A matrix is doubly stochastic if and only if it is a convex combination of permutation matrices. In coding, memory can be saved by representing a permutation matrix as an integer vector, where is the column index of the within the th row of. ![]() MATLAB functions that return permutation matrices can also return the permutation in vector form. Here is an example with the MATLAB lu function that illustrates how permuting a matrix can be done using the vector permutation representation. > A = gallery('frank',4), = lu(A) Pįor more on handling permutations in MATLAB see section 24.3 of MATLAB Guide.You are not returning the result in your function. =size(A) % number of rows and columnsįor j = 1:d % permute the elements of column j Perms = perms_of_(A) % save the result of the call in a variableįunction A = perms_of_(A) % declare the return variable to be A That is, you calculate a new A inside your function but you don't return it to the caller via the perms variable. This syntax of using the same variable name for input and output can sometimes result in inplace operations depending on how the function is called. Yes, this looks hard and it is indeed hard! To check if you understand thoroughly, try predicting a square Matrix's similar different permutations.E.g., calling the function like this inside another function will allow inplace operations: function some_functionĪ = perms_of_(A) % save the result of the call in a variable If you don't use specific inplace operation syntax in the caller then a deep copy will be returned to the caller. So, there will be 1 4x2 (4x2x1) matrix(itself!). * G = permute(A,) % this makes no difference, using to show the reasoningĤx2x1 ( row(1) dimension of A = 4, column(2) dimension of A = 2, page(3) dimension of A = 1 4 is row dimension, 2 is column dimension and 1 is page dimension for the generated G) * F = permute(A,) % this is transpose and same as Ģx4x1 ( column(2) dimension of A = 2, row(1) dimension of A = 4, page(3) dimension of A = 1 2 is row dimension, 4 is column dimension and 1 is page dimension for the generated F) So, there will be 4 2x1 (2x1x4) column matrixes. As in: ans(:,:,1) =Ģx1x4 ( column(2) dimension of A = 2, page(3) dimension of A = 1, row(1) dimension of A = 4 2 is row dimension, 1 is column dimension and 4 is page dimension for the generated E) So, there will be 2 4x1 (4x1x2) column matrixes. As in: ans(:,:,1) =Ĥx1x2 ( row(1) dimension of A = 4, page(3) dimension of A = 1, column(2) dimension of A = 2 4 is row dimension, 1 is column dimension and 2 is page dimension for the generated D) So, there will be 2 1x4 (1x4x2) row matrixes. As in: ans(:,:,1) =ġx4x2 ( page(3) dimension of A = 1, row(1) dimension of A = 4, column(2) dimension of A = 2 1 is row dimension, 4 is column dimension and 2 is page dimension for the generated C) So, there will be 4 1x2 (1x2x4) row matrixes. G = permute(A,) % means ġx2x4 ( page(3) dimension of A = 1, column(2) dimension of A = 2, row(1) dimension of A = 4 1 is row dimension, 2 is column dimension and 4 is page dimension for the generated B. % 3 = page, 2 = column and 1 = row dimensions):ī = permute(A,) % means Ĭ = permute(A,) % means ĭ = permute(A,) % means Į = permute(A,) % means į = permute(A,) % means % (numbers in the order argument of permute function indicates dimensions, Now let's move to the examples, Finally: % A has 4 rows, 2 columns and 1 page Order argument passed to permute swap these dimensions in the matrix and produce an awkward combination of arrays, I think permute is a misnomer for this effect. ![]() ![]() B=zeros(10,3) has 10 rows, 3 columns and 1 page, this order is important!) And if you don't specify a dimension, its default count is set to 1. Here are some examples to prevent you from suffering a similar excruciating pain:įirst, let's remember the dimensions' names of matrix in matlab: A = zeros(4,5,7), matrix A has 4 rows, 5 columns and 7 pages. Therefore, I used the F*ck word many times during " my journey of understanding the permute function". Wow, this is one of the hardest functions to figure out among all the different SDKs I have used up to now.
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