       • To: mathgroup at smc.vnet.net
• Subject: [mg87434] Re: Trace'ing Gradient in FindMinimum
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 10 Apr 2008 02:15:03 -0400 (EDT)
• References: <fti3st\$odo\$1@smc.vnet.net>

```Hi,

try

f[x_List] := (x.x - 10)^2
df[x : {__?NumericQ}] := (Sow[x]; 4 (x.x - 10) x)
init = RandomReal[1, {3}];

Reap[FindMinimum[f[x], {x, init}, Gradient -> df[x]]]

Regards
Jens

Art wrote:
> Can I track Gradient computations in FindMinimum using Trace? Here, tr
> is empty though df is evaluated several times:
>
> f[x_List] := (x.x - 10)^2
> df[x : {__?NumericQ}] := 4 (x.x - 10) x
> init = RandomReal[1, {1000}];
>
> tr =
>   Trace[
>     FindMinimum[f[x], {x, init}, Gradient -> df[x]],
>     df[x_] -> Norm[x]
>   ]
>
> But Tracing the evaluation of f[] is possible and yields the same as
> EvaluationMonitor:
>
> ev = {};
> tr =
>  ReleaseHold /@
>   Flatten@Trace[
>     FindMinimum[f[x], {x, init}, Gradient -> df[x],
>      EvaluationMonitor :> AppendTo[ev, Norm[x]] ],
>     f[x_] -> Norm[x]];
>
> Here, tr == ev.
>
> It looks like FindMinimum eats the function df and doesn't ever
> explicitly call it, but it doesn't eat f.
>
> I am trying to resolve an error where FindMinimum immediately
> complains my Gradient doesn't evaluate to a vector of reals for init
> and returns. Placing a Print inside df shows that FindMinimum does
> actually call df with init and when I separately evaluate df[init],
> there is no problem. I know I am doing something wrong so I was hoping
> to figure it out with Trace on df. I would also like to learn to use
> Trace.
>
> Second question: Is there a way to specify that FindMinimum should not
> try to find symbolic derivatives and such for it's arguments other
> than using patterns like x:{__?NumericQ}, which probably take time to
> compute. It would be nice for something like f[x_ /;
> And@@(MatrixQ[#,NumericQ]&/@x)] not to be evaluated each iteration. Is
> there a global \$TrustUserUnconditionally = True option?
>
> Thanks for any suggestions.
>

```

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