如何通过避免循环来优化代码？

Question

我遇到了一些需要花费大量时间运行的代码的问题。有人可以帮我吗？提前致谢！

all_dist=c()
ddim=dim(b)[1]
ddimi=ddim-1

for (k in 1:dim(b)[2]){
    for (i in seq(1,ddimi,1)){
        for (j in seq(i+1,ddim,1)){
        ze=(b[i,k])-(b[j,k])*(b[i,k])-(b[j,k])
        all_dist=c(all_dist,ze)
}}}

注意：

str(b)

num [1:5, 1:30007] -0.000292 -0.001384 -0.001412 -0.002603 -0.002848 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:30007] "V1" "V2" "V3" "V4" ...

Answer 1

For-loops 和使用c() 增加你的向量会减慢你的速度。最好尝试利用矢量化，并尽可能多地使用 *apply（或 map）函数。通过使用sapply 遍历列、创建组合并计算这些组合的乘积和差异，这两种方法都起到了作用：

mat <- sapply(b, function(x) {y <- combn(x, 2); y[1,] - y[2,] * y[1,] - y[2,]})

它应该很快——也许不如 user10488504 的非常有效的解决方案那么快，但仍然相当快。它还具有非常紧凑的语法，您可能还会发现输出是一个矩阵很有用，每列对应于b 中的一列。

数据：

set.seed(12345)
b <- as.data.frame(matrix(runif(5*30007, -.001, -.0003), byrow = T, nrow = 5))

Answer 2

set.seed(0)
b <- matrix(rnorm(5*30007), nrow=5)

all_dist=c()
ddim=dim(b)[1]
ddimi=ddim-1

system.time(
#With foor-Loop
for (k in 1:dim(b)[2]){
    for (i in seq(1,ddimi,1)){
        for (j in seq(i+1,ddim,1)){
        ze=(b[i,k])-(b[j,k])*(b[i,k])-(b[j,k])
        all_dist=c(all_dist,ze)
        }}}
)
#       User      System verstrichen 
#    104.568       3.636     108.206 


#Vectorized with matrix indices
system.time({
K <- 1:dim(b)[2]     #for (k in 1:dim(b)[2]){... creates this vector
I <- seq(1,ddimi,1)  #for (i in seq(1,ddimi,1)){... creates this vector
J <- unlist(lapply(I+1, function(x) seq(x,ddim,1)))  #for (j in seq(i+1,ddim,1)){... creates this vector

IK <- as.matrix(expand.grid(I, K))  #Get all combinations between I and K as you will have with the nested for loops of k and i
IK <- IK[rep(seq_len(nrow(IK)), rep((ddim-1):1,length.out=nrow(IK))),]  #IK-rows need to be repeated, as it is used repeatedly in the "for (j in seq(i+1,ddim,1)){" loop
JK <- as.matrix(expand.grid(j=J, k=K)) #Get all combinations between J and K as you will have with the nested for loops of k and j

#Now you have all the indexes of your for loop as vectors and can make the calculations
tt <- b[IK] - b[JK] * b[IK] - b[JK]
})
#      User      System verstrichen 
#      0.056       0.000       0.097 


identical(all_dist, tt)
#[1] TRUE

由于您只在左侧使用k，而不与其他循环交互，您可以通过简单地离开 k 循环和索引来部分矢量化。

system.time({
tt=c()
for (i in seq(1,ddimi,1)){
  for (j in seq(i+1,ddim,1)){
    tt=c(tt, (b[i,])-(b[j,])*(b[i,])-(b[j,]))
  }}
dim(tt)  <- c(30007, 10)
tt <- as.vector(t(tt))
})
#       User      System verstrichen 
#      0.017       0.000       0.017 
identical(all_dist, tt)
#[1] TRUE

或者您可以用索引向量替换内部的两个 for 循环，并创建一个应用循环而不是 k-for 循环：

system.time({
I <- seq(1,ddimi,1)
J <- unlist(lapply(I+1, function(x) seq(x,ddim,1)))
I <- I[rep(seq_along(I), rep((ddim-1):1,length.out=length(I)))]
tt  <- as.vector(apply(b, 2, function(x) {x[I] - x[J] * x[I] - x[J]}))
})
#       User      System verstrichen 
#      0.085       0.000       0.085 
identical(all_dist, tt)
#[1] TRUE

来自gersht的nice解决方案的使用时间：

system.time({
mat <- as.vector(sapply(as.data.frame(b), function(x) {y <- combn(x, 2); y[1,] - y[2,] * y[1,] - y[2,]}))
})
#       User      System verstrichen 
#      1.083       0.000       1.082 
identical(all_dist, mat)
#[1] TRUE