       Re: Sorting coefficients

• To: mathgroup at smc.vnet.net
• Subject: [mg124041] Re: Sorting coefficients
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 7 Jan 2012 05:16:41 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201060914.EAA26796@smc.vnet.net>

pts = Prepend[
Table[{Re, Im}[E^(k (2 \[Pi])/6 I)] //
Through, {k, 0, 5}], {0, 0}];

n = 1; Graphics[Text[n++, #] & /@ pts]

To sort by layer and then within layer

order2 = SortBy[pts,
{N[Last[#]], N[First[#]]} &];

Note that the coordinates need to be converted to Reals for the
canonical order to be the same as numerical order.

n = 1; Graphics[Text[n++, #] & /@ order2]

Sorting from lower left to upper right

order3 = SortBy[pts,
{Norm[N[#] - order2[]], Last[N[#]]} &];

n = 1; Graphics[Text[n++, #] & /@ order3]

Bob Hanlon

On Fri, Jan 6, 2012 at 4:14 AM, Chris Young <cy56 at comcast.net> wrote:
> I'm trying to get my points sorted first by rows first. But I'm having
> trouble figuring out how to do the kind of double sorting I need with
> Sort. SortBy seems very hard to figure out and I'm not sure if it's
> what I need here.
>
> I've just got a hexagonal layout of point coordinates, with another one
> on the origin, and I'm trying to sort everything from lower left to
> upper right. I.e., the usual ordering of going through the bottom row
> from left to right, then through the middle row from left to right, etc.
>
> Any help appreciated.
>
> Chris Young
> cy56 at comcast.net
>
>
> In:= Prepend[
>  Table[{Re, Im}[ E^(k (2 \[Pi])/6 I)] // Through, {k, 0, 5}], {0, 0}]
>
> Out= {{0, 0}, {1, 0}, {1/2, Sqrt/2}, {-(1/2), Sqrt/
>  2}, {-1, 0}, {-(1/2), -(Sqrt/2)}, {1/2, -(Sqrt/2)}}
>
> In:= Sort[%1043, #1[] < #2[] &]
>
> Out= {{1/2, -(Sqrt/2)}, {-(1/2), -(Sqrt/2)}, {-1, 0}, {1,
>  0}, {0, 0}, {-(1/2), Sqrt/2}, {1/2, Sqrt/2}}
>
> In:= Sort[%1046, #1[] < #2[] &]
>
> Out= {{-(1/2), -(Sqrt/2)}, {1/2, -(Sqrt/2)}, {0, 0}, {1,
>  0}, {-1, 0}, {1/2, Sqrt/2}, {-(1/2), Sqrt/2}}
>

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