R:将 FUN 应用于数组的 kxk 子部分 [英] R: Apply FUN to kxk subsections of array
问题描述
语言是 R.
我有一个 nxm 矩阵,我想将它分成 3x3 部分并计算每个部分的平均值(或任何函数).(如果有一个不是 3x3 的剩余部分,那么就使用剩下的部分).
I have an nxm matrix, and I'd like to partition it into 3x3 sections and calculate the mean (or any function) within each. (If there's a leftover bit that isn't 3x3 then use just what's left).
我确信有一种apply
-ish 方式来做到这一点——它就在我的舌尖上——但我的大脑目前正在让我失望.我想这有点像移动窗口问题,只是我想要不重叠的窗口(所以更容易).
I'm sure there's an apply
-ish way to do this -- it's on the tip of my tongue -- but my brain is currently failing me.
I suppose it's a bit like a moving window question except I want non-overlapping windows (so it's easier).
谁能想到一个内置函数来做到这一点?还是矢量化的方式?
这是我的循环版本:
winSize <- 3
mat <- matrix(runif(6*11),nrow=6,ncol=11)
nr <- nrow(mat)
nc <- ncol(mat)
outMat <- matrix(NA,nrow=ceiling(nr/winSize),
ncol=ceiling(nc/winSize))
FUN <- mean
for ( i in seq(1,nr,by=winSize) ) {
for ( j in seq(1,nc,by=winSize) ) {
# work out mean in 3x3 window, fancy footwork
# with pmin just to make sure we don't go out of bounds
outMat[ ceiling(i/winSize), ceiling(j/winSize) ] <-
FUN(mat[ pmin(i-1 + 1:winSize,nr), pmin(j-1 + 1:winSize,nc)])
}
}
干杯.
推荐答案
可以使用 row
和 col
提取行号和列号,然后计算每个块的坐标.
You can use row
and col
to extract the row and column numbers,
and then compute the coordinates of each block.
tapply(
mat,
list( floor((row(mat)-1)/winSize), floor((col(mat)-1)/winSize) ),
mean
)
这可以推广到高维数组,通过用以下函数替换 row
和 col
.
This can be generalized to higher-dimensional arrays, by replacing row
and col
with the following function.
a <- function( m, k ) {
stopifnot( "array" %in% class(m) || "matrix" %in% class(m) )
stopifnot( k == floor(k) )
stopifnot( k > 0 )
n <- length(dim(m))
stopifnot( k <= n )
i <- rep(
1:dim(m)[k],
each = prod(dim(m)[ 1:n < k ]),
times = prod(dim(m)[ 1:n > k ])
)
array(i, dim=dim(m))
}
# A few tests
m <- array(NA, dim=c(2,3))
all( row(m) == a(m,1) )
all( col(m) == a(m,2) )
# In dimension 3, it can be done manually:
m <- array(NA, dim=c(2,3,5))
all( a(m,1) == array( rep(1:dim(m)[1], times=prod(dim(m)[2:3])), dim=dim(m) ) )
all( a(m,2) == array( rep(1:dim(m)[2], each=dim(m)[1], times=dim(m)[3]), dim=dim(m) ) )
all( a(m,3) == array( rep(1:dim(m)[3], each=prod(dim(m)[-3])), dim=dim(m) ) )
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