加速对称矩阵的计算；使用外 [英] Speeding up calculation of symmetric matrices; use of outer

问题描述

我需要加快生成对称矩阵的计算.目前我有这样的事情:

<块引用>

X <- 1:50Y<- 1:50M <-外(X，Y，FUN = myfun)

其中 myfun 是一个相当复杂的矢量化但对称的函数 (myfun(x, y) = myfun(y, x)).

所以我的代码不必要地浪费时间计算下三角矩阵和上三角矩阵.

如何在不使用慢速 for 循环的情况下避免重复?

解决方案

如果你的函数很慢并且时间随着输入的大小而变化，你可以使用combn:

X <- 1:50Y <- 1:50#一个慢函数myfun <- 函数(x，y){res <- x * NAfor (i in seq_along(x)) {系统睡眠(0.01)res[i] <- x[i] * y[i]}资源}system.time(M <-外层(X, Y, FUN = myfun))#用户系统已过期#0.00 0.00 26.41系统时间({inds <- 组合(seq_len(长度(X))，2)M1 <- 矩阵(ncol = 长度(X)，nrow = 长度(Y))M1[lower.tri(M1)] <- myfun(X[inds[1,]], Y[inds[2,]])M1[上.tri(M1)] <-t(M1)[上.tri(M1)]diag(M1) <- myfun(X, Y)})#用户系统已过期#0.00 0.00 13.41all.equal(M, M1)#[1] 真

然而，最好的解决方案可能是通过 Rcpp 在 C++ 中实现.

I need to speed up a calculation that produces a symmetric matrix. Currently I have something like this:

X <- 1:50
Y<- 1:50
M <- outer(X, Y, FUN = myfun)

where myfun is a quite complicated, vectorized, but symmetrical function (myfun(x, y) = myfun(y, x)).

So my code unnecessarily wastes time calculating the lower triangular matrix as well as the upper triangular matrix.

How can I avoid that duplication without using slow for-loops?

解决方案

If your function is slow and timing scales with size of its input, you could use combn:

X <- 1:50
Y <- 1:50

#a slow function
myfun <- function(x, y) {
  res <- x * NA
  for (i in seq_along(x)) {
    Sys.sleep(0.01)
    res[i] <- x[i] * y[i]
    }
  res
}

system.time(M <- outer(X, Y, FUN = myfun))
#user  system elapsed 
#0.00    0.00   26.41 

system.time({
  inds <- combn(seq_len(length(X)), 2)
  M1 <- matrix(ncol = length(X), nrow = length(Y))

  M1[lower.tri(M1)] <-  myfun(X[inds[1,]], Y[inds[2,]])
  M1[upper.tri(M1)] <- t(M1)[upper.tri(M1)]
  diag(M1) <- myfun(X, Y)
})
#user  system elapsed 
#0.00    0.00   13.41

all.equal(M, M1)
#[1] TRUE

However, the best solution is probably to implement this in C++ via Rcpp.

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