![]() ![]() The SSCP matrix is part of the "normal equations" that are used to obtain least-squares estimates for regression parameters. If you have computed the SSCP matrix in one order, you can obtain it for any order without recomputing it. ![]() Fortunately, if you have computed the sum of squares and crossproducts matrix (SSCP) for the variables in the original order, it is trivial to permute the matrix to accommodate any other ordering of the variables. The order of variables is also used in regression techniques such as variable selection methods. For some statistics (for example, the Type I sequential sum of squares), the order of the variables in the model are important. Suppose you read in a design matrix where the columns of the matrix are in a specified order. Another application is the order of columns in a design matrix for linear regression models. In my previous article, I used a correlation matrix to demonstrate why it is useful to know how to permute rows and columns of a matrix. You don't have to remember which side of A to put the permutation matrix, nor whether to use a transpose operation.Īn application: Order of effects in a regression model 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. This example shows how to use the Permute Block to permute blocks by row or column. 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. B permute(A,dimorder) rearranges the dimensions of an array in the order specified by the vector dimorder. 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. P.s: Edit tags as appropriate, I added as many as made sense to me.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? I know about permutation matrices, but they only permute entire rows and columns not individual entries.įor example: Say I want to permute $x_ After, use interp1 and permute to resize the third dimension. For each 2D slice in your matrix, use interp2 to resize each slice to the output rows and columns using the above 2D grid. As a variation of my answer above, Ill note that if you want to generate M permutations of N objects (where the N objects are represented by the integers 1-N) you can use:, x sort (rand (N, M)) I can generate 100,000 permutations of 52 objects in 0.3 seconds on my machine. I want to permute two entries in $A$, any two entries as needed: In general, for any two entries $a_j,b_k$ in the matrix is it possible to do this with some matrix $B$ dependent on $a_j,b_k$? As such, the basic algorithm is this: Create a 2D grid of interpolated access values for each dimension following the procedure above. Let $A$ be an $8 \times 8$ matrix with integer coefficients. ![]()
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