Difference between revisions 929485 and 929486 on enwikiversity

{| align=right
|[[Walsh permutation]]; [[Walsh permutation; bit permutation|bit permutation]] [[File:Rdrup.svg|link=]]
|}

Finite permutations ''p'' and corresponding bit permutations ''P'' are composed in opposite directions:<br>⏎
⏎
⏎
⏎

<math>p_a * p_b * ... = p_x ~~~~ \Leftrightarrow ~~~~ ... * P_b * P_a = P_x</math>
⏎
⏎
⏎
⏎
__TOC__

⏎
⏎
==p<sub>1</sub> * p<sub>8</sub>==⏎
<math>p_1 * p_8  = p_9 ~~~~ \Leftrightarrow ~~~~ P_8 * P_1 = P_9</math>==

<source lang="matlab">
rowp1=[0 1 0 0;
       1 0 0 0;
       0 0 1 0;
       0 0 0 1];
rowp1*[1:4]'
(contracted; show full)    13
    15
%      The result is P9.
%      P1 before P8 = P9
</source>


==
p<sub>1</sub> * p<sub>3</sub> * p<sub>8</sub>==⏎
<math>p_1 * p_3 * p_8 = p_6 ~~~~ \Leftrightarrow ~~~~ P_8 * P_3 * P_1 = P_6</math>==

<source lang="matlab">
rowp1=[0 1 0 0;
       1 0 0 0;
       0 0 1 0;
       0 0 0 1];

(contracted; show full)    14
    15
%      The result is P6.
%      P1 before P3 before P8 = P6
</source>


==
p<sub>8</sub> * p<sub>3</sub> * p<sub>1</sub>==⏎
<math>p_8 * p_3 * p_1 = p_{22} ~~~~ \Leftrightarrow ~~~~ P_1 * P_3 * P_8 = P_{22}</math>==

<source lang="matlab">
rowp8*rowp3*rowp1*[1:4]'
ans =
     3
     4
     2
     1
%      The result is p22.
%      p8 after p3 after p1 = p22



ROWP1*ROWP3*ROWP8*[0:15]'
ans =
     0
     8
     4
    12
     1
     9
     5
    13
     2
    10
     6
    14
     3
    11
     7
    15
%      The result is P22.
%      P8 before P3 before P1 = P22
</source>


{{Lipedia}}
[[Category:Walsh permutation]]