Group Abstract

Message Boards

WOLFRAM COMMUNITY

1.6K Views

1 Reply

0 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Wolfram Language

Changing the order of a list of matrices

Hongyi Zhao

Posted 3 years ago

I try to generate the possible permutations on a list of matrices as follows: In[762]:= mats Permutations[#,{3}]&/@mats mats[[Ordering[#]]]&/@Permutations[Range[3]] Out[762]= {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}} Out[763]= {{{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{0, 0, 1/2}, {0, 0, 1}, {0, 0, 1/2}}, {{0, 0, 1}, {0, 0, 1/2}, {0, 0, 1/2}}}, {{{1/ 2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{1/2, 3/2, 0}, {0, 1, 0}, {-(1/2), 3/2, 0}}, {{-(1/2), 3/2, 0}, {1/2, 3/2, 0}, {0, 1, 0}}, {{-(1/2), 3/2, 0}, {0, 1, 0}, {1/2, 3/2, 0}}, {{0, 1, 0}, {1/ 2, 3/2, 0}, {-(1/2), 3/2, 0}}, {{0, 1, 0}, {-(1/2), 3/2, 0}, {1/2, 3/2, 0}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{3/ 2, -(1/2), 0}, {1, 0, 0}, {3/2, 1/2, 0}}, {{3/2, 1/2, 0}, {3/ 2, -(1/2), 0}, {1, 0, 0}}, {{3/2, 1/2, 0}, {1, 0, 0}, {3/ 2, -(1/2), 0}}, {{1, 0, 0}, {3/2, -(1/2), 0}, {3/2, 1/2, 0}}, {{1, 0, 0}, {3/2, 1/2, 0}, {3/2, -(1/2), 0}}}} Out[764]= {{{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}}, {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{3/ 2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}}, {{{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{3/2, -(1/2), 0}, {3/ 2, 1/2, 0}, {1, 0, 0}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}}, {{{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}}} As you can see, the above two methods give different results. I checked the related document, but still couldn't find the reason. Any tips will be appreciated. Regards, Zhao

I try to generate the possible permutations on a list of matrices as follows:

In[762]:= mats
Permutations[#,{3}]&/@mats
mats[[Ordering[#]]]&/@Permutations[Range[3]]

Out[762]= {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 
   0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 
   0}, {1, 0, 0}}}

Out[763]= {{{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{0, 0, 1/2}, {0, 
    0, 1}, {0, 0, 1/2}}, {{0, 0, 1}, {0, 0, 1/2}, {0, 0, 1/2}}}, {{{1/
    2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{1/2, 3/2, 0}, {0, 1, 
    0}, {-(1/2), 3/2, 0}}, {{-(1/2), 3/2, 0}, {1/2, 3/2, 0}, {0, 1, 
    0}}, {{-(1/2), 3/2, 0}, {0, 1, 0}, {1/2, 3/2, 0}}, {{0, 1, 0}, {1/
    2, 3/2, 0}, {-(1/2), 3/2, 0}}, {{0, 1, 0}, {-(1/2), 3/2, 0}, {1/2,
     3/2, 0}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{3/
    2, -(1/2), 0}, {1, 0, 0}, {3/2, 1/2, 0}}, {{3/2, 1/2, 0}, {3/
    2, -(1/2), 0}, {1, 0, 0}}, {{3/2, 1/2, 0}, {1, 0, 0}, {3/
    2, -(1/2), 0}}, {{1, 0, 0}, {3/2, -(1/2), 0}, {3/2, 1/2, 0}}, {{1,
     0, 0}, {3/2, 1/2, 0}, {3/2, -(1/2), 0}}}}

Out[764]= {{{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 
    0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 
    0}, {1, 0, 0}}}, {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{3/
    2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{1/2, 3/2, 0}, {-(1/2),
     3/2, 0}, {0, 1, 0}}}, {{{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 
    0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{3/2, -(1/2), 0}, {3/
    2, 1/2, 0}, {1, 0, 0}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0,
     0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 
    0}, {-(1/2), 3/2, 0}, {0, 1, 0}}}, {{{1/2, 3/2, 0}, {-(1/2), 3/2, 
    0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}, {{0,
     0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}}, {{{3/2, -(1/2), 0}, {3/2, 1/2,
     0}, {1, 0, 0}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 
    0}}, {{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}}}

As you can see, the above two methods give different results. I checked the related document, but still couldn't find the reason. Any tips will be appreciated.

Regards, Zhao

POSTED BY: Hongyi Zhao

1 Reply

Sort By:

Hongyi Zhao

Posted 3 years ago

A usage error caused this problem. The correct method is as follows: In[55]:= m={{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}} len=Length[m]; Permutations[m,{len}]//Sort; m[[Ordering[#]]]&/@Permutations[Range[len]]//Sort; %==%% Out[55]= {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 0}, {1, 0, 0}}} Out[59]= True

A usage error caused this problem. The correct method is as follows:

In[55]:= m={{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 
   0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 
   0}, {1, 0, 0}}}
len=Length[m];
Permutations[m,{len}]//Sort;
m[[Ordering[#]]]&/@Permutations[Range[len]]//Sort;
%==%%

Out[55]= {{{0, 0, 1/2}, {0, 0, 1/2}, {0, 0, 1}}, {{1/2, 3/2, 
   0}, {-(1/2), 3/2, 0}, {0, 1, 0}}, {{3/2, -(1/2), 0}, {3/2, 1/2, 
   0}, {1, 0, 0}}}

Out[59]= True

POSTED BY: Hongyi Zhao

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback