用1:n的唯一值创建n x n矩阵 [英] Create n by n matrix with unique values from 1:n
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问题描述
我想在R中生成一个随机的n×n矩阵,离散值的范围是1到n.棘手的是,我希望每个值在行和列中都唯一.
I want generate a random n by n matrix in R with discrete values ranging from 1 to n. The tricky part is that I want each value to be unique both in the row and on the column.
例如,如果n=3
,则矩阵如下所示:
For example, if n=3
the matrix could look like:
1 2 3
2 3 1
3 1 2
或者看起来像这样:
2 3 1
1 2 3
3 1 2
有人知道如何生成这种矩阵吗?
anyone has any idea of how to generate this kind of matrix?
推荐答案
您想要的被称为拉丁语正方形.这是一个函数(来自 R的食谱;另请参见此处和其他在线搜索结果)生成它们:
What you want is called a Latin square. Here's one function (from the Cookbook for R; see also here and a bunch of other search results online) allowing to generate them:
latinsquare <- function(len, reps=1, seed=NA, returnstrings=FALSE) {
# Save the old random seed and use the new one, if present
if (!is.na(seed)) {
if (exists(".Random.seed")) { saved.seed <- .Random.seed }
else { saved.seed <- NA }
set.seed(seed)
}
# This matrix will contain all the individual squares
allsq <- matrix(nrow=reps*len, ncol=len)
# Store a string id of each square if requested
if (returnstrings) { squareid <- vector(mode = "character", length = reps) }
# Get a random element from a vector (the built-in sample function annoyingly
# has different behavior if there's only one element in x)
sample1 <- function(x) {
if (length(x)==1) { return(x) }
else { return(sample(x,1)) }
}
# Generate each of n individual squares
for (n in 1:reps) {
# Generate an empty square
sq <- matrix(nrow=len, ncol=len)
# If we fill the square sequentially from top left, some latin squares
# are more probable than others. So we have to do it random order,
# all over the square.
# The rough procedure is:
# - randomly select a cell that is currently NA (call it the target cell)
# - find all the NA cells sharing the same row or column as the target
# - fill the target cell
# - fill the other cells sharing the row/col
# - If it ever is impossible to fill a cell because all the numbers
# are already used, then quit and start over with a new square.
# In short, it picks a random empty cell, fills it, then fills in the
# other empty cells in the "cross" in random order. If we went totally randomly
# (without the cross), the failure rate is much higher.
while (any(is.na(sq))) {
# Pick a random cell which is currently NA
k <- sample1(which(is.na(sq)))
i <- (k-1) %% len +1 # Get the row num
j <- floor((k-1) / len) +1 # Get the col num
# Find the other NA cells in the "cross" centered at i,j
sqrow <- sq[i,]
sqcol <- sq[,j]
# A matrix of coordinates of all the NA cells in the cross
openCell <-rbind( cbind(which(is.na(sqcol)), j),
cbind(i, which(is.na(sqrow))))
# Randomize fill order
openCell <- openCell[sample(nrow(openCell)),]
# Put center cell at top of list, so that it gets filled first
openCell <- rbind(c(i,j), openCell)
# There will now be three entries for the center cell, so remove duplicated entries
# Need to make sure it's a matrix -- otherwise, if there's just
# one row, it turns into a vector, which causes problems
openCell <- matrix(openCell[!duplicated(openCell),], ncol=2)
# Fill in the center of the cross, then the other open spaces in the cross
for (c in 1:nrow(openCell)) {
# The current cell to fill
ci <- openCell[c,1]
cj <- openCell[c,2]
# Get the numbers that are unused in the "cross" centered on i,j
freeNum <- which(!(1:len %in% c(sq[ci,], sq[,cj])))
# Fill in this location on the square
if (length(freeNum)>0) { sq[ci,cj] <- sample1(freeNum) }
else {
# Failed attempt - no available numbers
# Re-generate empty square
sq <- matrix(nrow=len, ncol=len)
# Break out of loop
break;
}
}
}
# Store the individual square into the matrix containing all squares
allsqrows <- ((n-1)*len) + 1:len
allsq[allsqrows,] <- sq
# Store a string representation of the square if requested. Each unique
# square has a unique string.
if (returnstrings) { squareid[n] <- paste(sq, collapse="") }
}
# Restore the old random seed, if present
if (!is.na(seed) && !is.na(saved.seed)) { .Random.seed <- saved.seed }
if (returnstrings) { return(squareid) }
else { return(allsq) }
}
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