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Re: Ordering function weird?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82693] Re: Ordering function weird?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 28 Oct 2007 04:10:00 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <ffv29v$aph$1@smc.vnet.net>

Claus wrote:

> say I've got two sets of number, x and y, which I want to rank. See the 
> example below. I totally expect and want the result of Ordering[x]. But 
> I neiter understand nor expect the result of Ordering[y]. Both Sort[x] 
> and Sort[{1, 2, 7, 8, 9, 1, 2}] are ok.

 From the online help, "Ordering[list] gives the *positions* in list at 
which each successive element of Sort[list] appears." (Emphasize added.)

In other words, *Ordering* returns a list of _indices_ rather than a 
list of sorted elements. For instance, Ordering[{1, 2, 7, 8, 9, 1, 2}] 
returns the list of indices {1, 6, 2, 7, 3, 4, 5} that must be read as, 
"If one wants the list of integers {1, 2, 7, 8, 9, 1, 2} in ascending 
order (the default), one must take the first integer of the original 
list (i.e. one), then the sixth integer (i.e. one again but at a 
different position), then the second (i.e. two), then the seventh (i.e. 
two again but also at a different position), then the third (i.e. 
seven), then the fourth (i.e. eight, and finally the fifth (i.e. nine) 
resulting in the new sorted in ascending order list {1, 1, 2, 2, 7, 8, 
9}, list which is identical to what is returned by Sort[{1, 2, 7, 8, 9, 
1, 2}].

In[1]:= x = {1, 2, 3, 6, 10, 3, 4};
y = {1, 2, 7, 8, 9, 1, 2};
Sort[x]
Sort[y]

Out[3]= {1, 2, 3, 3, 4, 6, 10}

Out[4]= {1, 1, 2, 2, 7, 8, 9}

In[5]:= Ordering[x]
Ordering[y]

Out[5]= {1, 2, 3, 6, 7, 4, 5}

Out[6]= {1, 6, 2, 7, 3, 4, 5}

In[7]:= x[[%%]]
y[[%%]]

Out[7]= {1, 2, 3, 3, 4, 6, 10}

Out[8]= {1, 1, 2, 2, 7, 8, 9}

In[9]:= {x[[Ordering[x]]] === Sort[x], y[[Ordering[y]]] === Sort[y]}

Out[9]= {True, True}

Regards,
-- 
Jean-Marc


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