我想知道为什么MATLAB在cholesky factorization上比Python和R快得多，即使至少Python也在使用英特尔的MKL。
MATLAB: Python: R:
----------------------------------------------
8.0034e-4 s 30.7093e-4 s 105.0849e-4 s
100.00 % 383.70 % 1313.00 %
作为一个例子，我使用了MATLAB生成的矩阵：
matrix = gallery('moler',600)
（600因为我实际代码中的矩阵有这个大小）
并将其存储为.csv文件。
代码：
MATLAB：
filename = './matrix.csv';
delimiter = ',';
formatSpec = [repmat('%f', 1,600) '%[^\n\r]'];
fileID = fopen(filename,'r');
dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'EmptyValue' ,NaN, 'ReturnOnError', false);
fclose(fileID);
x = [dataArray{1:end-1}];
clearvars filename delimiter formatSpec fileID dataArray;
t=zeros(1000, 1);
for i=1:length(t)
tic;
chol(x,'lower');
t(i)=toc;
end;
disp(['Mean: ' num2str(mean(t)) [' s']])
>> test
Mean: 0.00080034 s
的Python：
import time
import numpy as np
x = np.loadtxt('./matrix.csv', delimiter=',')
time_elapsed = np.zeros(1000)
for i in range(0, len(time_elapsed)):
t = time.time()
np.linalg.cholesky(x)
time_elapsed[i] = time.time() - t
print('Mean: '+str(time_elapsed.mean())+" s")
Python ./test.py
Mean: 0.00307093310356 s
R：
library(readr)
library(tictoc)
x <- read_csv("./matrix.csv", col_names = FALSE)
tic.clearlog()
for (i in 0:1000)
{
tic(i)
chol(x)
toc(log = TRUE, quiet = TRUE)
}
log.lst <- tic.log(format = FALSE)
tic.clearlog()
timings <- unlist(lapply(log.lst, function(x) x$toc - x$tic))
print(paste0("Mean: ", mean(timings), " s"))
source('./test.R')
[1] "Mean: 0.0105084915084904 s"
系统信息：
Intel（R）Xeon（R）CPU E5-2643 v3 @ 3.40GHz，6核心HT启用，64 GB Ram
OS：
uname -a
Linux 4.8.0-2-amd64 #1 SMP Debian 4.8.15-2 (2017-01-04) x86_64 GNU/Linux
MATLAB：
version
9.1.0.441655 (R2016b)
version -java
Java 1.7.0_60-b19 with Oracle Corporation Java HotSpot(TM) 64-Bit Server VM mixed mode
version -blas
Intel(R) Math Kernel Library Version 11.3.1 Product Build 20151021 for Intel(R) 64 architecture applications, CNR branch AVX2
version -lapack
Intel(R) Math Kernel Library Version 11.3.1 Product Build 20151021 for Intel(R) 64 architecture applications, CNR branch AVX2
Linear Algebra PACKage Version 3.5.0
R：
version
_
platform x86_64-pc-linux-gnu
arch x86_64
os linux-gnu
system x86_64, linux-gnu
status
major 3
minor 3.2
year 2016
month 10
day 31
svn rev 71607
language R
version.string R version 3.3.2 (2016-10-31)
nickname Sincere Pumpkin Patch
的Python：
conda --version
conda 4.3.11
python --version
Python 3.5.2 :: Anaconda custom (64-bit)
np.version.full_version
'1.11.2'
np.__config__.show()
blas_mkl_info:
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
library_dirs = ['~/anaconda3/lib']
include_dirs = ['~/anaconda3/include']
libraries = ['mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'iomp5', 'pthread']
lapack_mkl_info:
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
library_dirs = ['~/anaconda3/lib']
include_dirs = ['~/anaconda3/include']
libraries = ['mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'iomp5', 'pthread']
lapack_opt_info:
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
library_dirs = ['~/anaconda3/lib']
include_dirs = ['~/anaconda3/include']
libraries = ['mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'iomp5', 'pthread']
blas_opt_info:
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
library_dirs = ['~/anaconda3/lib']
include_dirs = ['~/anaconda3/include']
libraries = ['mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'iomp5', 'pthread']
openblas_lapack_info:
NOT AVAILABLE
mkl.get_version_string()
'Intel(R) Math Kernel Library Version 11.3.3 Product Build 20160413 for Intel(R) 64 architecture applications'