[sage-devel] Re: linear algebra functions
> > * getting rid of functions which implicitly assume left/right and making > > those functions explicitly say what they are returning, since, for > > example, a vast majority of linear algebra people would assume kernel() > > is the right kernel, while apparently a sizable contingent of number > > theory/sage people assume kernel() means left kernel. > > +1 to being explicit > +1: I remember that slogan in the Zen of Python "explicit is better than implicit" Pablo --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
Mike Hansen wrote: >> * introduction of eigen* functions > > +1 definitely. > >> * changing left/right_* functions to *_left/right to make tab completion >> and finding the functions much easier. > > The *_left and *_right are easier to find under tab completion, but > they are much uglier when reading code. I don't understand why not > just have both. In any case, this is mostly bikeshedding when > compared to the other changes. I think you're right about the advantages and disadvantages. The reason to have only one set is: 1. The python "way" of having only one way to do things, instead of multiple equivalent ways. [1] 2. prevent the littering of the namespace with identical functions that are just named differently. 3. When this was brought up on sage-devel before, people were even against the *_left/right names since there were then two functions for computing kernel, for example. Having 4 functions to compute the kernel seems a bit much. Personally, I think the ease of tab completion and finding the functions is more important than the adjective_noun form of function names. But in absence of other opinions, I'll make the patch just have left/right_* synonyms to the *_left/right functions, with no deprecation notice for the left/right_* functions. William also weighed in on IRC against the *_left/right naming convention. Thanks, Jason [1] "There should be one-- and preferably only one --obvious way to do it.", see http://www.python.org/dev/peps/pep-0020/ --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
> * introduction of eigen* functions +1 definitely. > * changing left/right_* functions to *_left/right to make tab completion > and finding the functions much easier. The *_left and *_right are easier to find under tab completion, but they are much uglier when reading code. I don't understand why not just have both. In any case, this is mostly bikeshedding when compared to the other changes. > * getting rid of functions which implicitly assume left/right and making > those functions explicitly say what they are returning, since, for > example, a vast majority of linear algebra people would assume kernel() > is the right kernel, while apparently a sizable contingent of number > theory/sage people assume kernel() means left kernel. +1 to being explicit --Mike --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
David Joyner wrote: > They installed fine and I'm testing it out now. Just to confirm: > in matrix2 you have > eigenspaces_left, eigenspaces_right, > eigenvalues_left, eigenvalues_right, Actually, there should be only eigenvalues(). There should also be eigenvectors_right/left and eigenmatrix_right/left. > kernel_left, kernel_right, > image_left (= row_space), image_right (=column_space), > but in functional and matrix_rational_dense, you only have kernel_left? The modifications to functional.py, matrix_rational_dense, and matrix_integer_dense are still being worked on. The main things I was testing was the modifications in matrix2.pyx. The plan is to carry the interface into any subclass that overrides any of these functions (including matrices over RDF and CDF too, as well as symbolic matrices). So the main changes: * introduction of eigen* functions * changing left/right_* functions to *_left/right to make tab completion and finding the functions much easier. * getting rid of functions which implicitly assume left/right and making those functions explicitly say what they are returning, since, for example, a vast majority of linear algebra people would assume kernel() is the right kernel, while apparently a sizable contingent of number theory/sage people assume kernel() means left kernel. Again, comments/suggestions/complaints? Thanks, Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
They installed fine and I'm testing it out now. Just to confirm: in matrix2 you have eigenspaces_left, eigenspaces_right, eigenvalues_left, eigenvalues_right, kernel_left, kernel_right, image_left (= row_space), image_right (=column_space), but in functional and matrix_rational_dense, you only have kernel_left? On Sat, Jul 19, 2008 at 2:49 PM, Jason Grout <[EMAIL PROTECTED]> wrote: > > David Joyner wrote: >> I think it's great that you are doing this. Does a patch exist yet? >> I'd like to try it out. > > > I put up a preliminary patch at > http://trac.sagemath.org/sage_trac/ticket/2816 > > The patch there depends on the patch at: > > http://trac.sagemath.org/sage_trac/ticket/3654 > > I'll work on the documentation later. I'm very interested in feedback > about the function names, though. > > Thanks, > > Jason > > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
David Joyner wrote: > I think it's great that you are doing this. Does a patch exist yet? > I'd like to try it out. I put up a preliminary patch at http://trac.sagemath.org/sage_trac/ticket/2816 The patch there depends on the patch at: http://trac.sagemath.org/sage_trac/ticket/3654 I'll work on the documentation later. I'm very interested in feedback about the function names, though. Thanks, Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
David Joyner wrote:
> I think it's great that you are doing this. Does a patch exist yet?
> I'd like to try it out.
Yes, on my computer. The documentation isn't there yet, though. I'll
try to put up something today.
Thanks,
Jason
>
> On Sat, Jul 19, 2008 at 11:06 AM, Jason Grout
> <[EMAIL PROTECTED]> wrote:
>> I've been working on writing eigenvalue/eigenvector functions, as
>> mentioned here:
>> http://groups.google.com/group/sage-devel/browse_thread/thread/c8d2001f2b19a9bc/2585039efd2fbd2f?lnk=gst&q=kernel#2585039efd2fbd2f
>>
>> Here is the interface as it now stands. Does anyone have any comments
>> or questions?
>>
>> * eigenspaces_left, eigenspaces_right: Like the current eigenspaces
>> function, but returns the algebraic multiplicity of the eigenvalue as
>> well in tuples like: (eigenvalue, eigenspace, algebraic multiplicity).
>> This way, existing code that depends on the first two elements of a
>> returned tuple being what they are still works. In the future, we might
>> consider using a dictionary like {"eigenvalue": eigenvaxill works. It
>> prints a deprecation warning and then calls eigenspaces_left.
>>
>> Also, the even_if_inexact argument is deprecated. Instead, a warning
>> message is printed if the function is called with an inexact base ring.
>>
>> Note that the eigenspace functions still return the eigenvalues up to
>> Galois conjugation, and the algebraic multiplicity applies to each
>> galois conjugate of the returned eigenvalue (at least, I think that's
>> how the math should work, right?)
>>
>> * eigenvalues: This function returns all the eigenvalues as elements of
>> QQbar: i.e., it returns all the galois conjugates of eigenvalues
>> returned in eigenspaces_left. For an nxn matrix, it returns n
>> eigenvalues, so the algebraic multiplicity is not explicitly returned,
>> but is implicit in the list.
>>
>> * eigenvectors_left, eigenvectors_right: These functions return tuples
>> of the form: (eigenvalue, list of eigenvectors, algebraic multiplicity).
>> The eigenvalues are elements of QQbar and are all distinct
>> eigenvalues. The list of eigenvectors is found by taking the basis of
>> the space returned in eigenspaces_* and then mapping it to QQbar^n by
>> the map that takes the eigenvalue to a particular galois conjugate.
>>
>> * eigenmatrix_left, eigenmatrix_right: This mimics the eig command in
>> Matlab: it returns a matrix D and a matrix P, where D is a diagonal
>> matrix of eigenvalues and P is a matrix of rows or columns corresponding
>> eigenvectors or zero vectors so that AP=PD or PA=DP (depending on left
>> or right).
>>
>> I'm also trying to get the kernel and image and other functions that
>> depend on left/right notions to signify they side they are computing.
>> Right now I changed them to *_left and *_right (instead of left_* and
>> right_*) and deprecating the left_* and right_* functions. I realize
>> that the *_left/right functions don't read as naturally as left/right_*
>> functions, but they make a lot more sense in tab completion; if someone
>> is looking to compute the kernel of a matrix, then it's harder to find
>> the function if it is called left/right_kernel than if it is called
>> kernel_left/right. For tab completion, I think it's better in general
>> to do an index-style noun_modifier than modifier_noun (as would be more
>> naturally spoken).
>>
>> Also, to address another point: there would be a lot functions with the
>> above changes. I'm following the philosophy expressed, I believe, by
>> Nick: that each function should clearly indicate what it is returning
>> and that arguments should not change the mathematical content of what is
>> being returned. I see left eigenvectors and right eigenvectors as
>> fundamentally different things, i.e., I wouldn't ever want to confuse
>> the two (well, I guess unless the matrix was symmetric :). That's why I
>> have two different functions instead of one eigenvectors(left=True) or
>> eigenvectors(right=True).
>>
>> I'm trying hard to get this done for 3.0.6 in time for an AIM workshop
>> on undergraduate linear algebra research that is introducing the
>> participants to Sage. Otherwise, I'm afraid that Sage won't be very
>> suitable for the workshop, not having an eigenvalues function, for example.
>>
>> Thanks,
>>
>> Jason
>>
>>
>
> >
>
--~--~-~--~~~---~--~~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-devel] Re: linear algebra functions
I think it's great that you are doing this. Does a patch exist yet?
I'd like to try it out.
On Sat, Jul 19, 2008 at 11:06 AM, Jason Grout
<[EMAIL PROTECTED]> wrote:
>
> I've been working on writing eigenvalue/eigenvector functions, as
> mentioned here:
> http://groups.google.com/group/sage-devel/browse_thread/thread/c8d2001f2b19a9bc/2585039efd2fbd2f?lnk=gst&q=kernel#2585039efd2fbd2f
>
> Here is the interface as it now stands. Does anyone have any comments
> or questions?
>
> * eigenspaces_left, eigenspaces_right: Like the current eigenspaces
> function, but returns the algebraic multiplicity of the eigenvalue as
> well in tuples like: (eigenvalue, eigenspace, algebraic multiplicity).
> This way, existing code that depends on the first two elements of a
> returned tuple being what they are still works. In the future, we might
> consider using a dictionary like {"eigenvalue": eigenvaxill works. It
> prints a deprecation warning and then calls eigenspaces_left.
>
> Also, the even_if_inexact argument is deprecated. Instead, a warning
> message is printed if the function is called with an inexact base ring.
>
> Note that the eigenspace functions still return the eigenvalues up to
> Galois conjugation, and the algebraic multiplicity applies to each
> galois conjugate of the returned eigenvalue (at least, I think that's
> how the math should work, right?)
>
> * eigenvalues: This function returns all the eigenvalues as elements of
> QQbar: i.e., it returns all the galois conjugates of eigenvalues
> returned in eigenspaces_left. For an nxn matrix, it returns n
> eigenvalues, so the algebraic multiplicity is not explicitly returned,
> but is implicit in the list.
>
> * eigenvectors_left, eigenvectors_right: These functions return tuples
> of the form: (eigenvalue, list of eigenvectors, algebraic multiplicity).
> The eigenvalues are elements of QQbar and are all distinct
> eigenvalues. The list of eigenvectors is found by taking the basis of
> the space returned in eigenspaces_* and then mapping it to QQbar^n by
> the map that takes the eigenvalue to a particular galois conjugate.
>
> * eigenmatrix_left, eigenmatrix_right: This mimics the eig command in
> Matlab: it returns a matrix D and a matrix P, where D is a diagonal
> matrix of eigenvalues and P is a matrix of rows or columns corresponding
> eigenvectors or zero vectors so that AP=PD or PA=DP (depending on left
> or right).
>
> I'm also trying to get the kernel and image and other functions that
> depend on left/right notions to signify they side they are computing.
> Right now I changed them to *_left and *_right (instead of left_* and
> right_*) and deprecating the left_* and right_* functions. I realize
> that the *_left/right functions don't read as naturally as left/right_*
> functions, but they make a lot more sense in tab completion; if someone
> is looking to compute the kernel of a matrix, then it's harder to find
> the function if it is called left/right_kernel than if it is called
> kernel_left/right. For tab completion, I think it's better in general
> to do an index-style noun_modifier than modifier_noun (as would be more
> naturally spoken).
>
> Also, to address another point: there would be a lot functions with the
> above changes. I'm following the philosophy expressed, I believe, by
> Nick: that each function should clearly indicate what it is returning
> and that arguments should not change the mathematical content of what is
> being returned. I see left eigenvectors and right eigenvectors as
> fundamentally different things, i.e., I wouldn't ever want to confuse
> the two (well, I guess unless the matrix was symmetric :). That's why I
> have two different functions instead of one eigenvectors(left=True) or
> eigenvectors(right=True).
>
> I'm trying hard to get this done for 3.0.6 in time for an AIM workshop
> on undergraduate linear algebra research that is introducing the
> participants to Sage. Otherwise, I'm afraid that Sage won't be very
> suitable for the workshop, not having an eigenvalues function, for example.
>
> Thanks,
>
> Jason
>
>
> >
>
--~--~-~--~~~---~--~~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
