r - 什么时候建议在 R 中使用稀疏矩阵？

Question

我最近一直在修补电源模拟，我有以下代码:

library(MASS)
library(Matrix)

simdat <- data.frame(mmm = rep(rep(factor(1:2,
                                          labels=c("m1", "m2")),
                                   each = 2),
                               times = 2800),
                 ttt = rep(factor(1:2,
                                  labels = c("t1", "t2")),
                           times = 5600),
                 sss = rep(factor(1:70),
                            each = 160),
                 iii = rep(rep(factor(1:40),
                               each = 4),
                           times = 70))

beta <- c(1, 2)

X1 <- model.matrix(~ mmm,
                   data = simdat)

Z1 <- model.matrix(~ ttt,
                   data = simdat)

X1和 Z1是 11200x2矩阵。在 Stackoverflow 的帮助下，我设法使我的计算比以前更高效:

funab <- function(){
    ran_sub <- mvrnorm(70, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    ran_ite <- mvrnorm(40, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    Mb <- as.vector(X1 %*% beta)

    M1 <- rowSums(Z1 * ran_sub[rep(1:70,
                                        each = 160),])

    M2 <- rowSums(Z1 * ran_ite[rep(rep(1:40, each = 4),
                                        times = 70),])

    Mout <- Mb + M1 + M2

    Y <- as.vector(Mout) + rnorm(length(Mout), mean = 0 , sd = 0.27)
}

Y那么将是一个长度为 11200 的向量.然后我多次复制这个函数(比如 1000 次):

sim <- replicate(n        = 1000,
                 expr     = funab()},
                 simplify = FALSE)

sim将是 11200x1000列表。鉴于我想更多地这样做，并且可能在 funab() 中包含更多代码我想知道是否建议对 X1 使用稀疏矩阵和 Z1在 funab() 的计算中像现在这样？

Answer 1

好的，我已经尝试按照我的问题的评论中给出的建议进行测试，并使用 microbenchmark 进行了测试。包裹。为了使复制和粘贴更容易，我将重复上面的代码:

library(MASS)
library(Matrix)

simdat <- data.frame(mmm = rep(rep(factor(1:2,
                                          labels=c("m1", "m2")),
                                   each = 2),
                               times = 2800),
                 ttt = rep(factor(1:2,
                                  labels = c("t1", "t2")),
                           times = 5600),
                 sss = rep(factor(1:70),
                            each = 160),
                 iii = rep(rep(factor(1:40),
                               each = 4),
                           times = 70))

beta <- c(1, 2)

X1 <- model.matrix(~ mmm,
                   data = simdat)

Z1 <- model.matrix(~ ttt,
                   data = simdat)

我现在创建与稀疏矩阵相同的矩阵:

sparseX1 <- sparse.model.matrix(~ mmm,
                                data = simdat)

sparseZ1 <- sparse.model.matrix(~ ttt,
                                data = simdat)

然后我设置了两个函数:

funab_sparse <- function(){
    ran_sub <- mvrnorm(70, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    ran_ite <- mvrnorm(40, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    Mb <- as.vector(sparseX1 %*% beta)

    M1 <- Matrix::rowSums(sparseZ1 * ran_sub[rep(1:70,
                                        each = 160),])

    M2 <- Matrix::rowSums(sparseZ1 * ran_ite[rep(rep(1:40, each = 4),
                                        times = 70),])

    Mout <- Mb + M1 + M2

    Y <- as.vector(Mout) + rnorm(length(Mout), mean = 0 , sd = 0.27)
}

funab <- function(){
    ran_sub <- mvrnorm(70, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    ran_ite <- mvrnorm(40, mu = c(0,0), Sigma = matrix(c(10, 3, 3, 2), ncol = 2))

    Mb <- as.vector(X1 %*% beta)

    M1 <- rowSums(Z1 * ran_sub[rep(1:70,
                                        each = 160),])

    M2 <- rowSums(Z1 * ran_ite[rep(rep(1:40, each = 4),
                                        times = 70),])

    Mout <- Mb + M1 + M2

    Y <- as.vector(Mout) + rnorm(length(Mout), mean = 0 , sd = 0.27)
}

library(microbenchmark)
res <- microbenchmark(funab(), funab_sparse(), times = 1000)

并得到结果:

> res <- microbenchmark(funab(), funab_sparse(), times = 1000)
> res
Unit: milliseconds
           expr      min       lq   median       uq      max neval
        funab() 2.200342 2.277006 2.309587 2.481627 69.99895  1000
 funab_sparse() 8.419564 8.568157 9.666248 9.874024 75.88907  1000

假设我没有犯任何重大错误，我可以得出结论，使用这种使用稀疏矩阵进行计算的特殊方法不会加速我的代码。