为什么犰狳在简单的逐行计算任务中比 C 风格数组慢

Question

我目前正在为大矩阵（数百万行，列数< 1000）的每个值计算少量，同时独立考虑每一行。

更准确地说，对于该矩阵的每行i、列j中的每个值M ( i , j ) ，其数量就是 [ M ( i , j ) -mean( i , s ) ] / std( i , s ) ，其中s是M ( i ,:) - j中的子集s ， 换句话说，s是行i中没有值j的所有值的子集。

我比较了两种实现，一种是 C 风格数组，另一种是犰狳，犰狳在执行时间方面大约慢了一倍。我预计执行时间类似或稍慢，但普通 C 数组似乎可以显着提高性能。

有什么特别的原因或我在某个地方错过的事情吗？这是一个使用以下命令编译的示例-O2 -lstdc++ -DARMA_DONT_USE_WRAPPER -lopenblas -llapack -lm：也尝试使用ARMA_NO_DEBUG没有成功。

#include <string>
#include <vector>
#include <iostream>
#include <fstream>
#include <algorithm>
#include <armadillo>
#include <chrono>

using namespace std::chrono;

/***************************
 * main()
 ***************************/
int main( int argc, char *argv[] )
{
    unsigned nrows = 2000000; //number of rows
    unsigned ncols = 100; //number of cols

    const arma::mat huge_mat = arma::randn(nrows, ncols); //create huge matrix

    const arma::uvec vec = arma::linspace<arma::uvec>( 0, huge_mat.n_cols-1, huge_mat.n_cols); //create a vector of [0,...,n]
    arma::rowvec inds = arma::zeros<arma::rowvec>( huge_mat.n_cols-1 ); //-1 since we remove only one value at each step.
    arma::colvec simuT = arma::zeros<arma::colvec>( ncols ); //let's store the results in this simuT vector.

    high_resolution_clock::time_point t1 = high_resolution_clock::now();

    //compute some normalization over each value of line of this huge matrix:
    for(unsigned i=0; i < nrows; i++) {
        const arma::rowvec current_line = huge_mat.row(i); //extract current line

        //for each observation in current_line:
        for(unsigned j=0; j < ncols; j++) {

            //Take care of side effects first:
            if( j == 0 )
                inds = current_line(arma::span(1, ncols-1));
            else
                if( j == 1 ) {
                    inds(0) = current_line(0);
                    inds(arma::span(1, ncols-2)) = current_line( arma::span(2, ncols-1) );
                } else
                    inds(arma::span(0, j-1)) = current_line( arma::span(0, j-1) );

            //Let's do some computation: huge_mat(i,j) - mean[huge_mat(i,:)] / std([huge_mat(i,:)]) //can compute the mean and std first... for each line.
            simuT(j) = (current_line(j) - arma::mean(inds))  / ( std::sqrt( 1+1/((double) ncols-1) ) * arma::stddev(inds) );
        }
    }

    high_resolution_clock::time_point t2 = high_resolution_clock::now();
    auto duration = duration_cast<seconds>( t2 - t1 ).count();
    std::cout << "ARMADILLO: " << duration << " secs\n";

    //------------------PLAIN C Array
    double *Mat_full;
    double *output;
    unsigned int i,j,k;
    double mean=0, stdd=0;
    double sq_diff_sum = 0, sum=0;
    double diff = 0;

    Mat_full = (double *) malloc(ncols * nrows * sizeof(double));
    output = (double *) malloc(nrows * ncols * sizeof(double));

    std::vector< std::vector<double> > V(huge_mat.n_rows);

    //Some UGLY copy from arma::mat to double* using a vector:
    for (size_t i = 0; i < huge_mat.n_rows; ++i)
        V[i] = arma::conv_to< std::vector<double> >::from(huge_mat.row(i));

    //then dump to Mat_full array:
    for (i=0; i < V.size(); i++)
        for (j=0; j < V[i].size(); j++)
            Mat_full[i + huge_mat.n_rows * j] = V[i][j];

    t1 = high_resolution_clock::now();

    for(i=0; i < nrows; i++)
        for(j=0; j < ncols; j++)
        {
            //compute mean of subset-------------------
            sum = 0;
            for(k = 0; k < ncols; k++)
                if(k!=j)
                {
                    sum = sum + Mat_full[i+k*nrows];
                }
            mean = sum / (ncols-1);

            //compute standard deviation of subset-----
            sq_diff_sum = 0;
            for(k = 0; k < ncols; k++)
                if(k!=j)
                {
                    diff = Mat_full[i+k*nrows] - mean;
                    sq_diff_sum += diff * diff;
                }
            stdd = sqrt(sq_diff_sum / (ncols-2));

            //export to plain C array:
            output[i*ncols+j] = (Mat_full[i+j*nrows] - mean) / (sqrt(1+1/(((double) ncols)-1))*stdd);
        }

    t2 = high_resolution_clock::now();
    duration = duration_cast<seconds>( t2 - t1 ).count();
    std::cout << "C ARRAY: " << duration << " secs\n";
}

特别是在比较执行时间时，对 arma::mean 和 arma::stddev 的调用似乎表现不佳。我没有对性能的尺寸效应进行任何深入分析，但似乎对于较小的nrows纯 C 值往往（非常）更快。对于使用此设置的简单测试，我得到：

ARMADILLO: 111 secs
C ARRAY: 79 secs

在执行时间。

编辑 这里是修改，我们按列而不是按行工作，并独立处理每一列，如 @rubenvb 和 @mtall 所建议的。结果执行时间略有减少（ARMADILLO: 104 secs现在），从而显示出比按行工作有一些改进：

#include <string>
#include <vector>
#include <iostream>
#include <fstream>
#include <algorithm>
#include <armadillo>
#include <chrono>

using namespace std::chrono;

/***************************
 * main()
 ***************************/
int main( int argc, char *argv[] )
{
    unsigned nrows = 100; //number of rows
    unsigned ncols = 2000000; //number of cols

    const arma::mat huge_mat = arma::randn(nrows, ncols); //create huge matrix

    const arma::uvec vec = arma::linspace<arma::uvec>( 0, huge_mat.n_rows-1, huge_mat.n_rows); //create a vector of [0,...,n]
    arma::colvec inds = arma::zeros<arma::colvec>( huge_mat.n_rows-1 ); //-1 since we remove only one value at each step.
    arma::rowvec simuT = arma::zeros<arma::rowvec>( nrows ); //let's store the results in this simuT vector.

    high_resolution_clock::time_point t1 = high_resolution_clock::now();

    //compute some normalization over each value of line of this huge matrix:
    for(unsigned i=0; i < ncols; i++) {
        const arma::colvec current_line = huge_mat.col(i); //extract current line

        //for each observation in current_line:
        for(unsigned j=0; j < nrows; j++) {

            //Take care of side effects first:
            if( j == 0 )
                inds = current_line(arma::span(1, nrows-1));
            else
                if( j == 1 ) {
                    inds(0) = current_line(0);
                    inds(arma::span(1, nrows-2)) = current_line( arma::span(2, nrows-1) );
                } else
                    inds(arma::span(0, j-1)) = current_line( arma::span(0, j-1) );

            //Let's do some computation: huge_mat(i,j) - mean[huge_mat(i,:)] / std([huge_mat(i,:)]) //can compute the mean and std first... for each line.
            simuT(j) = (current_line(j) - arma::mean(inds))  / ( std::sqrt( 1+1/((double) nrows-1) ) * arma::stddev(inds) );
        }
    }

    high_resolution_clock::time_point t2 = high_resolution_clock::now();
    auto duration = duration_cast<seconds>( t2 - t1 ).count();
    std::cout << "ARMADILLO: " << duration << " secs\n";
}

Answer 1

原因是犰狳在 mat 中使用列优先排序，而 C 数组使用行优先排序。这是一件大事，因为您的处理器可以使用指令向量化来一次处理多个元素，这需要连续的内存块。

要验证这是否是原因，请对列而不是行进行相同的计算，并检查差异。