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Re: Is there any efficient easy way to compare two lists with the same length with Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124385] Re: Is there any efficient easy way to compare two lists with the same length with Mathematica?
  • From: Andy Ross <andyr at wolfram.com>
  • Date: Wed, 18 Jan 2012 05:57:25 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On 1/17/2012 2:34 AM, Rex wrote:
> Given two lists `A={a1,a2,a3,...an}` and `B={b1,b2,b3,...bn}`, I would
> say `A>=B` if and only if all `ai>=bi`.
>
> There is a built-in logical comparison of two lists, `A==B`, but no
> `A>B`.
> Do we need to compare each element like this
>
> And@@Table[A[[i]]>=B[[i]],{i,n}]
>
> Any better tricks to do this?
>

If the vectors are very long and there isn't a good reason to expect 
that most false cases will occur early you might consider UnitStep.

a=RandomReal[{0,1},10^6];
b=a+1;
c=RandomReal[{0,1},10^6];

In[311]:= And@@Thread[b>a]//AbsoluteTiming
Out[311]= {0.858011,True}

In[312]:= Total[UnitStep[b-a]]==Length[b]//AbsoluteTiming
Out[312]= {0.046801,True}

In[313]:= And@@Thread[c>a]//AbsoluteTiming
Out[313]= {0.858011,False}

In[314]:= Total[UnitStep[c-a]]==Length[c]//AbsoluteTiming
Out[314]= {0.046801,False}

Andy Ross
Wolfram Research



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