Function for SortBy
$begingroup$
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
$endgroup$
add a comment |
$begingroup$
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
$endgroup$
4
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
2
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
1
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13
add a comment |
$begingroup$
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
$endgroup$
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
list-manipulation sorting
edited Jan 4 at 20:06
Hubble07
asked Jan 4 at 18:59
Hubble07Hubble07
2,990721
2,990721
4
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
2
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
1
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13
add a comment |
4
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
2
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
1
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13
4
4
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
2
2
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
1
1
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
EDITED TO ADD A SORT CRITERION
For the data sets, you are sorting on
- the number of negative numbers first, then
- the subset of just the nonnegative elements (using canonical ordering for lists), then
- the set gained when you replace negative terms with a '1' and nonnegative with '0'
The subset of just the negative elements (using canonical ordering)
funkySort[list_]:= SortBy[list,{
Count[#, _?Negative] &,
Select[#, NonNegative] &,
Negative,
Select[#, Negative] &
}]
slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]
True
True
True
$endgroup$
$begingroup$
Butslist != funkySort[list]
. Are you sure this works. It doesn't seem to work on my system. Do you get really getslist1
andslist2
when your function is applied to any random ordering of those lists.
$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrongfunkySort[ ]
from my notebook. Fixed it...
$endgroup$
– MikeY
Jan 5 at 17:00
add a comment |
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$begingroup$
EDITED TO ADD A SORT CRITERION
For the data sets, you are sorting on
- the number of negative numbers first, then
- the subset of just the nonnegative elements (using canonical ordering for lists), then
- the set gained when you replace negative terms with a '1' and nonnegative with '0'
The subset of just the negative elements (using canonical ordering)
funkySort[list_]:= SortBy[list,{
Count[#, _?Negative] &,
Select[#, NonNegative] &,
Negative,
Select[#, Negative] &
}]
slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]
True
True
True
$endgroup$
$begingroup$
Butslist != funkySort[list]
. Are you sure this works. It doesn't seem to work on my system. Do you get really getslist1
andslist2
when your function is applied to any random ordering of those lists.
$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrongfunkySort[ ]
from my notebook. Fixed it...
$endgroup$
– MikeY
Jan 5 at 17:00
add a comment |
$begingroup$
EDITED TO ADD A SORT CRITERION
For the data sets, you are sorting on
- the number of negative numbers first, then
- the subset of just the nonnegative elements (using canonical ordering for lists), then
- the set gained when you replace negative terms with a '1' and nonnegative with '0'
The subset of just the negative elements (using canonical ordering)
funkySort[list_]:= SortBy[list,{
Count[#, _?Negative] &,
Select[#, NonNegative] &,
Negative,
Select[#, Negative] &
}]
slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]
True
True
True
$endgroup$
$begingroup$
Butslist != funkySort[list]
. Are you sure this works. It doesn't seem to work on my system. Do you get really getslist1
andslist2
when your function is applied to any random ordering of those lists.
$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrongfunkySort[ ]
from my notebook. Fixed it...
$endgroup$
– MikeY
Jan 5 at 17:00
add a comment |
$begingroup$
EDITED TO ADD A SORT CRITERION
For the data sets, you are sorting on
- the number of negative numbers first, then
- the subset of just the nonnegative elements (using canonical ordering for lists), then
- the set gained when you replace negative terms with a '1' and nonnegative with '0'
The subset of just the negative elements (using canonical ordering)
funkySort[list_]:= SortBy[list,{
Count[#, _?Negative] &,
Select[#, NonNegative] &,
Negative,
Select[#, Negative] &
}]
slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]
True
True
True
$endgroup$
EDITED TO ADD A SORT CRITERION
For the data sets, you are sorting on
- the number of negative numbers first, then
- the subset of just the nonnegative elements (using canonical ordering for lists), then
- the set gained when you replace negative terms with a '1' and nonnegative with '0'
The subset of just the negative elements (using canonical ordering)
funkySort[list_]:= SortBy[list,{
Count[#, _?Negative] &,
Select[#, NonNegative] &,
Negative,
Select[#, Negative] &
}]
slist == funkySort[slist[[RandomPermutation[Length[slist]]]]]
slist1 == funkySort[slist1[[RandomPermutation[Length[slist1]]]]]
slist2 == funkySort[slist2[[RandomPermutation[Length[slist2]]]]]
True
True
True
edited Jan 6 at 18:48
J. M. is away♦
98.9k10311467
98.9k10311467
answered Jan 4 at 19:52
MikeYMikeY
3,768916
3,768916
$begingroup$
Butslist != funkySort[list]
. Are you sure this works. It doesn't seem to work on my system. Do you get really getslist1
andslist2
when your function is applied to any random ordering of those lists.
$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrongfunkySort[ ]
from my notebook. Fixed it...
$endgroup$
– MikeY
Jan 5 at 17:00
add a comment |
$begingroup$
Butslist != funkySort[list]
. Are you sure this works. It doesn't seem to work on my system. Do you get really getslist1
andslist2
when your function is applied to any random ordering of those lists.
$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrongfunkySort[ ]
from my notebook. Fixed it...
$endgroup$
– MikeY
Jan 5 at 17:00
$begingroup$
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.$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
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.$endgroup$
– Hubble07
Jan 5 at 14:25
$begingroup$
Oops, copied over the wrong
funkySort[ ]
from my notebook. Fixed it...$endgroup$
– MikeY
Jan 5 at 17:00
$begingroup$
Oops, copied over the wrong
funkySort[ ]
from my notebook. Fixed it...$endgroup$
– MikeY
Jan 5 at 17:00
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4
$begingroup$
Explain the core idea behind your sorted list. It certainly isn't clear what you're seeking.
$endgroup$
– David G. Stork
Jan 4 at 19:01
2
$begingroup$
Can you give some examples with more complicated data?
$endgroup$
– MikeY
Jan 4 at 19:33
1
$begingroup$
@MikeY I have added 2 more sorted sets.
$endgroup$
– Hubble07
Jan 4 at 20:10
$begingroup$
So if you sort your data like this, it can probably be counted and therefore indexed in closed form.
$endgroup$
– MikeY
Jan 5 at 20:05
$begingroup$
@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.
$endgroup$
– Hubble07
Jan 6 at 3:13