Re: Pattern matching "on the fly" + Developer`ClearCache[]
- To: mathgroup at smc.vnet.net
- Subject: [mg30119] Re: Pattern matching "on the fly" + Developer`ClearCache[]
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Sun, 29 Jul 2001 21:26:13 -0400 (EDT)
- References: <9jvr9h$dof$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
(1+x)^(10^6) (the original example). Andrzej's method is quicker as a
one-off calcuation. But the Series method that Bob and I suggested does some
cacheing and is quicker for repeats.
In fact it seems that it Series is not just cacheing but is loading code at
*any* first use.
Developer`ClearCache` does not seem to clear this code.
So ClearCache does not *always* give the worstcase timing.
Please note that Quit[] must be evaluated as a separate input on each
occasion.
ORIGINAL: (1+x)^(10^6)
Quit[]
(x^n_^:=0/;n>2; (*Andrzej*)
myexpand[f_,n_]:=
Fold[Expand[#1^2*If[#2\[Equal]1,f,1]]&,f,
Rest[IntegerDigits[n,2]]])//Timing
{0. Second,Null}
myexpand[(1+x),10^6];//Timing
{0.11 Second,Null}
No cacheing:
myexpand[(1+x),10^6];//Timing
{0.11 Second,Null}
Quit[]
(1+x)^(10^6)+O[x]^3//Normal;//Timing
{0.28 Second,Null}
(1+x)^(10^6)+O[x]^3//Normal;//Timing
{0.06 Second,Null}
Quit[]
*Any* use of Series seems to be sufficient.
Series[a,{b,c,0}];//Timing
{0.22 Second,Null}
(1+x)^(10^6)+O[x]^3//Normal;//Timing
{0. Second,Null}
Developer`ClearCache[] has little effect.
Developer`ClearCache[]
(1+x+O[x]^5)^(10^6)//Normal;//Timing
{0. Second,Null}
HIGHER POWER: (1+x)^(10^100)
Quit[]
(x^n_^:=0/;n>2;
myexpand[f_,n_]:=
Fold[Expand[#1^2*If[#2\[Equal]1,f,1]]&,f,
Rest[IntegerDigits[n,2]]])//Timing
{0. Second,Null}
myexpand[(1+x),10^100];//Timing
{1.92 Second,Null}
myexpand[(1+x),10^100];//Timing
{1.92 Second,Null}
Quit[]
(1+x)^(10^100)+O[x]^3//Normal;//Timing
{0.28 Second,Null}
(1+x)^(10^100)+O[x]^3//Normal;//Timing
{0. Second,Null}
Quit[]
*Any* use of Series seems to be sufficient.
Series[a,{b,c,0}];//Timing
{0.22 Second,Null}
(1+x)^(10^100)+O[x]^3//Normal;//Timing
{0. Second,Null}
Developer`ClearCache[] has little effect.
Developer`ClearCache[]
(1+x+O[x]^5)^(10^100)//Normal;//Timing
{0.05 Second,Null}
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565