Trace'ing Gradient in FindMinimum

*To*: mathgroup at smc.vnet.net*Subject*: [mg87384] Trace'ing Gradient in FindMinimum*From*: Art <grenander at gmail.com>*Date*: Wed, 9 Apr 2008 05:54:56 -0400 (EDT)

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.