The outer map makes sure all permutations are generated by considering all elements of lst as the first element. So the inner map produces all permutations that start with some i, which we've set to 1 here. Now map the lambda over these permutations: > (map (lambda (j) (cons i j)) (permute (remove i lst))) Looks good: the inner expression removes an element and generates permutations of the remainder of the list, recursively. Fix lst and apply the inner expression to one of its elements. Let's pick this apart, going from the inside out. But the part that calls again to permute and remove with i, what is that part doing? It is just removing the head of the list to generate subsets of the list having the head of the pair, element i, fixed until it runs out of elements? So what is exactly doing this line: (apply append(map(lambda (i) (map (lambda (j)(cons i j))įor me it seems that it just wants to create a pair with two elements: i and j, which they will become a list with the elements permuted (if we take the assumption that a list is just a bunch of concatenated pairs). For what I know map appies a function to every element of an argument (in this case a list), and apply just applies one function one time completely to all the arguments. The part that I quite do not get it, is the permute function. The first function remove, it seems straightforward that only gets rid of the caracter denoted by x, even if its repeated or not, by comparing it with the beginning of the list and calling recursively with the rest of it. (else (apply append(map(lambda (i) (map (lambda (j)(cons i j)) (else (cons (car lst) (remove x (cdr lst))))))
DEFINE PERMUTE CODE
The code is the following: (define (remove x lst) In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices.I have found the following piece of code that it makes permutation in Scheme. "A dynamical systems approach to weighted graph matching". Most authors choose one representation to be consistent with other notation they have introduced, so there is generally no need to supply a name. n-queens puzzle, a permutation matrix in which there is at most one entry in each diagonal and antidiagonal.Costas array, a permutation matrix in which the displacement vectors between the entries are all distinct.So, permutation matrices do indeed permute the order of elements in vectors multiplied with them.
Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows (when pre-multiplying, to form PA) or columns (when post-multiplying, to form AP) of the matrix A. In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. ( August 2022) ( Learn how and when to remove this template message) Please help to improve this article by introducing more precise citations.
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