[Date Index]
[Thread Index]
[Author Index]
Re: A pattern matching problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72546] Re: [mg72533] A pattern matching problem
*From*: János <janos.lobb at yale.edu>
*Date*: Sat, 6 Jan 2007 03:46:32 -0500 (EST)
*References*: <200701050706.CAA10424@smc.vnet.net>
On Jan 5, 2007, at 2:06 AM, carlos at colorado.edu wrote:
> Here is an interesting challenge in pattern matching. Suppose
> you are given an algebraic-differential expression exemplified by
>
> r = u[t+h]-2*u[t]+u[t-h]+a^2*u'[t+h/2]+4*u'[t-h/4]+
> c*u''[t+alfa*h]/12;
>
> Here u[t] is a function of time t, assumed infinitely differentiable,
> h is a time interval, and primes denote derivatives wrt t.
> Relation r==0 is called a delay-differential equation, and is the
> basic stuff in delayed automatic control (h is the signal "lag").
>
> The function name u and the lag h are always symbolic.
> Function u and its derivatives appear linearly in r, while
> h always appears linearly in arguments.
> Coefficients of h may be numeric or symbolic.
> Coefficients of u & derivatives may be numeric or symbolic.
>
> The challenge: given r, get the coefficients of h as a 2D list,
> row-ordered by derivative order. Zero coefficients may be omitted.
> For the above r, it should return
>
> {{1,-1},{1/2,-1/4},{alfa}}
>
> Envisioned module invocation: clist=LagCoefficients[r,u,t,h,m]
> with m=max u-derivative order to be considered. Skeleton:
>
> LagCoefficients[r_,u_,t_,h_,m_]:=Module[ {clist={}},
> ??????
> Return[clist]];
>
> Any ideas for ?????
Here is a newbie idea without too much pattern matching, because I
still have trouble with that :)
In[1]:=
r = u[t + h] - 2*u[t] +
u[t - h] +
a^2*Derivative[1][u][
t + h/2] +
4*Derivative[1][u][
t - h/4] +
c*(Derivative[2][u][
t + alfa*h]/12);
In[2]:=
(#1[[All,2]] & ) /@
Split[Inner[List,
Head /@ Extract[
DeleteCases[List @@ r,
x_ /; MemberQ[x, h,
{0, Infinity}] ==
False], Most /@
Position[DeleteCases[
List @@ r, x_ /;
MemberQ[x, h,
{0, Infinity}] ==
False], u]],
(Replace[#1, h ->
1] & ) /@
(First[#1] & ) /@
Extract[r, Most /@
Position[r, h]],
List], #1[[1]] ==
#2[[1]] & ]
Out[2]=
{{-1, 1}, {-(1/4), 1/2},
{alfa}}
I am sure the gurus will give you a less convoluted one :)
János
----------------------------------------------
Trying to argue with a politician is like lifting up the head of a
corpse.
(S. Lem: His Master Voice)
Prev by Date:
**Re: Orderless attribute for named functions and function arguments**
Next by Date:
**Re: glibc version problem**
Previous by thread:
**A pattern matching problem**
Next by thread:
**Re: A pattern matching problem**
| |