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Topic: Quantity[] (Units) slows things! Solutions?
Replies: 1   Last Post: Aug 17, 2013 2:04 AM

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 Kevin J. McCann Posts: 147 Registered: 12/7/04
Re: Quantity[] (Units) slows things! Solutions?
Posted: Aug 17, 2013 2:04 AM

I find the new way Mathematica deals with units and physical constants to be a
rather poor change to the old Units and PhysicalConstants packages. In
addition to the fact that asking for something like the speed of light
requires an internet connection, there is the slowdown in just the
handling of units as you found.

I used the old units package, which has its own problems, to rewrite:

<< Units`

lwc2[dBZ_, sigma_, n_] :=
Convert[((1/6)*Pi*(Gram/Centimeter^3)*
Sqrt[n*10^(dBZ/10)*
((Milli*Meter)^6/Meter^3)])/
E^((9*sigma^2)/2),
Gram/Centimeter^3]

Then

Timing[Table[
lwc2[dbz, 0.35, 200./(Centimeter^3)], {dbz, -100., -10., 0.1}]]

Takes about 0.5s as opposed to 23.5s on my computer.

Kevin

On 8/16/2013 3:07 AM, Frank Iannarilli wrote:
> Hi,
>
> This is for Mathematica9 which introduced units-handling via the Quantity[] function and its friends. It's a nice provision, but can slow things down substantially for production work, e.g. below shows a factor of 6500 slowdown!
>
> For example:
>
> lwc[dBZ_, sigma_, n_Quantity] := (1/6) Exp[-9 sigma^2/2] Pi
> Quantity[1.,"Grams"/("Centimeters"^3)]
> Sqrt[n (10^(dBZ/10))
> Quantity[1., ("Millimeters")^6/("Meters"^3)]]
>
> Timing[Table[lwc[dbz, 0.35,
> Quantity[200., 1/("Centimeters"^3)]],
> {dbz, -100., -10., 0.1}]]
>
> ===>>65 Seconds!
>
> whereas the unitless equivalent:
>
> lwcn[dBZ_, sigma_, n_] := (1/6) Exp[-9 sigma^2/2] Pi
> 1.0 Sqrt[n (10^(dBZ/10)) ]
>
> Timing[Table[lwcn[dbz, 0.35, 200.], {dbz, -100., -10., 0.1}]]
>
> ===>>0.01 Seconds!
>
>
> Can anyone suggest any tricks other than removing the units-handling?
>
>
>
>

Date Subject Author
8/16/13 Frank Iannarilli
8/17/13 Kevin J. McCann