Skip to main content

performance tuning - Is it possible to generate a message when precision upgrade occur?


I use Mathematica mostly for numerical simulation, so most of the time double precision (or machine precision) is enough for me. Mathematica has this nice feature of automatically upgrade to arbitrary precision, but sometimes it costs problems for me.


For instance here is a compiled function that calculate a modulus of a vector



mymod = Compile[{{x, _Real, 1}}, x.x]

Now a vector has a Gaussian distribution


ListPlot[Array[Exp[-(#)^2./10.] &, 500, {-100., 100.}]]

enter image description here


and we want to calculate its modulus


mymod[Array[Exp[-(#)^2./10.]&,500,{-100.,100.}]]
(* 9.8885 *)


we get the right answer but with a warning saying that the argument type is incorrect:



Argument {5.075958897549*10^-435,1.513073408369*10^-431,4.367658965168*10^-428,<<45>>,5.42928*10^-284,3.46203*10^-281,<<450>>} at position 1 should be a rank 1 tensor of machine-size real numbers.



That's because Exp has upgraded the machine precision number we use to arbitrary precision. And thus the uncompiled function is invoked.


Consider the situation where we use extensively the numerical functions in a fairly large package, this automatic upgrading of precision may occur at multiple places. Although the final answer may probably be correct, invoking the uncompiled functions may greatly degrade the performance.


One solution point out by Daniel Lichtblau here is to turn off the tracking of the underflow by setting "CatchMachineUnderflow"->False to every function that uses arbitrary precision. But first we need to find those functions.


So my question are:



  1. Is it possible to tell Mathematica to generate a message when the upgrading to an arbitrary precision occurs? Just like we can have a message if the unpacking of an array occurs.


  2. This precision problem seems to be quite common for people dealing with numerical calculation in Mathematica. What do you think are good ways to deal with this problem?




Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more