![]() ![]() The second syntax specifies the order of the rows. If you multiply A on the left (Q`*A), you permute the rows, as shown:Ī = shape ( 1: 25, 5, 5 ) /*, the first syntax means, "copy the columns in the order, 3, 5, 2, 4, and 1." I think this definition is easier to use.) If you multiply A on the right (A*Q), you permute the columns. (The permutation matrix is the transpose of the matrix that I used in the previous article. The following example defines a 5 x 5 matrix, A, with integer entries and a function that creates a permutation matrix. If you use matrix multiplication to permute columns of a matrix, you might not remember whether to multiply the permutation matrix on the left or on the right, but if you use subscripts, it is easy to remember the syntax. Subscripts enable you to permute rows and columns efficiently and intuitively. I ended the article by noting that "there is an easy alternative way" to permute rows and columns: use subscript notation. A previous article shows how to create a permutation matrix and how to use it to permute the order of rows and columns in a matrix. Permutation matrices have many uses, but their primary use in statistics is to rearrange the order of rows or columns in a matrix. Instead, use elementwise multiplication of rows and columns. That article recommends that you never multiply with a large diagonal matrix. Which discusses an efficient way to use diagonal matrices in matrix computations. The advice is similar to the tip in the article, "Never multiply with a large diagonal matrix," This article explains why it is not necessary to multiply by a permutation matrix in a matrix language. Never multiply with a large permutation matrix! Instead, use subscripts to permute rows and columns. This may not be the approach actually used by Matlab, though.Do you ever use a permutation matrix to change the order of rows or columns in a matrix? Did you know that there is a more efficient way in matrix-oriented languages such as SAS/IML, MATLAB, and R? Putting these three facts together shows that it is possible to do it without a significant amount of extra memory. Transposition can be done inline, requiring only a fixed amount of extra memory, independent of array size, or growing very slowly with array size. Permute(., ) %// interchange dims 3 and 4: we have dims Įach of these elementary operations (interchanging two dimensions) is essentially a transpose along a given plane of the multidimensional array, performed repeatedly along all other dimensions. Permute(., ) %// interchange dims 2 and 4: we have dims For example, permute(x, ) is equivalent to this sequence of elementary permute operations (the sequence is not unique): permute(., ) %// interchange dims 1 and 4: we have dims Permuting of dimensions can always be done as a sequence of elementary permute operations, where" elementary" means interchanging only two dimensions. This is only a guess, as I don't really know what permute does under the hood. While this is not exactly the best way to profile memory usage (better use a proper memory profiler, something like Intel Inspector XE), it does show to some degree that permute is indeed not working in-place. You can see how at its peak the function reached twice as much memory usage as when it returned. I also repeated the test under perfmon.exe which showed the same pattern: ![]() I then ran the function simply as: %clear aĪnd watched the memory usage It went from 1.8 gigs in use, and rose to 5.2 then quickly down to 3.6 gigs. I only have 8 gigs of RAM on my laptop, so to avoid thrashing I modified your function as: function out = mtest() I also set the "update speed" to "high" to get a finer time resolution. In Windows 10, I opened the "task manager" on the "performance" tab with the "memory" graphs in view. The permute method in fact does create a second copy of the matrix with the data permuted and returns it. Your argument is flawed because the MATLAB memory profiler is not telling you the truth! ![]()
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