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Some function like Position[] but uses criteria, not pattern?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99389] Some function like Position[] but uses criteria, not pattern?
  • From: "Nasser Abbasi" <nma at 12000.org>
  • Date: Tue, 5 May 2009 05:37:22 -0400 (EDT)
  • Reply-to: "Nasser Abbasi" <nma at 12000.org>

V 7.0

Position[]  works by returning position of elements which matches a pattern. 
This is all good and well.

But sometimes, I need to find the positions (i.e index) of elements that 
matches a criteria, not a pattern.

For example, using pattern

a = {1, 0, 4, -5, 8}
Position[a, 0]
Out[15]= {{2}}

But what if I wanted the position of the elements which, say, are larger 
than 3? this is not a pttern, but a criteria. Which in this example should 
find elements which are in position 3 and 5 in list 'a' above.

I can't type
Position[a, #1 > 3 & ]

Now, Select[] does take a criteria, good, so I could type

Select[a, #1 > 3 & ]
{4, 8}

But I wanted the positions of the elements, not the elements themselves.

I could use Select to find the elements, then use Position to find the 
position of these elements as follows

c = Select[a, #1 > 3 & ];
Flatten[(Position[a, #1] & ) /@ c]

Out[65]= {3, 5}

But I think this is bit messy. I think Position[] or new function similar, 
should have an option to return position of elements based on criteria, not 
just pattern. The above gets more messy for me, when I wanted to find 
position of elements in a matrix based on some criteria.

For example, find the position (i.e. row and column) index in a matrix (list 
of lists) of those elements which matches some criteria. Say >3.

thanks,
--Nasser





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