R：对相邻矩阵元素求和。如何加速？

我正在处理大约2500x250x50（lonxlatxtime）的大型矩阵。该矩阵仅包含1和0。我需要知道每个时间步周围24个元素的总和。到目前为止，我是这样做的：

xdim <- 2500
ydim <- 2500
tdim <- 50
a <- array(0:1,dim=c(xdim,ydim,tdim))
res <- array(0:1,dim=c(xdim,ydim,tdim))

for (t in 1:tdim){
  for (x in 3:(xdim-2)){
    for (y in 3:(ydim-2)){
      res[x,y,t] <- sum(a[(x-2):(x+2),(y-2):(y+2),t])
    }
  }
}

---

xdim您当前的代码由于冗余子集设置和计算而产生大量开销。如果你想提高速度，就把这个清理干净


在
xdim中，有一种解决方案对于大型阵列来说非常快速：

res <- apply(a, 3, function(a) t(filter(t(filter(a, rep(1, 5), circular=TRUE)), rep(1, 5), circular=TRUE)))
dim(res) <- c(xdim, ydim, tdim)

下面是您当前正在使用的（NAs处于边缘）以及此示例在我的笔记本电脑上花费的时间：

f1 <- function(a, xdim, ydim, tdim){
  res <- array(NA_integer_,dim=c(xdim,ydim,tdim))
  for (t in 1:tdim){
    for (x in 3:(xdim-2)){
      for (y in 3:(ydim-2)){
        res[x,y,t] <- sum(a[(x-2):(x+2),(y-2):(y+2),t])
      }
    }
  }
  return(res)
}

system.time(res1 <- f1(a, xdim, ydim, tdim))
#   user  system elapsed
# 14.813   0.005  14.819

f1简介
我不得不说，阵列的设置背后隐藏着很多东西。不过，问题的其余部分并不重要。因此，有两种方法可以真正做到这一点：

@Alex给出的Bruteforce（用C++编写）
观察复制模式
使用OpenMP进行暴力强制
如果我们想“暴力”它，那么我们可以使用@Alex给出的建议，对犰狳使用
OpenMP

#include <RcppArmadillo.h>

// [[Rcpp::depends(RcppArmadillo)]]

// Add a flag to enable OpenMP at compile time
// [[Rcpp::plugins(openmp)]]

// Protect against compilers without OpenMP
#ifdef _OPENMP
  #include <omp.h>
#endif

// [[Rcpp::export]]
arma::cube cube_parallel(arma::cube a, arma::cube res, int cores = 1) {

  // Extract the different dimensions
  unsigned int tdim = res.n_slices;

  unsigned int xdim = res.n_rows;

  unsigned int ydim = res.n_cols;

  // Same calculation loop
  #pragma omp parallel for num_threads(cores)
  for (unsigned int t = 0; t < tdim; t++){
    // pop the T
    arma::mat temp_mat = a.slice(t);

    // Subset the rows
    for (unsigned int x = 2; x < xdim-2; x++){

      arma::mat temp_row_sub = temp_mat.rows(x-2, x+2);

      // Iterate over the columns with unit accumulative sum
      for (unsigned int y = 2; y <  ydim-2; y++){
        res(x,y,t) = accu(temp_row_sub.cols(y-2,y+2));
      }
    }
  }

  return res;
}

输出：

, , 1

     [,1] [,2] [,3]
[1,]    0    0    0
[2,]    1    1    1

, , 2

     [,1] [,2] [,3]
[1,]    0    0    0
[2,]    1    1    1

案例2:

xdim <- 2
ydim <- 3
tdim <- 2
a <- array(0:1,dim=c(xdim,ydim,tdim))

xdim <- 3
ydim <- 3
tdim <- 3
a <- array(0:1,dim=c(xdim,ydim,tdim))

, , 1

     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    1    0    1
[3,]    0    1    0

, , 2

     [,1] [,2] [,3]
[1,]    1    0    1
[2,]    0    1    0
[3,]    1    0    1

, , 3

     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    1    0    1
[3,]    0    1    0

xdim <- 3
ydim <- 4
tdim <- 2
a <- array(0:1,dim=c(xdim,ydim,tdim))

, , 1

     [,1] [,2] [,3] [,4]
[1,]    0    1    0    1
[2,]    1    0    1    0
[3,]    0    1    0    1

, , 2

     [,1] [,2] [,3] [,4]
[1,]    0    1    0    1
[2,]    1    0    1    0
[3,]    0    1    0    1

案例3:

xdim <- 2
ydim <- 3
tdim <- 2
a <- array(0:1,dim=c(xdim,ydim,tdim))

xdim <- 3
ydim <- 3
tdim <- 3
a <- array(0:1,dim=c(xdim,ydim,tdim))

, , 1

     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    1    0    1
[3,]    0    1    0

, , 2

     [,1] [,2] [,3]
[1,]    1    0    1
[2,]    0    1    0
[3,]    1    0    1

, , 3

     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    1    0    1
[3,]    0    1    0

xdim <- 3
ydim <- 4
tdim <- 2
a <- array(0:1,dim=c(xdim,ydim,tdim))

, , 1

     [,1] [,2] [,3] [,4]
[1,]    0    1    0    1
[2,]    1    0    1    0
[3,]    0    1    0    1

, , 2

     [,1] [,2] [,3] [,4]
[1,]    0    1    0    1
[2,]    1    0    1    0
[3,]    0    1    0    1

模式黑客
好的，基于上面的讨论，我们选择编写一些代码来利用这个独特的模式

创建交替向量
在这种情况下，交替向量在两个不同的值之间切换

#include <RcppArmadillo.h>
// [[Rcpp::depends(RcppArmadillo)]]

// ------- Make Alternating Vectors

arma::vec odd_vec(unsigned int xdim){

  // make a temporary vector to create alternating 0-1 effect by row.
  arma::vec temp_vec(xdim);

  // Alternating vector (anyone have a better solution? )
  for (unsigned int i = 0; i < xdim; i++) {
    temp_vec(i) = (i % 2 ? 0 : 1);
  }

  return temp_vec;
}

arma::vec even_vec(unsigned int xdim){

  // make a temporary vector to create alternating 0-1 effect by row.
  arma::vec temp_vec(xdim);

  // Alternating vector (anyone have a better solution? )
  for (unsigned int i = 0; i < xdim; i++) {
    temp_vec(i) = (i % 2 ? 1 : 0); // changed
  }

  return temp_vec;
}

调用主函数
这是将所有内容组合在一起的核心功能。这为我们提供了所需的距离阵列

// --- Main Engine

// Create the desired cube information
// [[Rcpp::export]]
arma::cube dim_to_cube(unsigned int xdim = 4, unsigned int ydim = 4, unsigned int tdim = 3) {

  // Initialize values in A
  arma::cube res(xdim,ydim,tdim);

  if(xdim % 2 == 0){
    res.each_slice() = calc_matrix(make_even_matrix(xdim, ydim));
  }else{

    if(ydim % 2 == 0){

      res.each_slice() = calc_matrix(make_odd_matrix_case1(xdim, ydim));

    }else{

      arma::mat first_odd_mat = calc_matrix(make_odd_matrix_case1(xdim, ydim));

      arma::mat sec_odd_mat = calc_matrix(make_odd_matrix_case2(xdim, ydim));

      for(unsigned int t = 0; t < tdim; t++){
        res.slice(t) = (t % 2 ? sec_odd_mat : first_odd_mat);
      }

    }

  }

  return res;
}

用于计时的脚本：

cpp_parallel = cube_parallel(a,res, 1)
alex_1core = alex(a,res,xdim,ydim,tdim)
cpp_cache = dim_to_cube(xdim,ydim,tdim)
op_answer = cube_r(a,res,xdim,ydim,tdim)

all.equal(cpp_parallel, op_answer)
all.equal(cpp_cache, op_answer)
all.equal(alex_1core, op_answer)

xdim <- 20
ydim <- 20
tdim <- 5
a <- array(0:1,dim=c(xdim,ydim,tdim))
res <- array(0:1,dim=c(xdim,ydim,tdim))


ga = microbenchmark::microbenchmark(r_1core = cube_r(a,res,xdim,ydim,tdim),
                                    alex_1core = alex(a,res,xdim,ydim,tdim),
                                    cpp_1core = cube_parallel(a,res, 1), 
                                    cpp_2core = cube_parallel(a,res, 2), 
                                    cpp_3core = cube_parallel(a,res, 3),
                                    cpp_cache = dim_to_cube(xdim,ydim,tdim))

cpp\u parallel=cube\u parallel（a，res，1）
alex_1core=alex（a、res、xdim、ydim、tdim）
cpp_cache=dim_到_多维数据集（xdim、ydim、tdim）
op_answer=cube_r（a、res、xdim、ydim、tdim）
全部相等（cpp_平行，op_答案）
all.equal（cpp_缓存，op_应答）
全部相等（alex_1core，op_答案）
xdim使用RcppArmadillo
！设置
xdim因为它是长lat，你想让邻域在边缘环绕吗？
res[x，y，t]真的很好而且详细。变成Rcpp画廊的故事？是的。我会尽量在本周提交。期待着。这个方案相当简单；拥有当地的杰基尔并不是一件小事，但你不必拥有它。不管怎么说，你对Rmarkdown很在行……已经在本地为TCP和SMAC（Github pages rocks！）
Unit: microseconds
       expr      min        lq       mean    median        uq       max neval
    r_1core 3538.022 3825.8105 4301.84107 3957.3765 4043.0085 16856.865   100
 alex_1core 2790.515 2984.7180 3461.11021 3076.9265 3189.7890 15371.406   100
  cpp_1core  174.508  180.7190  197.29728  194.1480  204.8875   338.510   100
  cpp_2core  111.960  116.0040  126.34508  122.7375  136.2285   162.279   100
  cpp_3core   81.619   88.4485  104.54602   94.8735  108.5515   204.979   100
  cpp_cache   40.637   44.3440   55.08915   52.1030   60.2290   302.306   100

cpp_parallel = cube_parallel(a,res, 1)
alex_1core = alex(a,res,xdim,ydim,tdim)
cpp_cache = dim_to_cube(xdim,ydim,tdim)
op_answer = cube_r(a,res,xdim,ydim,tdim)

all.equal(cpp_parallel, op_answer)
all.equal(cpp_cache, op_answer)
all.equal(alex_1core, op_answer)

xdim <- 20
ydim <- 20
tdim <- 5
a <- array(0:1,dim=c(xdim,ydim,tdim))
res <- array(0:1,dim=c(xdim,ydim,tdim))


ga = microbenchmark::microbenchmark(r_1core = cube_r(a,res,xdim,ydim,tdim),
                                    alex_1core = alex(a,res,xdim,ydim,tdim),
                                    cpp_1core = cube_parallel(a,res, 1), 
                                    cpp_2core = cube_parallel(a,res, 2), 
                                    cpp_3core = cube_parallel(a,res, 3),
                                    cpp_cache = dim_to_cube(xdim,ydim,tdim))