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

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more