R:总结相邻的矩阵元素。如何加速？

Question

我正在处理大约 2500x2500x50 (lonxlatxtime) 的大型矩阵。矩阵只包含 1 和 0。我需要知道每个时间步长 24 个周围元素的总和。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])
    }
  }
}

这有效，但对于我的需要来说太慢了。有没有人请教如何加快速度？

Answer 1

介绍

我不得不说，在阵列的设置背后有很多隐藏的东西。不过，剩下的问题是微不足道的。因此，有两种方法可以真正做到这一点:

@Alex 给出的蛮力(用 C++ 编写)

观察复制模式

使用 OpenMP 进行暴力破解

如果我们想“蛮力”它，那么我们可以使用@Alex 给出的建议来使用 OpenMP与 Armadillo

#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;
}

复制模式

然而，更聪明的方法是了解 array(0:1, dims)正在 build 中。

最为显着地:

案例1:如果xdim是偶数，则只有矩阵的行交替。

情况 2:如果 xdim是奇数和 ydim是奇数，然后行交替以及矩阵交替。

案例 3:如果 xdim是奇数和 ydim是偶数，则只有行交替

例子

让我们看看实际案例以观察模式。

案例1:

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

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

输出:

, , 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

案例3:

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

输出:

, , 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，基于上述讨论，我们选择编写一些代码来利用这种独特的模式。

创建交替向量

在这种情况下，交替矢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;
}

创建矩阵的三种情况

如上所述，矩阵存在三种情况。偶数、第一奇数和第二奇数情况。

// --- Handle the different cases 

// [[Rcpp::export]]
arma::mat make_even_matrix(unsigned int xdim, unsigned int ydim){

  arma::mat temp_mat(xdim,ydim);

  temp_mat.each_col() = even_vec(xdim);

  return temp_mat;
}

// xdim is odd and ydim is even
// [[Rcpp::export]]
arma::mat make_odd_matrix_case1(unsigned int xdim, unsigned int ydim){

  arma::mat temp_mat(xdim,ydim);

  arma::vec e_vec = even_vec(xdim);
  arma::vec o_vec = odd_vec(xdim);

  // Alternating column 
  for (unsigned int i = 0; i < ydim; i++) {
    temp_mat.col(i) = (i % 2 ? o_vec : e_vec);
  }

  return temp_mat;
}

// xdim is odd and ydim is odd    
// [[Rcpp::export]]
arma::mat make_odd_matrix_case2(unsigned int xdim, unsigned int ydim){

  arma::mat temp_mat(xdim,ydim);

  arma::vec e_vec = even_vec(xdim);
  arma::vec o_vec = odd_vec(xdim);

  // Alternating column 
  for (unsigned int i = 0; i < ydim; i++) {
    temp_mat.col(i) = (i % 2 ? e_vec : o_vec); // slight change
  }

  return temp_mat;
}

计算引擎

与之前的解决方案相同，只是没有 t因为我们不再需要重复计算。

// --- Calculation engine

// [[Rcpp::export]]
arma::mat calc_matrix(arma::mat temp_mat){

  unsigned int xdim = temp_mat.n_rows;

  unsigned int ydim = temp_mat.n_cols;

  arma::mat res = temp_mat;

  // 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) = accu(temp_row_sub.cols(y-2,y+2));
    }
  }

  return res;
}

调用主函数

这是将所有内容拼凑在一起的核心功能。这为我们提供了所需的距离数组。

// --- 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;
}

定时

现在，真正的事实是它的表现如何:

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

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))