R:将矩阵拆分为任意数量的块 [英] R: split matrix into arbitrary number of blocks

问题描述

说我有一个值矩阵

    set.seed(1)
    A <- matrix(runif(25),ncol=5)

我想为这个大小相等的矩阵内的近似正方形邻域计算一些统计信息.这些输出中的任何一种都可以:

I'd like to calculate some statistics for approximately square neighborhoods within this matrix of approximately equal size. Either of these kinds of output would do:

    N1 <-  matrix(c(rep(c("A","A","B","B","B"),2),rep(c("C","C","D","D","D"),3)),ncol=5)
    N2 <-  matrix(c(rep(c("A","A","A","B","B"),3),rep(c("C","C","D","D","D"),2)),ncol=5)
    N1
         [,1] [,2] [,3] [,4] [,5]
    [1,] "A"  "A"  "C"  "C"  "C" 
    [2,] "A"  "A"  "C"  "C"  "C" 
    [3,] "B"  "B"  "D"  "D"  "D" 
    [4,] "B"  "B"  "D"  "D"  "D" 
    [5,] "B"  "B"  "D"  "D"  "D" 

    N2
         [,1] [,2] [,3] [,4] [,5]
    [1,] "A"  "A"  "A"  "C"  "C" 
    [2,] "A"  "A"  "A"  "C"  "C" 
    [3,] "A"  "A"  "A"  "D"  "D" 
    [4,] "B"  "B"  "B"  "D"  "D" 
    [5,] "B"  "B"  "B"  "D"  "D" 

其他近似值也可以，因为我总是可以旋转矩阵.然后，我可以使用这些邻域矩阵通过tapply()来计算统计信息，如下所示:

other approximations are also OK, since I can always rotate the matrix. Then I can use these neighborhood matrices to calculate stats using tapply(), like this:

    tapply(A,N1,mean)
            A         B         C         D 
    0.6201744 0.5057402 0.4574495 0.5594227

我想要的是一个函数，该函数可使我具有任意维度的矩阵，并具有任意数量的块状邻域，例如N1或N2.我很难弄清楚这种功能如何处理所需的块数甚至不是平方的情况. N1和N2具有4个邻域，但是说我想要5个类似这样的输出:

What I want is a function that can make me a matrix of arbitrary dimensions with an arbitrary number of block-like neighborhoods like N1 or N2. I'm having a hard time trying to figure out how such a function would deal with situations where the desired number of blocks are not even squares. N1 and N2 have 4 neighborhoods, but say I wanted 5 for some output something like this:

    N3 <-  matrix(c("A","A","B","B","B","A","A","C","C","C","D","D","C","C","C",
            "D","D","E","E","E","D","D","E","E","E"),ncol=5)
         [,1] [,2] [,3] [,4] [,5]
    [1,] "A"  "A"  "D"  "D"  "D" 
    [2,] "A"  "A"  "D"  "D"  "D" 
    [3,] "B"  "C"  "C"  "E"  "E" 
    [4,] "B"  "C"  "C"  "E"  "E" 
    [5,] "B"  "C"  "C"  "E"  "E" 

是否有人知道可以进行这种拆分的现有功能，或者对如何进行拆分有任何想法?谢谢！

Does anyone know of an existing function that can do this kind of split, or have any ideas on how to make one? Thank you!

[] 考虑到文森特的建议，我的最后职责是:

[] My final function, taking into account Vincent's advice:

    DecideBLocks <- function(A,nhoods){
        nc <- ncol(A)
        nr <- nrow(A)
        nhood_side <- floor(sqrt((nc*nr)/nhoods))
        Neighborhoods <- matrix(paste(ceiling(col(A)/nhood_side), ceiling(row(A)/nhood_side), sep="-"), nc=ncol(A)) 
        nhoods.out <- length(unique(c(Neighborhoods)))
        if (nhoods.out != nhoods){
            cat(nhoods.out,"neighborhoods created.\nThese were on average",nhood_side,"by",nhood_side,"cells\nit's a different number than that stated the function tries to round things to square neighborhoods\n")
        }
        return(Neighborhoods)
    }
    A <- matrix(rnorm(120),12)
    B <- DecideBLocks(A,13)

推荐答案

您可以尝试使用row和col函数: 他们将问题减少到一维问题. 以下定义了大小最大为2 * 2的块.

You can try to play with the row and col functions: they reduce the problem to a 1-dimensional one. The following defines blocks of size at most 2*2.

matrix( 
  paste(
    ceiling(col(A)/2), 
    ceiling(row(A)/2), 
    sep="-"), 
  nc=ncol(A) 
)

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