Re: Sorting by date

• To: mathgroup at smc.vnet.net
• Subject: [mg72670] Re: Sorting by date
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sun, 14 Jan 2007 05:06:53 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <eoa6ji\$mi6\$1@smc.vnet.net>

```Clifford Martin wrote:
> Hi All,
>
> I have a list of lists that looks like so:
>
>
> {{3, 137.5, 13978, {2005, 2, 8}}, {3, 138.5, 12519, {2005, 1, 4}}, {3, 171.9, 15835, {2005, 4, 12}}, {3, 142.8, 17137, {2005, 11, 19}},
>   {3, 161.1, 18881, {2006, 1, 18}}, {3, 108.7, 20055, {2006, 2, 28}}, {3, 157, 21498, {2006, 9, 14}}, {3, 118.1, 10891, {2004, 11, 12}}}
>
> The last element per vector is a date. I'd like to sort the list so that the vectors are arranged in ascending order of date, i.e. the vector containing {2004,11,12}  should be first and and the vector containing {2006,9,14}  should be last. Any help would be appreciated.
>
> Thanks
>
> Cliff

Hi Cliff,

The most efficient way to order your list should be by using the
function *Ordering* [1]: "Ordering[list] gives the positions in list at
which each successive element of Sort[list] appears." For instance,

In[1]:=
data ={{3, 137.5, 13978, {2005, 2, 8}}, {3, 138.5, 12519, {2005, 1, 4}},
{3, 171.9, 15835, {2005, 4, 12}}, {3, 142.8, 17137, {2005, 11, 19}},
{3, 161.1, 18881, {2006, 1, 18}}, {3, 108.7, 20055, {2006, 2, 28}},
{3, 157, 21498, {2006, 9, 14}}, {3, 118.1, 10891, {2004, 11, 12}}};

In[2]:=
data[[Ordering[data[[All,4]]]]]

Out[2]=
{{3, 118.1, 10891, {2004, 11, 12}}, {3, 138.5, 12519, {2005, 1, 4}},
{3, 137.5, 13978, {2005, 2, 8}}, {3, 171.9, 15835, {2005, 4, 12}},
{3, 142.8, 17137, {2005, 11, 19}}, {3, 161.1, 18881, {2006, 1, 18}},
{3, 108.7, 20055, {2006, 2, 28}}, {3, 157, 21498, {2006, 9, 14}}}

How does this work? We want to sort the main list (data in our example)
according to the sublists that compose the fourth column of data.

In[3]:=
data[[All,4]]

Out[3]=
{{2005, 2, 8}, {2005, 1, 4}, {2005, 4, 12}, {2005, 11, 19}, {2006, 1,
18}, {2006, 2, 28},
{2006, 9, 14}, {2004, 11, 12}}

So, we want our list sorted in ascending order, as in

In[4]:=
Sort[data[[All,4]]]

Out[4]=
{{2004, 11, 12}, {2005, 1, 4}, {2005, 2, 8}, {2005, 4, 12}, {2005, 11,
19}, {2006, 1, 18},
{2006, 2, 28}, {2006, 9, 14}}

The function *Ordering* gives us a list of the position of the element
as if they were sorted by the command sort above.

In[5]:=
Ordering[data[[All,4]]]

Out[5]=
{8, 2, 1, 3, 4, 5, 6, 7}

Now, we just have to use this result and the function Part with our
original list. Voila!

Regards,
Jean-Marc

[1] http://documents.wolfram.com/mathematica/functions/Ordering

```

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