Function for SortBy












2














Let's say I have the following list



list = {{-1, 0, 0, 1}, {-1, 0, 1, 0}, {-1, 1, 0, 0}, {0, -1, 0, 1}, 
{0, -1, 1, 0}, {0, 0, -1, 1}, {0, 0, 1, -1}, {0, 1, -1, 0},
{0, 1, 0, -1}, {1, -1, 0, 0}, {1, 0, -1, 0}, {1, 0, 0, -1}}


What sort function (sfunc) used in SortBy [list, sfunc] can give me slist?



slist = {{0, 0, 1, -1}, {0, 0, -1, 1}, {0, -1, 0, 1}, {-1, 0, 0, 1}, 
{0, 1, 0, -1}, {0, 1, -1, 0}, {0, -1, 1, 0}, {-1, 0, 1, 0},
{1, 0, 0, -1}, {1, 0, -1, 0}, {1, -1, 0, 0}, {-1, 1, 0, 0}}


Few examples of sorted data



slist1 =  {{0, 0, 1, -2}, {0, 0, -2, 1}, {0, -2, 0, 1}, {-2, 0, 0, 1}, {0, 1, 0, -2}, {0, 1, -2, 0}, {0, -2, 1, 0}, {-2, 0, 1, 0}, {1, 0, 0, -2}, {1, 0, -2, 0}, {1, -2, 0, 0}, {-2, 1, 0, 0}, {0, 1, -1, -1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1},{-1, -1, 0, 1}, {1, 0, -1, -1}, {1, -1, 0, -1}, {1, -1, -1, 0}, {-1, 1, 0, -1}, {-1, 1, -1, 0}, {-1, -1, 1, 0}}


slist2 = {{0, 0, 2, -2}, {0, 0, -2, 2}, {0, -2, 0, 2}, {-2, 0, 0, 2}, {0, 1, 1, -2}, {0, 1, -2, 1}, {0, -2, 1, 1}, {-2, 0, 1, 1}, {0, 2, 0, -2}, {0, 2, -2, 0}, {0, -2, 2, 0}, {-2, 0, 2, 0}, {1, 0, 1, -2}, {1, 0, -2, 1}, {1, -2, 0, 1}, {-2, 1, 0, 1}, {1, 1, 0, -2}, {1, 1, -2, 0}, {1, -2, 1, 0}, {-2, 1, 1, 0}, {2, 0, 0, -2}, {2, 0, -2, 0}, {2, -2, 0, 0}, {-2, 2, 0, 0}, {0, 2, -1, -1}, {0, -1, 2, -1}, {0, -1, -1, 2}, {-1, 0, 2, -1}, {-1, 0, -1, 2}, {-1, -1, 0, 2}, {1, 1, -1, -1}, {1, -1, 1, -1}, {1, -1, -1, 1}, {-1, 1, 1, -1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {2, 0, -1, -1}, {2, -1, 0, -1}, {2, -1, -1, 0}, {-1, 2, 0, -1}, {-1, 2, -1, 0}, {-1, -1, 2, 0}}









share|improve this question




















  • 4




    Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
    – David G. Stork
    yesterday






  • 2




    Can you give some examples with more complicated data?
    – MikeY
    yesterday






  • 1




    @MikeY I have added 2 more sorted sets.
    – Hubble07
    yesterday










  • So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
    – MikeY
    15 hours ago












  • @MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
    – Hubble07
    8 hours ago
















2














Let's say I have the following list



list = {{-1, 0, 0, 1}, {-1, 0, 1, 0}, {-1, 1, 0, 0}, {0, -1, 0, 1}, 
{0, -1, 1, 0}, {0, 0, -1, 1}, {0, 0, 1, -1}, {0, 1, -1, 0},
{0, 1, 0, -1}, {1, -1, 0, 0}, {1, 0, -1, 0}, {1, 0, 0, -1}}


What sort function (sfunc) used in SortBy [list, sfunc] can give me slist?



slist = {{0, 0, 1, -1}, {0, 0, -1, 1}, {0, -1, 0, 1}, {-1, 0, 0, 1}, 
{0, 1, 0, -1}, {0, 1, -1, 0}, {0, -1, 1, 0}, {-1, 0, 1, 0},
{1, 0, 0, -1}, {1, 0, -1, 0}, {1, -1, 0, 0}, {-1, 1, 0, 0}}


Few examples of sorted data



slist1 =  {{0, 0, 1, -2}, {0, 0, -2, 1}, {0, -2, 0, 1}, {-2, 0, 0, 1}, {0, 1, 0, -2}, {0, 1, -2, 0}, {0, -2, 1, 0}, {-2, 0, 1, 0}, {1, 0, 0, -2}, {1, 0, -2, 0}, {1, -2, 0, 0}, {-2, 1, 0, 0}, {0, 1, -1, -1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1},{-1, -1, 0, 1}, {1, 0, -1, -1}, {1, -1, 0, -1}, {1, -1, -1, 0}, {-1, 1, 0, -1}, {-1, 1, -1, 0}, {-1, -1, 1, 0}}


slist2 = {{0, 0, 2, -2}, {0, 0, -2, 2}, {0, -2, 0, 2}, {-2, 0, 0, 2}, {0, 1, 1, -2}, {0, 1, -2, 1}, {0, -2, 1, 1}, {-2, 0, 1, 1}, {0, 2, 0, -2}, {0, 2, -2, 0}, {0, -2, 2, 0}, {-2, 0, 2, 0}, {1, 0, 1, -2}, {1, 0, -2, 1}, {1, -2, 0, 1}, {-2, 1, 0, 1}, {1, 1, 0, -2}, {1, 1, -2, 0}, {1, -2, 1, 0}, {-2, 1, 1, 0}, {2, 0, 0, -2}, {2, 0, -2, 0}, {2, -2, 0, 0}, {-2, 2, 0, 0}, {0, 2, -1, -1}, {0, -1, 2, -1}, {0, -1, -1, 2}, {-1, 0, 2, -1}, {-1, 0, -1, 2}, {-1, -1, 0, 2}, {1, 1, -1, -1}, {1, -1, 1, -1}, {1, -1, -1, 1}, {-1, 1, 1, -1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {2, 0, -1, -1}, {2, -1, 0, -1}, {2, -1, -1, 0}, {-1, 2, 0, -1}, {-1, 2, -1, 0}, {-1, -1, 2, 0}}









share|improve this question




















  • 4




    Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
    – David G. Stork
    yesterday






  • 2




    Can you give some examples with more complicated data?
    – MikeY
    yesterday






  • 1




    @MikeY I have added 2 more sorted sets.
    – Hubble07
    yesterday










  • So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
    – MikeY
    15 hours ago












  • @MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
    – Hubble07
    8 hours ago














2












2








2







Let's say I have the following list



list = {{-1, 0, 0, 1}, {-1, 0, 1, 0}, {-1, 1, 0, 0}, {0, -1, 0, 1}, 
{0, -1, 1, 0}, {0, 0, -1, 1}, {0, 0, 1, -1}, {0, 1, -1, 0},
{0, 1, 0, -1}, {1, -1, 0, 0}, {1, 0, -1, 0}, {1, 0, 0, -1}}


What sort function (sfunc) used in SortBy [list, sfunc] can give me slist?



slist = {{0, 0, 1, -1}, {0, 0, -1, 1}, {0, -1, 0, 1}, {-1, 0, 0, 1}, 
{0, 1, 0, -1}, {0, 1, -1, 0}, {0, -1, 1, 0}, {-1, 0, 1, 0},
{1, 0, 0, -1}, {1, 0, -1, 0}, {1, -1, 0, 0}, {-1, 1, 0, 0}}


Few examples of sorted data



slist1 =  {{0, 0, 1, -2}, {0, 0, -2, 1}, {0, -2, 0, 1}, {-2, 0, 0, 1}, {0, 1, 0, -2}, {0, 1, -2, 0}, {0, -2, 1, 0}, {-2, 0, 1, 0}, {1, 0, 0, -2}, {1, 0, -2, 0}, {1, -2, 0, 0}, {-2, 1, 0, 0}, {0, 1, -1, -1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1},{-1, -1, 0, 1}, {1, 0, -1, -1}, {1, -1, 0, -1}, {1, -1, -1, 0}, {-1, 1, 0, -1}, {-1, 1, -1, 0}, {-1, -1, 1, 0}}


slist2 = {{0, 0, 2, -2}, {0, 0, -2, 2}, {0, -2, 0, 2}, {-2, 0, 0, 2}, {0, 1, 1, -2}, {0, 1, -2, 1}, {0, -2, 1, 1}, {-2, 0, 1, 1}, {0, 2, 0, -2}, {0, 2, -2, 0}, {0, -2, 2, 0}, {-2, 0, 2, 0}, {1, 0, 1, -2}, {1, 0, -2, 1}, {1, -2, 0, 1}, {-2, 1, 0, 1}, {1, 1, 0, -2}, {1, 1, -2, 0}, {1, -2, 1, 0}, {-2, 1, 1, 0}, {2, 0, 0, -2}, {2, 0, -2, 0}, {2, -2, 0, 0}, {-2, 2, 0, 0}, {0, 2, -1, -1}, {0, -1, 2, -1}, {0, -1, -1, 2}, {-1, 0, 2, -1}, {-1, 0, -1, 2}, {-1, -1, 0, 2}, {1, 1, -1, -1}, {1, -1, 1, -1}, {1, -1, -1, 1}, {-1, 1, 1, -1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {2, 0, -1, -1}, {2, -1, 0, -1}, {2, -1, -1, 0}, {-1, 2, 0, -1}, {-1, 2, -1, 0}, {-1, -1, 2, 0}}









share|improve this question















Let's say I have the following list



list = {{-1, 0, 0, 1}, {-1, 0, 1, 0}, {-1, 1, 0, 0}, {0, -1, 0, 1}, 
{0, -1, 1, 0}, {0, 0, -1, 1}, {0, 0, 1, -1}, {0, 1, -1, 0},
{0, 1, 0, -1}, {1, -1, 0, 0}, {1, 0, -1, 0}, {1, 0, 0, -1}}


What sort function (sfunc) used in SortBy [list, sfunc] can give me slist?



slist = {{0, 0, 1, -1}, {0, 0, -1, 1}, {0, -1, 0, 1}, {-1, 0, 0, 1}, 
{0, 1, 0, -1}, {0, 1, -1, 0}, {0, -1, 1, 0}, {-1, 0, 1, 0},
{1, 0, 0, -1}, {1, 0, -1, 0}, {1, -1, 0, 0}, {-1, 1, 0, 0}}


Few examples of sorted data



slist1 =  {{0, 0, 1, -2}, {0, 0, -2, 1}, {0, -2, 0, 1}, {-2, 0, 0, 1}, {0, 1, 0, -2}, {0, 1, -2, 0}, {0, -2, 1, 0}, {-2, 0, 1, 0}, {1, 0, 0, -2}, {1, 0, -2, 0}, {1, -2, 0, 0}, {-2, 1, 0, 0}, {0, 1, -1, -1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1},{-1, -1, 0, 1}, {1, 0, -1, -1}, {1, -1, 0, -1}, {1, -1, -1, 0}, {-1, 1, 0, -1}, {-1, 1, -1, 0}, {-1, -1, 1, 0}}


slist2 = {{0, 0, 2, -2}, {0, 0, -2, 2}, {0, -2, 0, 2}, {-2, 0, 0, 2}, {0, 1, 1, -2}, {0, 1, -2, 1}, {0, -2, 1, 1}, {-2, 0, 1, 1}, {0, 2, 0, -2}, {0, 2, -2, 0}, {0, -2, 2, 0}, {-2, 0, 2, 0}, {1, 0, 1, -2}, {1, 0, -2, 1}, {1, -2, 0, 1}, {-2, 1, 0, 1}, {1, 1, 0, -2}, {1, 1, -2, 0}, {1, -2, 1, 0}, {-2, 1, 1, 0}, {2, 0, 0, -2}, {2, 0, -2, 0}, {2, -2, 0, 0}, {-2, 2, 0, 0}, {0, 2, -1, -1}, {0, -1, 2, -1}, {0, -1, -1, 2}, {-1, 0, 2, -1}, {-1, 0, -1, 2}, {-1, -1, 0, 2}, {1, 1, -1, -1}, {1, -1, 1, -1}, {1, -1, -1, 1}, {-1, 1, 1, -1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {2, 0, -1, -1}, {2, -1, 0, -1}, {2, -1, -1, 0}, {-1, 2, 0, -1}, {-1, 2, -1, 0}, {-1, -1, 2, 0}}






list-manipulation sorting






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited yesterday

























asked yesterday









Hubble07

2,904720




2,904720








  • 4




    Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
    – David G. Stork
    yesterday






  • 2




    Can you give some examples with more complicated data?
    – MikeY
    yesterday






  • 1




    @MikeY I have added 2 more sorted sets.
    – Hubble07
    yesterday










  • So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
    – MikeY
    15 hours ago












  • @MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
    – Hubble07
    8 hours ago














  • 4




    Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
    – David G. Stork
    yesterday






  • 2




    Can you give some examples with more complicated data?
    – MikeY
    yesterday






  • 1




    @MikeY I have added 2 more sorted sets.
    – Hubble07
    yesterday










  • So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
    – MikeY
    15 hours ago












  • @MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
    – Hubble07
    8 hours ago








4




4




Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
– David G. Stork
yesterday




Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
– David G. Stork
yesterday




2




2




Can you give some examples with more complicated data?
– MikeY
yesterday




Can you give some examples with more complicated data?
– MikeY
yesterday




1




1




@MikeY I have added 2 more sorted sets.
– Hubble07
yesterday




@MikeY I have added 2 more sorted sets.
– Hubble07
yesterday












So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
– MikeY
15 hours ago






So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
– MikeY
15 hours ago














@MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
– Hubble07
8 hours ago




@MikeY Yes I have decided to use this sorting. I have edited by bounty question. If you have time then you could answer that, then I can gladly give you the bounty.
– Hubble07
8 hours ago










1 Answer
1






active

oldest

votes


















8














EDITED TO FIX ERROR COPYING OVER FUNCTION



For the data sets, you are sorting on




  1. the number of negative numbers first, then

  2. the subset of just the nonnegative elements (using canonical ordering for lists), then

  3. the binary term gained when you replace a negative term with a '1' and a nonnegative with a '0'


  4. The canonical ordering otherwise



     funkySort[list_]:= SortBy[list,{
    Count[#, _?Negative] &,
    Select[#, NonNegative] &,
    Negative
    }]


    slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
    slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
    slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]




True



True



True







share|improve this answer























  • But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
    – Hubble07
    21 hours ago










  • Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
    – MikeY
    18 hours ago











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes









8














EDITED TO FIX ERROR COPYING OVER FUNCTION



For the data sets, you are sorting on




  1. the number of negative numbers first, then

  2. the subset of just the nonnegative elements (using canonical ordering for lists), then

  3. the binary term gained when you replace a negative term with a '1' and a nonnegative with a '0'


  4. The canonical ordering otherwise



     funkySort[list_]:= SortBy[list,{
    Count[#, _?Negative] &,
    Select[#, NonNegative] &,
    Negative
    }]


    slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
    slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
    slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]




True



True



True







share|improve this answer























  • But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
    – Hubble07
    21 hours ago










  • Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
    – MikeY
    18 hours ago
















8














EDITED TO FIX ERROR COPYING OVER FUNCTION



For the data sets, you are sorting on




  1. the number of negative numbers first, then

  2. the subset of just the nonnegative elements (using canonical ordering for lists), then

  3. the binary term gained when you replace a negative term with a '1' and a nonnegative with a '0'


  4. The canonical ordering otherwise



     funkySort[list_]:= SortBy[list,{
    Count[#, _?Negative] &,
    Select[#, NonNegative] &,
    Negative
    }]


    slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
    slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
    slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]




True



True



True







share|improve this answer























  • But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
    – Hubble07
    21 hours ago










  • Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
    – MikeY
    18 hours ago














8












8








8






EDITED TO FIX ERROR COPYING OVER FUNCTION



For the data sets, you are sorting on




  1. the number of negative numbers first, then

  2. the subset of just the nonnegative elements (using canonical ordering for lists), then

  3. the binary term gained when you replace a negative term with a '1' and a nonnegative with a '0'


  4. The canonical ordering otherwise



     funkySort[list_]:= SortBy[list,{
    Count[#, _?Negative] &,
    Select[#, NonNegative] &,
    Negative
    }]


    slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
    slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
    slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]




True



True



True







share|improve this answer














EDITED TO FIX ERROR COPYING OVER FUNCTION



For the data sets, you are sorting on




  1. the number of negative numbers first, then

  2. the subset of just the nonnegative elements (using canonical ordering for lists), then

  3. the binary term gained when you replace a negative term with a '1' and a nonnegative with a '0'


  4. The canonical ordering otherwise



     funkySort[list_]:= SortBy[list,{
    Count[#, _?Negative] &,
    Select[#, NonNegative] &,
    Negative
    }]


    slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
    slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
    slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]




True



True



True








share|improve this answer














share|improve this answer



share|improve this answer








edited 18 hours ago

























answered yesterday









MikeY

2,162410




2,162410












  • But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
    – Hubble07
    21 hours ago










  • Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
    – MikeY
    18 hours ago


















  • But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
    – Hubble07
    21 hours ago










  • Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
    – MikeY
    18 hours ago
















But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
– Hubble07
21 hours ago




But slist != funkySort[list] . Are you sure this works. It doesn't seem to work on my system. Do you get really get slist1 and slist2 when your function is applied to any random ordering of those lists.
– Hubble07
21 hours ago












Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
– MikeY
18 hours ago




Oops, copied over the wrong funkySort[ ] from my notebook. Fixed it...
– MikeY
18 hours ago


















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