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Re: Length of a held expression
*To*: mathgroup at smc.vnet.net
*Subject*: [mg96588] Re: Length of a held expression
*From*: Nikolaus Rath <Nikolaus at rath.org>
*Date*: Mon, 16 Feb 2009 16:41:09 -0500 (EST)
*References*: <gn8jdj$7qa$1@smc.vnet.net>
Hi,
Nikolaus Rath <Nikolaus at rath.org> writes:
> Hello,
>
> How can I get the length of a list in a Hold[] expression?
It seems that in my attempt to produce a short example, I also
simplified away the actual problem. So here it comes in slightly
longer form.
I have written a function that propagates uncertainties in the
parameters of a function into the uncertainty of the result. It is
used as follows:
error[a*b, {a, b}, {aErr, bErr}]
--> {a b, Sqrt[Abs[aErr b]^2 + Abs[a bErr]^2]}
so it yields the formula again, together with its error.
However, usually the parameter already have values assigned to them
when I call the function. As was correctly pointed out, I can easily
circumvent this problem by packing the call into a Block[]:
a = 10;
b = 20;
aErr = 1;
bErr = 2;
Block[{a,b},
error[a*b, {a, b}, {aErr, bErr}]]
However, I was wondering if it might not be possible to handle this
case entirely in the error function, so that I can call
a = 10;
b = 20;
aErr = 1;
bErr = 2;
error[a*b, {a, b}, {aErr, bErr}]
and get the correct result. *So I am not really solving an actual
problem here*, I'm just playing with Mathematica's programming model
to see if it would allows me to do such a thing.
I figured out that, in order to be really able to work with the
unevaluated expression I cannot to wrap it in Hold[], but I have to
"escape" all the parameters that might otherwise be evaluated. So what
I'm doing is this:
SetAttributes[error, HoldAll];
error::varno = "There must be the same number of variables and errors";
error[expr_, vars_, errs_] :=
Module[{safeExpr, safeVars, res, escapeRule, restoreRule, varno},
varno = Length[vars];
If[varno != Length[errs],
Message[error::varno];
Throw[$Failed];
];
(* This replaces the given variables (which may have global definition=
s) by local ones *)
escapeRule = Table[
Extract[Hold[vars], {1, i}, HoldPattern] -> safeVars[i],
{i, varno}];
(* This restores the original values of the variables *)
restoreRule = Table[safeVars[i] -> vars[[i]], {i, varno}];
(* Escape variables, so that we can differentiate the expression *)
safeExpr = ReleaseHold[Hold[expr] /. escapeRule];
(* Calculate result with error *)
{expr,
Sqrt[Plus @@ Table[
Abs[D[safeExpr, safeVars[i]] errs[[i]] /. restoreRule ]^2,
{i, varno}]]}
]
This indeed works nicely, except for one thing: in order to replace
all the global variables in the expression by local ones, I have to
iterate over the list of parameters, which in turn requires me to know
it's length.
However, if I'm calculating the length with Length[vars] as above,
vars is evaluated first which may, in theory, change its length. (I
cannot really come up with an example where this may actually happen,
but as I said I'm not trying to solve a real problem anyway).
Now that I've written this all up so nicely, I also realize that the
solution with Length[Unevaluated[vars]] will also work for this case.
I'm mailing this anyway now, since I've already spend so much time
writing it. Maybe someone else can come up with a more elegant version
to do the above, so this mail wasn't entirely pointless :-).
Best,
-Nikolaus
--
=C2=BBTime flies like an arrow, fruit flies like a Banana.=C2=AB
PGP fingerprint: 5B93 61F8 4EA2 E279 ABF6 02CF A9AD B7F8 AE4E 425C
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