gmane.comp.mathematics.maxima.general

Re: fit nonlinear model to data - better way to code it?

Jaime Villate — 2012-05-18T12:03:56

If I remember correctly, parallel substitution

[p1,p2,p3]: ans[1]

was added a few years ago by Robert, but function ev() has not been modified
to accept a similar syntax:

p1, [p1,p2,p3]=[3,4,5];

You still have to use the syntax:

   p1, [p1=3, p2=4, p=5];

and the same goes for subst:

   subst([p1=3, p2=4, p=5], p1);

rather than

   subst([p1,p2,p3]=[3,4,5],p1);

which is not implemented yet.

Regards,
Jaime

implicit_taylor and implicit_derivative without solve

Evgeniy Maevskiy — 2012-05-18T11:56:38

One may compute Taylor's polynom for implicit function (and therefore 
compute implicit_derivative) without solve equations.

F - an expression on x[1],x[2],... and y
a - list - the fixed point x
b - number - the fixed value y

F(a,b) must be 0

n - the degree of Taylor's polynom


my_implicit_taylor(F,a,b,n):=block(
     [x:makelist(x[i],i,length(a)),dx:makelist(dx[i],i,length(a)),D,df],
     if is(ev(F,x:a,y:b)#0) then
         return("Unable to compute taylor polynom: F(a,b)#0"),
     diff(F,y),
     D:ev(%%,x:a,y:b),
     if is(D=0) then
         return("Unable to compute taylor polynom: D=0"),
     F:taylor(ev(F,x:a+dx,y:b+dy),endcons(dy,dx),0,n),
     df:0,
     for k:1 thru n do df:df-1/D*expand(taylor(ev(F,dy:df),dx,0,k)),
     expand(b+df)
)$

my_implicit_taylor(x[1]-log(y),[0],1,7);


For implicit vector-function:

F - list of expressions on x[1],... and y[1],...
a - list
b - list

my_implicit_taylor(F,a,b,n):=block(
     [x:makelist(x[i],i,length(a)), y:makelist(y[i],i,length(b)),
dx:makelist(dx[i

More on how to print complicated objects...

Rupert Swarbrick — 2012-05-18T08:47:23

Hi,

Another question I've been wondering about is exactly what to
display. That is, if you have some expression EXPR, there seem to be two
ways to output it in Maxima: either just printing it or calling grind on
it.

Am I right in thinking that grind() is conceptually equivalent to print
in Lisp with *print-readably* true, and that the usual display is more
similar to princ?

If so, I can merrily elide details in my dimension function for my
objects (however it gets invoked), and ensure that they all get output
by grind().

Do I have the right model here?

Rupert
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Re: Complicated objects in Maxima

Rupert Swarbrick — 2012-05-18T08:42:16

Something like the following seems to work.

Rupert

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Re: fit nonlinear model to data - better way to code it?

Rupert Swarbrick — 2012-05-18T08:24:28

Hmm, I was going to suggest that

  ev(f(x), [p1,p2,p3] = ans[1])

should work, but surprisingly it doesn't. For example:

  (%i14) p1, [p1,p2,p3]=[3,4,5];
  (%o14)                                p1

Does anyone know if there is a reason for this? It seems at odds with

  (%i15) [p1,p2,p3]: ans[1];
  (%o15)   [- .2694298415835076, - .4248176441471781, 1.331747718996615]
  (%i16) p1;
  (%o16)                        - .2694298415835076


Rupert
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Package NumericalIO

Evgeniy Maevskiy — 2012-05-18T08:37:28

It might be useful ...

1) ... to rewrite function read_list and others for reading list (array, 
matrix) of expressions (not only of numbers).

write_data(
   matrix([2/5,3/7,-1/2],[0.5,-1.247,12.57]),
   "D:/Compmath/temp_matrix", comma
)$

- it works correctly

read_matrix("D:/Compmath/temp_matrix", comma);

- returns a rubbish

my_read_matrix(fn):=block([f,A,s],
     if (file_search(fn)=fn) then (
         f:openr(fn),
         A:matrix(),
         while (s:readline(f))#false do
             A:addrow(A,eval_string(concat("[",s,"]")))
     ),
     A
)$

my_read_matrix("D:/Compmath/temp_matrix");

- works correctly

2) ... to add some functions for write and read arbitrary text-file, for 
example:

(defun $fwrite (f &rest c)
     (with-open-file (stream f :direction :output)
         (loop for s in c
             do (write-line s stream))))

Usage:

fwrite("D:/Compmath/temp_file.txt",
     "a string",
     "another string",
     "again another string"
)$

Re: wxdraw2d

Richard Hennessy — 2012-05-18T06:05:37

Hi:

I just wanted to let you know I was able to remember the link.  The new 
draw.lisp fixes this error too.  Thanks for working on it.

Richard


-----Original Message----- 
From: Richard Hennessy
Sent: Thursday, May 17, 2012 7:25 PM
To: biomates< at >telefonica.net ; Andrej Vodopivec
Cc: Maxima List
Subject: Re: [Maxima] wxdraw2d

Hi Mario and Andrej:

Thanks, I tried Andrej's solution and that worked and I want to try yours.
Can you post the link to git?  I had it bookmarked, but I lost some of my
bookmarks recently and I don't remember how to get to git.

Rich


-----Original Message----- 
From: Mario Rodriguez
Sent: Thursday, May 17, 2012 7:58 AM
To: Andrej Vodopivec
Cc: Maxima List
Subject: Re: [Maxima] wxdraw2d

El mié, 16-05-2012 a las 00:27 +0200, Mario Rodriguez escribió:



I've found a workaround for this problem, with some help from the
Gnuplot team.

Changes have been uploaded to the git repository one minute ago.

wxdraw?d should now work both in 4.6 and 4.4 versions.

(Sorry, Richard, for the d

transcendentals, zero denominators, Haskell

Richard Fateman — 2012-05-18T05:39:53

I don't follow  all this,but I will look at it more
http://hackage.haskell.org/packages/archive/numbers/latest/doc/html/src/Data-Number-FixedFunctions.html#line-142

Re: Multiplying out (noncommutative) exponentials

Stavros Macrakis — 2012-05-18T05:09:40

A simpler way to expand non-commutative powers and products if it's OK to
also expand commutative ones:

      dot_expand(ex) := block([dotexptsimp:false],expand(ex))$

I should have mentioned in the email below that Maxima does not understand
much about these non-unique non-commutative products, so it's often a good
idea to use dot_expand:

    is( equal( a . (b . a)^^2 . b, (a.b)^^3 ) )   =>  unknown

but

    is( equal( dot_expand( a . (b . a)^^2 . b) , dot_expand( (a.b)^^3 ) ) )
  =>  true

On the other hand, I don't think Maxima has any built-in way of doing
(a.b)^^-1 => b^^-1 . a^^-1, so I think you'll need to write your own code
for, e.g. b.(a.b)^^-1 == a

               -s

On Thu, May 17, 2012 at 3:31 PM, Stavros Macrakis <macrakis< at >alum.mit.edu>wrote:

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Re: Multiplying out (noncommutative) exponentials

Stavros Macrakis — 2012-05-18T02:43:59


Checked my files ... sure enough, there are notes and code fragments, but
nothing very useful....

           -s
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Re: Complicated objects in Maxima

Stavros Macrakis — 2012-05-18T02:33:59


Well, perhaps if all you do is "carry them around", but if you start using
them in expressions, I am pretty sure that most parts of Maxima will assume
that a non-numeric atom is a symbolic variable (a Lisp symbol) without
explicitly testing for it, and it will probably be assumed real.  Call such
an 'opaque object' Q; then Q-Q => 0, Q*Q => Q^2, etc. Clearly this is not
correct if Q is say an interval object.

But if you *don't* use these objects in algebraic expressions, you're
probably OK, though you should really have clean input and output syntax
for them, unlike say the current way Lisp arrays display.

           -s
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Re: Complicated objects in Maxima

Robert Dodier — 2012-05-18T02:08:15


Well, in a sense, there isn't a problem; non-cons atoms (e.g. arrays,
hash tables) are pretty much inert in Maxima. So if the goal is just to
construct such things and then carry them around, it seems like Maxima
would be happy enough with that.

I'd be interested to hear what Rupert has in mind when he says he wants
to use CLOS. Maybe what he wants to do is within the realm of Maxima as
it stands, maybe not.


That would work too.



Well, I wouldn't want to replace the existing defstruct unless we have
a working reimplementation in hand.

Incidentally, if you want to give a sketch of introducing methods into
the existing defstruct, I would be interested to hear about it.

best

Robert Dodier

Re: Complicated objects in Maxima

Robert Dodier — 2012-05-18T01:28:49


Well, I can't really tell what's at stake yet. Why don't you post your
patch so others can try it out. I'll give it a try.

best

Robert Dodier

Re: Complicated objects in Maxima

Robert Dodier — 2012-05-18T01:26:33


Hmm, that sounds interesting. How would that work? What is an example?

best

Robert Dodier

Re: fit nonlinear model to data - better way to code it?

Ether Jones — 2012-05-18T00:47:28





If I do it that way, it breaks the following line of code:  trendline: ev(f(x),p=ans[1]);




________________________________
 From: Raymond Toy <toy.raymond< at >gmail.com>
To: Ether Jones <maxima< at >etherjones.us> 
Cc: maxima <maxima< at >math.utexas.edu> 
Sent: Thursday, May 17, 2012 7:36 PM
Subject: Re: [Maxima] fit nonlinear model to data - better way to code it?
 




On Thu, May 17, 2012 at 12:25 PM, Ether Jones <maxima< at >etherjones.us> wrote:



I guess this actually works, but p is supposed to be a list of the parameters and f(x) should be an expression containing the parameters:

f(x) := p1 + p2/(x-p3)

minpack(f(x)-y,[p1,p2,p3],guess);

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Re: Complicated objects in Maxima

Steve Haflich — 2012-05-18T00:39:03

   defstruct stuff usually does not use lists, unless you specify that.
   It uses some kind
   of packed array-ish thing.

The important thing defstruct and defclass provide is the addition of a
class to the class lattice upon which method discrimination (and
subclass testing) can be done.  The issues of representaton and slot
access are mere details.

It is an interesting question whether, had generic functions and a
discriminable and extensible class lattice existed in Lisp 40+ years
ago, whether this would have been useful to the internal protocols of
Ma[xi,csy]ma because each subexpression could be minutely subclassed
about all it's internal propertes.  That question is arguably still
intellectually interesting, but alas any answer to that question is not
relevant to current work on Maxima.

Re: fit nonlinear model to data - better way to code it?

Raymond Toy — 2012-05-17T23:36:20


I guess this actually works, but p is supposed to be a list of the
parameters and f(x) should be an expression containing the parameters:

f(x) := p1 + p2/(x-p3)

minpack(f(x)-y,[p1,p2,p3],guess);

Ray
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Re: wxdraw2d

Richard Hennessy — 2012-05-17T23:25:47

Hi Mario and Andrej:

Thanks, I tried Andrej's solution and that worked and I want to try yours. 
Can you post the link to git?  I had it bookmarked, but I lost some of my 
bookmarks recently and I don't remember how to get to git.

Rich


-----Original Message----- 
From: Mario Rodriguez
Sent: Thursday, May 17, 2012 7:58 AM
To: Andrej Vodopivec
Cc: Maxima List
Subject: Re: [Maxima] wxdraw2d

El mié, 16-05-2012 a las 00:27 +0200, Mario Rodriguez escribió:



I've found a workaround for this problem, with some help from the
Gnuplot team.

Changes have been uploaded to the git repository one minute ago.

wxdraw?d should now work both in 4.6 and 4.4 versions.

(Sorry, Richard, for the delay)

--
Mario

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Re: limit of erfc

Richard Fateman — 2012-05-17T21:20:47

This topic has been addressed a few times.  One (probably incomplete) 
solution is to
represent inf  as  a rational number type,   (1/0),  und as (0/0)  minf 
as (-1 / 0)  and combine them
as appropriate.

((rat) 0 0)  multiplied by <anything>   is then   0*anything / 0   or 
und.   (that is,  ((rat) 0 0). )

oddly enough, a lot of the work is done by REMOVING code, namely no 
longer checking
for division by zero.

some additional code to display 0/0 as und etc.

I wrote a paper on this...

RJF

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Re: limit of erfc

Raymond Toy — 2012-05-17T20:37:12


I had done some work on this long ago and I think Dieter has done some more
recent (better) work.  But, AFAIK, all attempts are incomplete.

Ray
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Re: Complicated objects in Maxima

Richard Fateman — 2012-05-17T20:18:48

defstruct stuff usually does not use lists, unless you specify that.  It 
uses some kind
of packed array-ish thing.