RE: Re: Pattern Matching in Lists

• To: mathgroup at smc.vnet.net
• Subject: [mg35609] RE: [mg35586] Re: Pattern Matching in Lists
• From: "DrBob" <majort at cox-internet.com>
• Date: Mon, 22 Jul 2002 02:11:12 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Selwyn's code is almost always a little faster than Allan's (though not
much).  The difference is around 4% for lists of 2,000,000 entries.

Here are results for thirty trials of the two arithmetic methods, with 2
million entries each time, using a paired t-test:

Needs["Statistics`HypothesisTests`"]
f1[w_]:=Count[Partition[w, 2,1],{1,0}]
f2[w_]:=Count[Drop[w,-1] - Drop[w,1],1]
f3[w_]:=Count[Drop[w+2RotateRight[w],1],2]
trial:=(n=2000000;w = Table[Random[Integer], {n}];
First@Timing[#[w];]/Second&/@{f2,f3}
)

{t1, t2} = Transpose[(trial & ) /@ Range[30]];
Mean /@ {t1, t2}
r = MeanTest[t1 - t2, 0, FullReport -> True]
meanDiff = (FullReport /. r)[[1,1,1]];
Print["% difference = ", meanDiff/Mean[t1]]

{0.5864333333333358, 0.5621333333333306}

{FullReport -> TableForm[
{{"Mean", "TestStat",
"Distribution"},
{0.024300000000005186,
3.3246821117809677,
StudentTDistribution[
29]}},
{None, {"Mean",
"TestStat",
"Distribution"}}],
OneSidedPValue ->
0.0012041503843005326}

"% difference = "0.0414369351

That's a 4% difference and a p-value of about 0.1%.

Bobby Treat

-----Original Message-----
From: Allan Hayes [mailto:hay at haystack.demon.co.uk]
To: mathgroup at smc.vnet.net
Subject: [mg35609] [mg35586] Re: Pattern Matching in Lists

[second posting in view of reported technical problem]

Anthony,
Take
w = Table[Random[Integer], {200000}

My first thought was, and several posts used this,

Count[Partition[w, 2,1],{1,0}]//Timing

{3.24 Second,49851}

Later it occured to me to use arithmetic, which turned out to be twice
as
fast:

Count[ Drop[w,-1] - Drop[w,1],1]//Timing

{1.49 Second,49851}

This is close to Selwyn Hollis's code

Count[Drop[w+2RotateRight[w],1],2]//Timing

{1.6 Second,49851}

--
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

"Anthony Mendes" <amendes at zeno.ucsd.edu> wrote in message
news:ah5qce\$59o\$1 at smc.vnet.net...
> Hello,
>
> Suppose w={1,1,1,0,0,1,0,1,0,0,1,0,0}.
>
> How can I count the number of occurrences of a 1 in w immediately
> followed by a 0 in w?
>
> I have tried every incarnation of Count[] I can think of; for example,
>
> Count[w,{___,1,0,___}]
>
> does not seem to work.  In general, how can I count the number of
> occurrences of a 1 followed by a 0 in a list of 1's and 0's?  Thank
you!
>
>
> --
> Tony
> _____________________
> amendes at math.ucsd.edu
>
>

```

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