Re: FindRoot + Compile = incompatible (?)

*To*: mathgroup at smc.vnet.net*Subject*: [mg111315] Re: FindRoot + Compile = incompatible (?)*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Tue, 27 Jul 2010 04:17:58 -0400 (EDT)*References*: <i2joiv$fsk$1@smc.vnet.net>

On 2010.07.26. 12:38, Scot T. Martin wrote: > Has anyone ever run into the problem of trying to use Compile'd functions > within FindRoot? > > The error message is: > > "CompiledFunction::cfsa: Argument y at position 1 should be a machine-size > real number." > > [Yes, the function still evaluates but in doing so the purpose of compile > & speed gets defeated.] > > The explanation for this error messages is found in ref/FindRoot: > > "FindRoot first localizes the values of all variables, then evaluates f > with the variables being symbolic [1], and then repeatedly evaluates the > result numerically." [1] That's why Compile[] fails. > > Here is a specific example of code that shows the problem: > > ***** > > func = Compile[{x}, x^2]; > > FindRoot[func[y] == 1, {y, 0.5, 1.5}] > > ***** > > Anyone have thoughts on how to work around this aspect so that Compile'd > functions can work within FindRoot and thus accelerate evaluation thereof? > [Or is there an inherent reason why they shouldn't?] > > [My actual function is not "func"; my actual func is 3x faster as a > Compile'd, hence my motivation to get FindRoot to work.] > Hello, As you noticed, the problem appears because func[y] is evaluated by FindRoot even before a number is substituted for y. A workaround is to define a function that is evaluated for numeric arguments only: func2[x_?NumericQ] := func[x] FindRoot[func2[y] == 1, {y, 0.5, 1.5}]