Re: Re: A pattern matching problem
- To: mathgroup at smc.vnet.net
- Subject: [mg72551] Re: [mg72544] Re: A pattern matching problem
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sat, 6 Jan 2007 23:27:05 -0500 (EST)
- References: <enksb3$9nt$1@smc.vnet.net> <200701060838.DAA03832@smc.vnet.net>
This does not seem to return the answer in the form requested by the
O.P. One similar approach that seems to work is
r = u[t + h] - 2*u[t] + u[t - h] + a2*Derivative[1][u][t + h/2] +
4*Derivative[1][u][t - h/4] +
c*(Derivative[2][u][t + alfa*h]/12);
Prepend[Last /@
Transpose /@
Split[Cases[r, Derivative[i_][u][expr_] :> {i, Coefficient[expr,
h]},
{2}], #1[[1]] == #2[[1]] & ],
Cases[r, u[expr_] :> Coefficient[expr, h], Infinity]
{{0, -1, 1}, {-(1/4), 1/2}, {alfa}}
The extra 0 in {0,-1,1} is due to the presence of the term u[t],
which does not involve h as an argument, and I did no think it work
the trouble to use DeleteCases or something of that kind to get rid
of it.
Andrzej Kozlowski
On 6 Jan 2007, at 08:38, Jens-Peer Kuska wrote:
> Hi,
>
> what is with
>
> r = u[t + h] - 2*u[t] + u[t - h] + a2*u'[t + h/2] + 4*u'[t - h/4] + c*
> u''[t + alfa*h]/12;
>
> (Cases[r, u[_] |
> Derivative[__][u][_], Infinity] /. {u[
> arg_] :> {0, arg}, Derivative[i_][u][arg_] :> {i,
> arg}}) /. {order_Integer, arg_} :> {order, D[arg, h]}
>
> Regards
> Jens
>
> 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 ?????
>>
>
- References:
- Re: A pattern matching problem
- From: Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>
- Re: A pattern matching problem