>]

As I've previously mentioned to Paul, I need a single precision version
of 'interp()', so I can use it on large single precision arrays, without
returning a double precision array.

In my own copy of NumPy, I've written such a routine, and added it to
'arrayfns.c '.  Naturally, I want to see this functionality built into
the official release, so I do not have to apply my own patches to new
releases.  

Can we decide how such single precision needs are accomodated?  Should
there be a keyword argument on the 'interp()' call, that calls the
single precision version?  Or should the caller invoke 'interpf()',
rather than 'interp()?'  

I don't much care what the solution looks like, as long as people agree
that:
1) we need such functionality in NumPy.

2) we can establish a precedent on how single precision vs double
precision methods are invoked.

Please let me know your opinions on how this should be resolved.

Thanks much!

-- 
Joe VanAndel  	          
National Center for Atmospheric Research
http://www.atd.ucar.edu/~vanandel/
Internet: van...@uc...

RE: [Numpy-discussion] Documentation

[Paul F. D. <pau...@ho...>]

>     Who is maintaining the Python manual actually?
> 
Me.

Re: [Numpy-discussion] Documentation

[Pablo B. K. <pb...@dg...>]

Paul Barrett wrote:

> I have a couple of question about the Numpy documentation:
>
> 1. Is there a recent version of the Numerical Python manual available
>    anywhere?  I can't find it at the SourceForge and I've tried
>    xfiles.llnl.org, but can't get through.  (But from what Paul Dubois
>    has said recently about the LLNL site, I shouldn't expect to
>    either.)
>
> 2. Have any changes been made to the documentation since about Q1
>    1999?  I think my current version dates from about this period.
>
>  -- Paul

    Who is maintaining the Python manual actually?

--
Pablo Bleyer Kocik |"And all this science I don't understand
pbleyer            | It's just my job five days a week
    @dgf.uchile.cl | A rocket man, a rocket man..." - Elton John

from sys import*;from string import*;a=argv;[s,p,q]=filter(lambda x:x[:1]!=
'-',a);d='-d'in a;e,n=atol(p,16),atol(q,16);l=(len(q)+1)/2;o,inb=l-d,l-1+d
while s:s=stdin.read(inb);s and map(stdout.write,map(lambda i,b=pow(reduce(
lambda x,y:(x<<8L)+y,map(ord,s)),e,n):chr(b>>8*i&255),range(o-1,-1,-1)))

[Numpy-discussion] Documentation

[Paul B. <Ba...@st...>]

I have a couple of question about the Numpy documentation:

1. Is there a recent version of the Numerical Python manual available
   anywhere?  I can't find it at the SourceForge and I've tried
   xfiles.llnl.org, but can't get through.  (But from what Paul Dubois
   has said recently about the LLNL site, I shouldn't expect to
   either.)

2. Have any changes been made to the documentation since about Q1
   1999?  I think my current version dates from about this period.

 -- Paul

[Numpy-discussion] Moving archives to Sourceforge.

[Les S. <god...@ne...>]

Travis:

> qI'm responding, but I don't know the answer to your question.  I am not
familiar with Mailman, or how to move archives on to sourceforge, or if it
is even possible.

i have been in contact with Paul Dubois and i am tracking down the
feasibility of making the transfer happen. it amounts to cat'ing the
mailbox from the matrix sig archive onto the sourceforge archive, and
re-running the archiver on the resulting mailbox (according to barry
warsaw).

so we need to find out if sourceforge allows us to fiddle with the
mailbox in that fashion.

les schaffer

[Numpy-discussion] Moving archives to Sourceforge.

[Travis O. <Oli...@ma...>]

I'm responding, but I don't know the answer to your question.  I am not
familiar with Mailman, or how to move archives on to sourceforge, or if it
is even possible.

Sorry for the inadequate help, but I suspect that you are not getting a
response because nobody knows.

Sincerely,

Travis Oliphant

[Numpy-discussion] old matric-SIG archives

[Les S. <god...@ne...>]

well, let me try it this way:

1.) Is this list the place where people who have the capability of
moving the old matrix-sig archives from python.org to sourceforge hang
out?

2.) If you're here and listening, i see that the sourceforge archives
are already searchable, so.... if we moved the old matrix-sig archives
over to sourceforge, is there more work need done to make __them__
searchable? i volunteer to make this happen.


les schaffer

-- 
____        Les Schaffer              ___| --->> Engineering R&D <<---
Theoretical & Applied Mechanics          |  Designspring, Inc. 
Center for Radiophysics & Space Research |  http://www.designspring.com/
Cornell Univ.  sch...@ta...  |  le...@de...

Re: [Numpy-discussion] Volunteer sought for BLAS/LINPACK restructure

[Michael H. <mh...@bl...>]

Hello,

"Paul F. Dubois" <pau...@ho...> writes:
> We are seeking a volunteer developer for Numeric who will remove the
> current BLAS/LINPACK lite stuff in favor of linking to whatever the
> native version is on a particular machine.

I don't have much time to help out with the python interface, but I
have some (mostly) machine-translated C/C++ header files for LAPACK
that might be useful.  These files could be SWIGged as a starting
point for a python binding.

Even better, the perl (*yuck*) script that does the translation could
be modified to prototype input vs. output arrays differently (the
script determines which arrays are input vs. output from the comment
lines from the Fortran source).  Then SWIG typemaps could be written
that handle input/output correctly and much of the wrapping job would
be automated.  Of course all this won't help with row vs. column
storage format.  The header files and a translation script can be
obtained from

    http://monsoon.harvard.edu/~mhagger/download/

Unfortuantely I don't have the same thing for BLAS, mostly because the
comments in the BLAS Fortran files are less careful and consistent,
making machine interpretation more difficult.

Please let me know if you find these headers useful.

Yours,
Michael

-- 
Michael Haggerty
mh...@bl...

Re: [Numpy-discussion] Volunteer sought for BLAS/LINPACK restructure

[<hi...@di...>]

> We are seeking a volunteer developer for Numeric who will remove the current
> BLAS/LINPACK lite stuff in favor of linking to whatever the native version
> is on a particular machine. The current default is that you have to work

This should take several volunteers; nobody has access to all machine
types!

> A truly excited volunteer would widen the amount of stuff that the interface
> can get to. They would work via the CVS tree; see

That is not necessary; a full BLAS/LAPACK interface has existed for
years, written by Doug Heisterkamp. In fact, the lapack_lite module
is simply a subset of it.

By some strange coincidence I have worked a bit on this just a few
days ago. I have added a compilation/installation script and
added thread support (such that LAPACK calls don't block other threads).
You can pick it up at
                  ftp://dirac.cnrs-orleans.fr/pub/
as a tar archive and as RPMs for (RedHat) Linux.

Konrad.
-- 
-------------------------------------------------------------------------------
Konrad Hinsen                            | E-Mail: hi...@cn...
Centre de Biophysique Moleculaire (CNRS) | Tel.: +33-2.38.25.55.69
Rue Charles Sadron                       | Fax:  +33-2.38.63.15.17
45071 Orleans Cedex 2                    | Deutsch/Esperanto/English/
France                                   | Nederlands/Francais
-------------------------------------------------------------------------------

[Numpy-discussion] moving matrix-SIG archives to SourceForge

[Les S. <god...@ne...>]

Is there any chance of getting the old matrix-SIG archives moved over
to SourceForge location and have them made searchable?

i wanted to look up stuff on broadcast rules in NumPy and remembered
there were posts on it in the old archives, but i dont see any way to
search the things.

thanks

les schaffer

[Numpy-discussion] Volunteer sought for BLAS/LINPACK restructure

[Paul F. D. <pau...@ho...>]

We are seeking a volunteer developer for Numeric who will remove the current
BLAS/LINPACK lite stuff in favor of linking to whatever the native version
is on a particular machine. The current default is that you have to work
harder to get the good ones than our bad ones; we want to reverse that.

We have gotten a lot of complaints about the current situation and while we
are aware of the counter arguments the Council of Nummies has reached a
consensus to do this.

A truly excited volunteer would widen the amount of stuff that the interface
can get to. They would work via the CVS tree; see
http://numpy.sourceforge.net. Please reply to du...@us....

> -----Original Message-----
> From: num...@li...
> [mailto:num...@li...]On Behalf Of James
> R. Webb
> Sent: Monday, February 07, 2000 10:04 PM
> To: num...@li...
> Cc: mat...@py...
> Subject: [Numpy-discussion] Re: [Matrix-SIG] An Experiment in
> code-cleanup.
>
>
> There is now a linux native BLAS available through links at
> http://www.cs.utk.edu/~ghenry/distrib/  courtesy of the ASCI Option Red
> Project.
>
> There is also ATLAS (http://www.netlib.org/atlas/).
>
> Either library seems to link into NumPy without a hitch.
>
> ----- Original Message -----
> From: "Beausoleil, Raymond" <be...@ex...>
> To: <num...@li...>
> Cc: <mat...@py...>
> Sent: Tuesday, February 08, 2000 2:31 PM
> Subject: RE: [Matrix-SIG] An Experiment in code-cleanup.
>
>
> > I've been reading the posts on this topic with considerable
> interest. For
> a
> > moment, I want to emphasize the "code-cleanup" angle more literally than
> the
> > functionality mods suggested so far.
> >
> > Several months ago, I hacked my personal copy of the NumPy
> distribution so
> > that I could use the Intel Math Kernel Library for Windows. The IMKL is
> > (1) freely available from Intel at
> > http://developer.intel.com/vtune/perflibst/mkl/index.htm;
> > (2) basically BLAS and LAPACK, with an FFT or two thrown in for good
> > measure;
> > (3) optimized for the different x86 processors (e.g., generic
> x86, Pentium
> > II & III);
> > (4) configured to use 1, 2, or 4 processors; and
> > (5) configured to use multithreading.
> > It is an impressive, fast implementation. I'm sure there are similar
> native
> > libraries available on other platforms.
> >
> > Probably due to my inexperience with both Python and NumPy, it took me a
> > couple of days to successfully tear out the f2c'd stuff and get the IMKL
> > linking correctly. The parts I've used work fine, but there are probably
> > other features that I haven't tested yet that still aren't up
> to snuff. In
> > any case, the resulting code wasn't very pretty.
> >
> > As long as the NumPy code is going to be commented and cleaned
> up, I'd be
> > glad to help make sure that the process of using a native BLAS/LAPACK
> > distribution (which was probably compiled using Fortran storage
> and naming
> > conventions) is more straightforward. Among the more tedious issues to
> > consider are:
> > (1) The extent of the support for LAPACK. Do we want to stick
> with LAPACK
> > Lite?
> > (2) The storage format. If we've still got row-ordered matrices
> under the
> > hood, and we want to use native LAPACK libraries that were
> compiled using
> > column-major format, then we'll have to be careful to set all
> of the flags
> > correctly. This isn't going to be a big deal, _unless_ NumPy
> will support
> > more of LAPACK when a native library is available. Then, of
> course, there
> > are the special cases: the IMKL has both a C and a Fortran interface to
> the
> > BLAS.
> > (3) Through the judicious use of header files with compiler-dependent
> flags,
> > we could accommodate the various naming conventions used when
> the FORTRAN
> > libraries were compiled (e.g., sgetrf_ or SGETRF).
> >
> > The primary output of this effort would be an expansion of the
> "Compilation
> > Notes" subsection of Section 15 of the NumPy documentation, and some
> header
> > files that made the recompilation easier than it is now.
> >
> > Regards,
> >
> > Ray
> >
> > ============================
> > Ray Beausoleil
> > Hewlett-Packard Laboratories
> > mailto:be...@hp...
> > Vox: 425-883-6648
> > Fax: 425-883-2535
> > HP Telnet: 957-4951
> > ============================
> >
> > _______________________________________________
> > Matrix-SIG maillist  -  Mat...@py...
> > http://www.python.org/mailman/listinfo/matrix-sig
> >
>
>
> _______________________________________________
> Numpy-discussion mailing list
> Num...@li...
> http://lists.sourceforge.net/mailman/listinfo/numpy-discussion

RE: [Numpy-discussion] numpy on NT

[David A. <Da...@Ac...>]

> A colleague is attempting to install numpy on an NT machine.  How is
> this done?  I tried to help, but the install procedure is apparently
> different from what I am accustomed on Unix.
>
> It appears that the python-numpy-15.2.zip is a precompiled
> distribution ready for dumping into some directory.  Since it doesn't
> contain a setup.py, I presume that Distutils isn't necessary.

Indeed.  You can just unzip it straight in to your main Python directory
(typically C:\Program Files\Python).

> Also, what is the accepted way of setting PYTHONPATH on NT?

Go to the control panel, click on the System icon, pick the Environment tab,
and add an entry (usually in the USER section) for PYTHONPATH.

But you only need to do so if you don't want to install NumPy in the main
Python directory.

--david

[Numpy-discussion] numpy on NT

[JEFFERY C. <co...@ru...>]

A colleague is attempting to install numpy on an NT machine.  How is
this done?  I tried to help, but the install procedure is apparently
different from what I am accustomed on Unix. 

It appears that the python-numpy-15.2.zip is a precompiled
distribution ready for dumping into some directory.  Since it doesn't
contain a setup.py, I presume that Distutils isn't necessary.

Also, what is the accepted way of setting PYTHONPATH on NT?

Thanks,

Jeff

Re: [Numpy-discussion] python FAQTS

[Nathan W. <na...@sy...>]

Please don't hesitate to ask if there are any changes / improvements to
FAQTs that could be made to help your project.

Cheers,

Nathan

> Done. Also added link on python.faqts.com to Numerical and Pyfort.

RE: [Numpy-discussion] python FAQTS

[Paul F. D. <pau...@ho...>]

Done. Also added link on python.faqts.com to Numerical and Pyfort.

> -----Original Message-----
> From: num...@li...
> [mailto:num...@li...]On Behalf Of Joe
> Van Andel
> Sent: Thursday, March 02, 2000 7:22 AM
> To: num...@li...
> Cc: na...@sy...
> Subject: [Numpy-discussion] python FAQTS
> 
> Could we add a link to the (Numeric) Python Knowledge Base to Numeric
> Python's home on
> sourceforge?
> 

[Numpy-discussion] python FAQTS

[Joe V. A. <van...@at...>]

I just started looking at the new Python Knowledge Base, maintained at
http://python.faqts.com

This looks like a nice simple way of maintaining FAQs and link
collections.  I've already registered, and started building links to
various packages that work with Numeric Python.  

Since sourceforge.net doesn't seem to offer these collaborative FAQ
building tools, I'd propose that we should add to the existing Numeric
Python FAQs, and expand the link collection that I've (just) started.

Could we add a link to the (Numeric) Python Knowledge Base to Numeric
Python's home on
sourceforge?



-- 
Joe VanAndel  	          
National Center for Atmospheric Research
http://www.atd.ucar.edu/~vanandel/
Internet: van...@uc...

[Numpy-discussion] Re: Numpy-discussion digest, Vol 1 #20 - 5 msgs

[Greg K. <gp...@be...>]

Look at Scientific Python (see
http://starship.python.net/crew/hinsen/scientific.html )
for some differentiation routines.


> From: Hassan Aurag <au...@cr...>
> Date: Wed, 01 Mar 2000 14:32:48 GMT
> To: Gma...@li..., num...@li...
> Subject: [Numpy-discussion] Derivatives
>
> Hi,
>
> attached is a file called Derivative.py.
>
> It computes derivatives and is based on an algorithm found in
> Numerical Recipes in C.
>
> What to do you think about it and has anyone started a "serious"
> calculus oriented subpackage for Numerical Python in general?

[Numpy-discussion] Survey results

[Travis O. <Oli...@ma...>]

I'm still here working away at the code cleanup of Numerical Python.  I
know some of you may be interested in the results of a survey related to
that effort. 

Here are the results so far:  

1: How long have your been using NumPy:

19 response:  
<= 1 year:  8
 1-3 years:  6
 4-5 years:  5

2: How important is NumPy to your daily work now? (1-Depend on it, 
      5-Dabble with it)

 1 - 17
 2 -  5
 3 -  5
 4 -  3

Avg: 1.8


3: How would you rate the current functionality of NumPy? (1-Love it,
     5-Hate it)

1 - 2
2 - 19
3 - 8
4 - 1

Avg: 2.27


4: How important is it to you for NumPy to get into the Python core?
     (1-Very Important, 5-Not Important)

1 - 8
2 - 14
3 - 4
3 - 4

Avg: 2.1


5: How much interest do you have in improving NumPy? (1-Unlimited, 5-None)

1 - 10
2 - 13
3 - 7

Avg: 1.9


6: How concerned are you about alterations to the underlying C-structure 
    of NumPy? (1-Very concerned, 5-Don't care))

1 - 3
2 - 2
3 - 8
4 - 5
5 - 12

Avg: 3.7


7:  How important is memory conservation to you? (1-Very important, 5-Not
     important)

1 - 11
2 - 10
3 - 6
4 - 1
5 - 2

Avg: 2.1


8: How important is it to you that the underlying code to NumPy be easy to
   understand? (1-Very important, 5-Not important)

1 - 7
2 - 13
3 - 5
4 - 5

Avg: 2.3


9: How important is it to you that NumPy be fast? (1-Very important, 5-Not
important)

1 - 22
2 - 7
3 - 1

Avg: 1.3


10: How happy are you with the current coercion rules (including 
    spacesaving arrays)? (1-Happy, 5-Miserable)

1 - 3
2 - 13
3 - 10 
4 - 2

Avg: 2.4


11: Should mixed-precision arithmetic cast to the largest memory type
    (yes) or the least memory type (no)?

Yes - 23
No  - 6


12: Should object arrays (typecode='O') remain a part of NumPy? (1-Agree, 
     5-Disagree)

1 - 13
2 - 3
3 - 10
4 - 2

Avg: 2.1


13: Should slices (e.g. x[3:10]) be changed to be copies? 

Yes - 12 
No  - 16


So, as you can see the results were pretty clear in some areas and quite
controversial in other areas.  

Have fun interpreting them...

Travis

Re: [Numpy-discussion] Derivatives (fwd)

[Hassan A. <au...@cr...>]

 Mathematica does it correctly. How is another question. 
But I guess the idea is to pass it through some kind of database of 
exact solutions then optionally evaluate it.

 Mathematica is very good at that (symbolic stuff)


>>>>>>>>>>>>>>>>>> Original Message <<<<<<<<<<<<<<<<<<

On 3/1/00, 4:40:35 PM, "Zow" Terry Brugger <zo...@pe...> wrote 
regarding [Numpy-discussion] Derivatives (fwd):


> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1

> Content-Type: text/plain; charset=us-ascii

> Hassan,
>       This seemed relevant to pass back to the numeric list - hope you 
don't mind.
> My comments follow.

> - ------- Forwarded Message

> Date:    Wed, 01 Mar 2000 19:46:42 +0000
> From:    Hassan Aurag <au...@cr...>
> To:      zo...@ll..., Gma...@li...
> Subject: Re: [Gmath-devel] Re: [Numpy-discussion] Derivatives



>  I have to agree with you on most counts that Numerical Recipes in 
C=20
> is not a full-blown encyclopedia on all subtleties of doing 
numerical=20
> computations.

>  However it does its job greatly for a big class of stuff I am=20
> interested in: minimization, non-linear system of equations solving=20
> (The newton routine given there is good, accurate and fast.)

>  There are errors and problems as in most other numerical books. In=20
> truth, I don't think there is anything fully correct out there.

>  When trying to make computations you have to do a lot of testing 
and=20
> a lot of thought even if the algorithm seems perfect. That applies 
to=20
> all books, recipes et al.

>  I have just discovered that tan(pi/2) =3D 1.63317787284e+16 in=20
> numerical python. And we all know this is bad. It should be 
infinity=20
> period. We should define a symbol called infinity and put the 
correct=20
> definition of tan, sin .... for all known angles then interpolate 
if=20
> needed for the rest, or whatever is used to actually compute those 
thing=
> s.

>  Peace

> <snip>
> - ------- End of Forwarded Message

> I believe you're actually talking about the math module, not the 
numeric
> module (I'm not aware of tan or pi definitions in numeric, but I 
haven't
> bothered to double check that). Never the less, I think it has 
relevance here
> as Numeric is all about doing serious number crunching. This problem 
is caused
> by the lack of infinite precision in python. Of course, how is it even
> possible to perform infinite precision on non-rational numbers?

> The obvious solution is to allow the routine (tan() in this case) to 
recognize
> named constants that have relevance in their domain (pi in this case). 
This
> would fix the problem:

> math.tan(math.pi) = -1.22460635382e-16

> but it still doesn't solve your problem because the named constant 
would have
> the mathematical operation performed on it before it's passed into the
> function, ruining whatever intimate knowledge of the given named 
constant that
> routine has.

> Perhaps you could get the routine to recognize rational math on named
> constants (the problem with that solution is how do you not burden 
other
> routines with the knowledge of how to process that expression). 
Assuming you
> had that, even for your example, should the answer be positive or 
negative
> infinity?

> Another obvious solution is just to assume that any floating point 
overflow is
> infinity and any underflow is zero. This obviously won't work because 
some
> asymptotic functions (say 1/x^3) will overflow or underflow at values 
for x
> for which the correct answer is not properly infinity or zero.

> It is interesting to note that Matlab's behaviour is the same as 
Python's,
> which would indicate to me that there's not some easy solution to this 
problem
> that Guido et. al. overlooked. I haven't really researched the problem 
at all
> (although now I'm interested), but I'd be interested if anyone has a 
proposal
> for (or reference to) how this problem can be solved in a general 
purpose
> programming language at all (as there exists the distinct possibility 
that it
> can not be done in Python without breaking backwards compatibility).

> Terry



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[Numpy-discussion] Derivatives (fwd)

[Zow T. B. <zo...@pe...>]

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Hassan,
	This seemed relevant to pass back to the numeric list - hope you don't mind. 
My comments follow.

- ------- Forwarded Message

Date:    Wed, 01 Mar 2000 19:46:42 +0000
From:    Hassan Aurag <au...@cr...>
To:      zo...@ll..., Gma...@li...
Subject: Re: [Gmath-devel] Re: [Numpy-discussion] Derivatives



 I have to agree with you on most counts that Numerical Recipes in C=20
is not a full-blown encyclopedia on all subtleties of doing numerical=20
computations.

 However it does its job greatly for a big class of stuff I am=20
interested in: minimization, non-linear system of equations solving=20
(The newton routine given there is good, accurate and fast.)

 There are errors and problems as in most other numerical books. In=20
truth, I don't think there is anything fully correct out there.

 When trying to make computations you have to do a lot of testing and=20
a lot of thought even if the algorithm seems perfect. That applies to=20
all books, recipes et al.

 I have just discovered that tan(pi/2) =3D 1.63317787284e+16 in=20
numerical python. And we all know this is bad. It should be infinity=20
period. We should define a symbol called infinity and put the correct=20
definition of tan, sin .... for all known angles then interpolate if=20
needed for the rest, or whatever is used to actually compute those thing=
s.

 Peace

<snip>
- ------- End of Forwarded Message

I believe you're actually talking about the math module, not the numeric 
module (I'm not aware of tan or pi definitions in numeric, but I haven't 
bothered to double check that). Never the less, I think it has relevance here 
as Numeric is all about doing serious number crunching. This problem is caused 
by the lack of infinite precision in python. Of course, how is it even 
possible to perform infinite precision on non-rational numbers?

The obvious solution is to allow the routine (tan() in this case) to recognize 
named constants that have relevance in their domain (pi in this case). This 
would fix the problem:

math.tan(math.pi) = -1.22460635382e-16

but it still doesn't solve your problem because the named constant would have 
the mathematical operation performed on it before it's passed into the 
function, ruining whatever intimate knowledge of the given named constant that 
routine has.

Perhaps you could get the routine to recognize rational math on named 
constants (the problem with that solution is how do you not burden other 
routines with the knowledge of how to process that expression). Assuming you 
had that, even for your example, should the answer be positive or negative 
infinity?

Another obvious solution is just to assume that any floating point overflow is 
infinity and any underflow is zero. This obviously won't work because some 
asymptotic functions (say 1/x^3) will overflow or underflow at values for x 
for which the correct answer is not properly infinity or zero.

It is interesting to note that Matlab's behaviour is the same as Python's, 
which would indicate to me that there's not some easy solution to this problem 
that Guido et. al. overlooked. I haven't really researched the problem at all 
(although now I'm interested), but I'd be interested if anyone has a proposal 
for (or reference to) how this problem can be solved in a general purpose 
programming language at all (as there exists the distinct possibility that it 
can not be done in Python without breaking backwards compatibility).

Terry



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