Re: Taylor expansion does not expand well

[James Sherman Jr.]

On Thu, Dec 10, 2015 at 4:06 PM, Nicholas Jankowski <address@hidden> wrote:
> On Thu, Dec 10, 2015 at 3:42 PM, Nicholas Jankowski <address@hidden>
> wrote:
>>
>> On Thu, Dec 10, 2015 at 2:08 PM, James Sherman Jr. <address@hidden>
>> wrote:
>>>
>>> On Thu, Dec 10, 2015 at 12:36 PM, Nicholas Jankowski
>>> <address@hidden> wrote:
>>> > On Thu, Dec 10, 2015 at 12:05 PM, Andy Buckle <address@hidden>
>>> > wrote:
>>> >>
>>> >>
>>> >>
>>> >> On 10 December 2015 at 16:56, Jonathan Camilleri
>>> >> <address@hidden>
>>> >> wrote:
>>> >>>
>>> >>> How does this work please?
>>> >>>
>>> >>> f=[1,3,3]
>>> >>> f =
>>> >>>
>>> >>>    1   3   3
>>> >>>
>>> >>> octave:2> g = taylor(1,'expansionPoint',1,'order',4)
>>> >>>
>>> >>> Error:
>>> >>> error: 'taylor' undefined near line 1 column 5
>>> >>>
>>> >>> What does this error mean please?
>>> >>>
>>> >>>
>>> >>> I am using http://octave-online.net/.
>>> >>>
>>> >>> See post at
>>> >>>
>>> >>> http://math.stackexchange.com/questions/209320/where-do-the-factorials-come-from-in-the-taylor-series.
>>> >>> See https://en.wikipedia.org/wiki/Taylor_series.
>>> >>> Documentation at
>>> >>> http://octave.sourceforge.net/symbolic/function/@sym/taylor.html
>>> >>> would be
>>> >>> helpful if it included more clear examples, preferably ones which are
>>> >>> complete.
>>> >>>
>>> >>> You may use data sets to include tutorials if you wish, as I fail to
>>> >>> see
>>> >>> a complete implementation in place.
>>> >>>
>>> >>
>>> >> "'taylor' undefined" means it can't find the function, taylor. Do you
>>> >> have
>>> >> the symbolic package installed and loaded?
>>> >>
>>> >> If you do
>>> >>
>>> >> pkg list
>>> >>
>>> >> do you see a star next to symbolic?
>>> >>
>>> >>
>>> >>
>>> >> --
>>> >> /* andy buckle */
>>> >>
>>> >> _______________________________________________
>>> >> Help-octave mailing list
>>> >> address@hidden
>>> >> https://lists.gnu.org/mailman/listinfo/help-octave
>>> >>
>>> >
>>> > I just checked out octave-online.net, and symbolic 2.1.0 should be
>>> > installed
>>> > and loaded by default. (list below).  I'm running a newer version
>>> > (2,2,2).
>>> > Jon, it is part of the symbolic package, and for it to work you have to
>>> > call
>>> > it with symbolically declared variables.  (try: help sym)
>>> >
>>> > Depending on how I try to call taylor, I get the same response. I'm not
>>> > sure
>>> > what the expected behavior is:
>>> >
>>> >>> a = sym('a')
>>> > a = (sym) a
>>> >
>>> > taylor(a)
>>> > a = (sym) a
>>> >
>>> >>> taylor(sin(a))
>>> > ans = (sym)
>>> >
>>> >     5    3
>>> >    a    a
>>> >   --- - -- + a
>>> >   120   6
>>> >
>>> > Alll good.
>>> >
>>> > now, calling with a nonsymbolically defined argument:
>>> >
>>> >>> b = [1:10];
>>> >>> taylor(sin(b))
>>> > error: 'taylor' undefined near line 1 column 1
>>> >
>>> > Seems like it should give a better answer than that, as this seems like
>>> > it
>>> > can't find taylor, when it's just called incorrectly. does that have
>>> > something to do with how the interpreter looks for the package
>>> > function?
>>> >
>>> > What's more, trying the same on octave-online.net:
>>> >
>>> > octave:10> a=sym ('a')
>>> > a = (sym) a
>>> >
>>> > octave:11> taylor(a)
>>> > error: structure has no member '
>>> > '
>>> > error: called from:
>>> > error:   /usr/local/share/octave/packages/symbolic-2.1.0/@sym/symvar.m
>>> > at
>>> > line 98, column 14
>>> > error:   /usr/local/share/octave/packages/symbolic-2.1.0/@sym/taylor.m
>>> > at
>>> > line 46, column 7
>>> >
>>> >
>>> > Is this just a 2.1.0 bug?
>>> >
>>> > octave:2> pkg list
>>> >
>>> >  Package Name         | Version | Installation directory
>>> > ---------------------+---------+-----------------------
>>> >      communications *|   1.2.0 |
>>> > .../share/octave/packages/communications-1.2.0
>>> >             control *|   2.6.6 |
>>> > /usr/local/share/octave/packages/control-2.6.6
>>> >        econometrics *|   1.1.1 |
>>> > .../share/octave/packages/econometrics-1.1.1
>>> >           financial *|   0.4.0 |
>>> > .../local/share/octave/packages/financial-0.4.0
>>> > fuzzy-logic-toolkit *|   0.4.4 |
>>> > .../octave/packages/fuzzy-logic-toolkit-0.4.4
>>> >             general *|   1.3.4 |
>>> > /usr/local/share/octave/packages/general-1.3.4
>>> >            geometry *|   1.7.0 |
>>> > /usr/local/share/octave/packages/geometry-1.7.0
>>> >                  io *|   2.2.7 |
>>> > /usr/local/share/octave/packages/io-2.2.7
>>> >      linear-algebra *|   2.2.1 |
>>> > .../share/octave/packages/linear-algebra-2.2.1
>>> >           mechanics *|   1.3.1 |
>>> > .../local/share/octave/packages/mechanics-1.3.1
>>> >       miscellaneous *|   1.2.1 |
>>> > .../share/octave/packages/miscellaneous-1.2.1
>>> >                 nan  |   2.7.1 |
>>> > /usr/local/share/octave/packages/nan-2.7.1
>>> >              odepkg *|   0.8.4 |
>>> > /usr/local/share/octave/packages/odepkg-0.8.4
>>> >               optim *|   1.4.1 |
>>> > /usr/local/share/octave/packages/optim-1.4.1
>>> >         optiminterp *|   0.3.4 |
>>> > .../share/octave/packages/optiminterp-0.3.4
>>> >            parallel *|   2.2.0 |
>>> > /usr/local/share/octave/packages/parallel-2.2.0
>>> >              signal *|   1.3.0 |
>>> > /usr/local/share/octave/packages/signal-1.3.0
>>> >             splines *|   1.2.7 |
>>> > /usr/local/share/octave/packages/splines-1.2.7
>>> >          statistics *|   1.2.4 |
>>> > .../share/octave/packages/statistics-1.2.4
>>> >             strings *|   1.1.0 |
>>> > /usr/local/share/octave/packages/strings-1.1.0
>>> >              struct *|  1.0.10 |
>>> > /usr/local/share/octave/packages/struct-1.0.10
>>> >            symbolic *|   2.1.0 |
>>> > /usr/local/share/octave/packages/symbolic-2.1.0
>>> >
>>> >
>>> >
>>> >
>>> >
>>> > _______________________________________________
>>> > Help-octave mailing list
>>> > address@hidden
>>> > https://lists.gnu.org/mailman/listinfo/help-octave
>>> >
>>>
>>> Just to compare this to current MATLAB behavior, if you try and call
>>> taylor with a matrix of doubles, you get the following error message:
>>>
>>> > Undefined function 'taylor' for input arguments of type 'double'.
>>>
>>> So, I guess its slightly better error message, since you might be able
>>> to deduce from there that you're calling it incorrectly.
>>
>>
>>
>> Is this the expected/preferred behavior for this function? Can create a
>> bug report for either a 'correct' error message or at least 'improved
>> message requested'
>>
>
> my entirely fallible Google-fu failed to find a related bug report. Created
> one here: https://savannah.gnu.org/bugs/?46662

I guess my question would be, do you want an (I apologize for my lack
of knowledge in this area) an "Octave-level" type of solution where
octave would generate the error because there is no such thing as a
taylor function for non-symbolic variables, or would you just want
error message within the function "taylor" to do something like:

if ~issymbolic(inputs)
  error('inputs to taylor must be symbolic');