Permute 2 2 3
Output2 = permute ( input1 2 3 ); size ( output) size ( output1) size ( output2) Output: Conclusion. In this article, we have seen how to use permute and ipermute command and how to arrange elements in matrix or multidimensional array or vector. By using permute command we can handle large data and n number of elements. Mac软件：Permute 3 v3.5.16 最纯粹简洁的多媒体转码软件 2021年02月09日 5721点热度 5人点赞 2条评论 Permute是最容易使用的媒体转换器，它易于使用，无需配置，拖放界面，它将满足转换所有媒体文件的需求。.
Permute the Order in Various Objects
Provides the generic function andmethods for permuting the order of various objectsincluding vectors, dendrograms (also hclust objects),the order of observations in a dist object, the rows and columns of a matrix, all dimensions of an array given a suitable ser_permutationobject.
- Keywords
- manip
Usage
Arguments
_*_wp(6%2C9%2C1%2C2).svg/850px-Walsh_permutation_wp(8%2C12%2C2%2C3)_*_wp(6%2C9%2C1%2C2).svg.png "Permute 2 2 3")
an object (a list, a vector, a dist object, a matrix, an array or any other object which provides dim and standard subsetting with '[').
an object of class ser_permutation which contains suitable permutation vectors for x.
additional arguments for the permutation function.
Details
The permutation vectors in ser_permutation are suitable if the number of permutation vectors matches the numberof dimensions of x and if the length of each permutation vectorhas the same length as the corresponding dimension of x.
For 1-dimensional/1-mode data (list, vector, dist), order can also be a single permutation vector of class ser_permutation_vector or data which can be automatically coerced to this class(e.g. a numeric vector).
For dendrograms and hclust, subtrees are rotated torepresent the order best possible. If the order is not achived perfectlythen the user is warned. This behavior can be changed with the extraparameter incompatible which can take the values 'warn' (default), 'stop' or 'ignore'.
See Also
ser_permutation,dist in package stats.
Aliases
- permute
- permute.dist
- permute.numeric
- permute.list
- permute.matrix
- permute.array
- permute.data.frame
- permute.hclust
- permute.dendrogram
Examples
Community examples
Permute 2
Result
| Permutations, nPr = |
| = | 30 |
| Combinations, nCr = |
| = | 15 |
Permutations and combinations are part of a branch of mathematics called combinatorics, which involves studying finite, discrete structures. Permutations are specific selections of elements within a set where the order in which the elements are arranged is important, while combinations involve the selection of elements without regard for order. A typical combination lock for example, should technically be called a permutation lock by mathematical standards, since the order of the numbers entered is important; 1-2-9 is not the same as 2-9-1, whereas for a combination, any order of those three numbers would suffice. There are different types of permutations and combinations, but the calculator above only considers the case without replacement, also referred to as without repetition. This means that for the example of the combination lock above, this calculator does not compute the case where the combination lock can have repeated values, for example 3-3-3.
Permutations
The calculator provided computes one of the most typical concepts of permutations where arrangements of a fixed number of elements r, are taken from a given set n. Essentially this can be referred to as r-permutations of n or partial permutations, denoted as nPr, nPr, P(n,r), or P(n,r) among others. In the case of permutations without replacement, all possible ways that elements in a set can be listed in a particular order are considered, but the number of choices reduces each time an element is chosen, rather than a case such as the 'combination' lock, where a value can occur multiple times, such as 3-3-3. For example, in trying to determine the number of ways that a team captain and goal keeper of a soccer team can be picked from a team consisting of 11 members, the team captain and the goal keeper cannot be the same person, and once chosen, must be removed from the set. The letters A through K will represent the 11 different members of the team:
A B C D E F G H I J K 11 members; A is chosen as captain
B C D E F G H I J K 10 members; B is chosen as keeper
As can be seen, the first choice was for A to be captain out of the 11 initial members, but since A cannot be the team captain as well as the goal keeper, A was removed from the set before the second choice of the goal keeper B could be made. The total possibilities if every single member of the team's position were specified would be 11 × 10 × 9 × 8 × 7 × ... × 2 × 1, or 11 factorial, written as 11!. However, since only the team captain and goal keeper being chosen was important in this case, only the first two choices, 11 × 10 = 110 are relevant. As such, the equation for calculating permutations removes the rest of the elements, 9 × 8 × 7 × ... × 2 × 1, or 9!. Thus, the generalized equation for a permutation can be written as:
| nPr = |
|
Or in this case specifically:
| 11P2 = |
| = |
| = 11 × 10 = 110 |
Again, the calculator provided does not calculate permutations with replacement, but for the curious, the equation is provided below:
nPr = nr
Combinations
Permute 2 2 3 X 4
Combinations are related to permutations in that they are essentially permutations where all the redundancies are removed (as will be described below), since order in a combination is not important. Combinations, like permutations, are denoted in various ways including nCr, nCr, C(n,r), or C(n,r), or most commonly as simply| ( | n | ) |
| r |
are chosen to be strikers in those respective orders, only that they are chosen. The possible number of arrangements for all n people, is simply n!, as described in the permutations section. To determine the number of combinations, it is necessary to remove the redundancies from the total number of permutations (110 from the previous example in the permutations section) by dividing the redundancies, which in this case is 2!. Again, this is because order no longer matters, so the permutation equation needs to be reduced by the number of ways the players can be chosen, A then B or BPermute 2 2 3/4
then A, 2, or 2!. This yields the generalized equation for a combination as that for a permutation divided by the number of redundancies, and is typically known as the binomial coefficient:Permute 2 2 300
| nCr = |
|
Or in this case specifically:
Permute 2 2 3 X 2
| 11C2 = |
| = |
| = 55 |
It makes sense that there are fewer choices for a combination than a permutation, since the redundancies are being removed. Again for the curious, the equation for combinations with replacement is provided below:
| nCr = |
|