# Re: Sorting of Data Lists

```CFreitas@swri.edu wrote:
>
> I have two equal length vector sets of data.  I wish to form a third
> vector  whose elements are the minimum values from each component of
> the other two  vectors; i.e., if a(i) < b(i), then c(i) = a(i), else
> c(i) = b(i).  I have  tried many different methods within Mathematica
> 3.0 and have not been  successful.  I would appreciate any suggestions
> as to how to accomplish this  task.
> Thank you.
>
> Dr. Christopher J. Freitas
> Principal Engineer - Computational Mechanics Southwest Research
> Institute
> Voice: 210-522-2137, Fax: 210-522-3042

Here is the kind of data you have, right?:
a=Table[Random[Integer,{0,100}],{25}]
{3,9,42,55,38,10,28,40,3,13,52,80,87,21,30,14,43,9,64,42,76,30,53,5,19}

b=Table[Random[Integer,{0,100}],{25}]
{27,97,82,65,45,89,41,80,24,42,69,12,22,99,86,52,32,59,64,40,3,22,60,25,22}

First group the two lists into a list of lists. both={a,b}
{{3,9,42,55,38,10,28,40,3,13,52,80,87,21,30,14,43,9,64,42,76,30,53,5,19},{27,

97,82,65,45,89,41,80,24,42,69,12,22,99,86,52,32,59,64,40,3,22,60,25,22}}

both is essentially an array with two rows of 25 numbers each.  The
transpose
of this array is an array with 25 rows, each with two numbers, the
corresponding entries in a and b.

Transpose[both]
{{3,27},{9,97},{42,82},{55,65},{38,45},{10,89},{28,41},{40,80},{3,24},{13,

42},{52,69},{80,12},{87,22},{21,99},{30,86},{14,52},{43,32},{9,59},{64,
64},{42,40},{76,3},{30,22},{53,60},{5,25},{19,22}}

Now it's easy to pick the maximum from each pair to get the desired
result.
Map[Apply[Max,#]&,Transpose[both]]
{27,97,82,65,45,89,41,80,24,42,69,80,87,99,86,52,43,59,64,42,76,30,60,25,22}

Ken Levasseur
Math. Sci.
UMass Lowell
http://www.wolfram.com/training/companies/levasseur.html

```

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