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POwhat should I expect when I use Eigen dense matrix data structure?
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I need to use matrix data structure in my program, while C++ has 2d arrays, it's very low level, while some libraries like Eigen provide a higher level of matrix data structure. But in my opinion, no matter how good a library performs in some high-skilled operations such as svd, the fast speed on basic operations, including read(access), write, sum, dot, should be a pre-requirement of such libraries. Because in real applications, such basic operations may be much more frequent than those high-skilled ones, if a library is slow on such operations, it may turn out to be a burden or even bottleneck of the system. So I write some very simple programs using both 2d array and Eigen3 dense matrix (MatrixXd), and compare their performances on 4 basic operations, it turns out that most of the time, 2d array wins Eigen3, which is quite disappointing. I list some of my test result below (the code is in the end appendix): <blockquote> 10000X10000 matrix, compile command: g++ -o test.o test.cpp -O0 -msse2 Eigen: [!COST] init: 6.8 sec. [!COST] read: 14.85 sec. [!COST] write: 23.02 sec. [!COST] sum: 3.28 sec. [!COST] dot: 3.12 sec. CPP: [!COST] init: 1.81 sec. [!COST] read: 2.4 sec. [!COST] write: 3.4 sec. [!COST] sum: 0.63 sec. [!COST] dot: 0.52 sec. 10000X10000 matrix, compile command: g++ -o test.o test.cpp -O3 -msse2 Eigen: [!COST] init: 2.44 sec. [!COST] read: 2.16 sec. [!COST] write: 2.18 sec. [!COST] sum: 0.26 sec. [!COST] dot: 0.26 sec. CPP: [!COST] init: 1.71 sec. [!COST] read: 2.06 sec. [!COST] write: 2.24 sec. [!COST] sum: 0.15 sec. [!COST] dot: 0.06 sec. </blockquote> However, I still have some doubts about this, maybe I should not expect higher level abstraction of matrix structure should work as fast as its raw version, if so, what should I expect using library such as Eigen? Please note that in my program, there are some high-skilled operations as SVD, while there are more basic operations such as access the matrix and write the matrix. Appendix, test.cpp: <pre><code>#include <iostream> #include <Eigen/Dense> #include <ctime> using Eigen::MatrixXf; inline int cpp_testor_read(float **m, const int M, const int N) { float randomTmp = 0; for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { randomTmp += m[i][j]; randomTmp -= m[j][i]; } return randomTmp; } inline int eigen_testor_read(MatrixXf m, const int M, const int N) { float randomTmp = 0; for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { randomTmp += m(i, j); randomTmp -= m(j, i); } return randomTmp; } inline int cpp_testor_write(float **m, const int M, const int N) { for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { m[i][j] += m[j][i]; m[j][i] -= m[i][j]; } return m[rand()%10000][rand()%10000]; } inline int eigen_testor_write(MatrixXf m, const int M, const int N) { for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { m(i, j) += m(j, i); m(j, i) -= m(i, j); } return m(rand()%10000, rand()%10000); } inline int cpp_testor_sum(float **m, const int M, const int N, float val) { for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { m[i][i] += m[i][j]; } return m[rand()%1000][rand()%1000]; } inline int eigen_testor_sum(MatrixXf m, const int M, const int N, float val) { m += m; return m(0, 0); } inline int cpp_testor_dot(float **m, const int M, const int N, float val) { float randomTmp = 0; for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) { m[i][j] *= val; } return m[rand()%1000][rand()%1000]; } inline int eigen_testor_dot(MatrixXf m, const int M, const int N, float val) { m *= val; return m(0, 0); } float** cpp_generator_mtarix(const int M, const int N) { float **m = new float*[M]; for (int i = 0; i < M; i ++) m[i] = new float[N]; return m; } MatrixXf& eigen_generator_matrix(const int M, const int N) { static MatrixXf m(M,N); return m; } int main() { const int M = 10000; const int N = M; int antiopt = 0; srand(time(NULL)); float val1 = rand()%10000 + 1; float val2 = rand()%10000 + 1; std::cout<< M << " " << N << std::endl; std::cout<<"Eigen:" << std::endl; size_t t = clock(); //MatrixXf m = eigen_generator_matrix(M, N); MatrixXf m(M,N); for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) m(i,j) = rand()%1000 + 1; t = clock() - t; std::cout<< "[!COST] init: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += eigen_testor_read(m,M,N); t = clock() - t; std::cout<< "[!COST] read: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += eigen_testor_write(m,M,N); t = clock() - t; std::cout<< "[!COST] write: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += eigen_testor_sum(m,M,N, val1); t = clock() - t; std::cout<< "[!COST] sum: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += eigen_testor_dot(m,M,N, val2); t = clock() - t; std::cout<< "[!COST] dot: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; std::cout<<"CPP:" << std::endl; t = clock(); //float **mm = cpp_generator_mtarix(M, N); float **mm = new float*[M]; for (int i = 0; i < M; i ++) mm[i] = new float[N]; for (int i = 0; i < M; i ++) for (int j = 0; j < N; j ++) mm[i][j] = rand()%1000 + 1; t = clock() - t; std::cout<< "[!COST] init: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += cpp_testor_read(mm,M,N); t = clock() - t; std::cout<< "[!COST] read: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += cpp_testor_write(mm,M,N); t = clock() - t; std::cout<< "[!COST] write: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += cpp_testor_sum(mm,M,N, val1); t = clock() - t; std::cout<< "[!COST] sum: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; t = clock(); antiopt += cpp_testor_dot(mm,M,N, val2); t = clock() - t; std::cout<< "[!COST] dot: " << t/float(CLOCKS_PER_SEC) << " sec." <<std::endl; std::cout<<antiopt<<std::endl; } </code></pre>
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what should I expect when I use Eigen dense matrix data structure?
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