Perm sign: Difference between revisions
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|desc=Computes the sign of a permutation | |desc=Computes the sign of a permutation | ||
|rel=[[perm_inv]] | |rel=[[perm_inv]] | ||
|cat=[[List of functions#Helper_functions|Helper functions]] | |||
|upd=November 21, 2012 | |upd=November 21, 2012 | ||
|v= | |v=0.50 | ||
|helper=1}} | |helper=1}} | ||
<tt>'''perm_sign'''</tt> is a [[List of functions|function]] that computes the [http://en.wikipedia.org/wiki/Parity_of_a_permutation sign of a permutation]. The output of the function is either 1, indicating the permutation is even, or -1, indicating the permutation is odd. | <tt>'''perm_sign'''</tt> is a [[List of functions|function]] that computes the [http://en.wikipedia.org/wiki/Parity_of_a_permutation sign of a permutation]. The output of the function is either 1, indicating the permutation is even, or -1, indicating the permutation is odd. | ||
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===Small examples=== | ===Small examples=== | ||
The identity permutation is even: | The identity permutation is even: | ||
< | <syntaxhighlight> | ||
>> perm_sign(1:4) | >> perm_sign(1:4) | ||
| Line 23: | Line 24: | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
The permutation that transposes 3 and 4 is odd: | The permutation that transposes 3 and 4 is odd: | ||
< | <syntaxhighlight> | ||
>> perm_sign([1,2,4,3,5]) | >> perm_sign([1,2,4,3,5]) | ||
| Line 32: | Line 33: | ||
-1 | -1 | ||
</ | </syntaxhighlight> | ||
===A large example=== | ===A large example=== | ||
This function has no trouble with large permutations. The following code determines the sign of a random permutation of 1:1000000 in under 1/2 of a second on a standard desktop computer: | This function has no trouble with large permutations. The following code determines the sign of a random permutation of 1:1000000 in under 1/2 of a second on a standard desktop computer: | ||
< | <syntaxhighlight> | ||
>> perm_sign(randperm(1000000)) | >> perm_sign(randperm(1000000)) | ||
| Line 42: | Line 43: | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=perm_sign|helper=1}} | |||
Latest revision as of 16:26, 29 September 2014
| perm_sign | |
| Computes the sign of a permutation | |
| Other toolboxes required | none |
|---|---|
| Related functions | perm_inv |
| Function category | Helper functions |
| This is a helper function that only exists to aid other functions in QETLAB. If you are an end-user of QETLAB, you likely will never have a reason to use this function. |
perm_sign is a function that computes the sign of a permutation. The output of the function is either 1, indicating the permutation is even, or -1, indicating the permutation is odd.
Syntax
- SGN = perm_sign(PERM)
Argument descriptions
- PERM: A vector containing a permutation of the integers 1, 2, ..., n.
Examples
Small examples
The identity permutation is even:
>> perm_sign(1:4)
ans =
1The permutation that transposes 3 and 4 is odd:
>> perm_sign([1,2,4,3,5])
ans =
-1A large example
This function has no trouble with large permutations. The following code determines the sign of a random permutation of 1:1000000 in under 1/2 of a second on a standard desktop computer:
>> perm_sign(randperm(1000000))
ans =
1Source code
Click here to view this function's source code on github.