Speed up R matrix computation with smallest effort.
给R提速有两个方法：
1. 使用Intel compiler
2. 使用更快的矩阵运算库
其中我使用第一个方法并没有看到显著的速度提升，所以这里介绍第2种方法，保证矩阵运算至少提速2倍。
我使用的是R-2.13.1版本，矩阵库使用GotoBLAS。
根据下面这个链接，
http://r.789695.n4.nabble.com/configure-can-t-find-dgemm-in-MKL10-td920212.html
GotoBLAS比Intel MKL快。据说，GotoBLAS比ATLAS也要快。
具体步骤如下：
（1）建立一个shell 源文件：
export FFLAGS="-march=native -O3"
export CFLAGS="-march=native -O3 -DMKL_ILP64"
export CXXFLAGS="-march=native -O3 -DMKL_ILP64"
export FCFLAGS="-march=native -O3"
./configure --enable-R-shlib --enable-BLAS-shlib --with-blas --with-lapack --prefix=/net/dumbo/home/zhanxw/software/Rmkl
之后用make, make install安装。
（2）下载GotoBLAS，在源目录’make’即可，得到的BLAS库文件名是’libgoto2.so’
（3）建立符号链接。在R安装目录下e.g. /lib64/R/lib，已经有一个R默认的BLAS动态连接库libRblas.so，把这个改成链接到libgoto2.so的符号链接。
这3步之后，R就会使用GotoBLAS作为矩阵运算库。在我们的服务器上，benchmark结果如下：
# GCC + default BLAS
R Benchmark 2.5
===============
Number of times each test is run__________________________: 3
I. Matrix calculation
---------------------
Creation, transp., deformation of a 2500x2500 matrix (sec): 0.764666666666666
2400x2400 normal distributed random matrix ^1000____ (sec): 0.596666666666666
Sorting of 7,000,000 random values__________________ (sec): 0.833333333333333
2800x2800 cross-product matrix (b = a' * a)_________ (sec): 4.425
Linear regr. over a 3000x3000 matrix (c = a \ b')___ (sec): 2.30366666666667
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 1.13650194597564
II. Matrix functions
--------------------
FFT over 2,400,000 random values____________________ (sec): 0.778666666666666
Eigenvalues of a 640x640 random matrix______________ (sec): 1.406
Determinant of a 2500x2500 random matrix____________ (sec): 2.28733333333334
Cholesky decomposition of a 3000x3000 matrix________ (sec): 2.02366666666667
Inverse of a 1600x1600 random matrix________________ (sec): 1.933
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 1.76516531172197
III. Programmation
------------------
3,500,000 Fibonacci numbers calculation (vector calc)(sec): 1.06166666666667
Creation of a 3000x3000 Hilbert matrix (matrix calc) (sec): 0.601666666666669
Grand common divisors of 400,000 pairs (recursion)__ (sec): 2.56866666666667
Creation of a 500x500 Toeplitz matrix (loops)_______ (sec): 0.757666666666661
Escoufier's method on a 45x45 matrix (mixed)________ (sec): 0.595000000000013
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.785128552514896
Total time for all 15 tests_________________________ (sec): 22.9366666666667
Overall mean (sum of I, II and III trimmed means/3)_ (sec): 1.16349747864837
--- End of test ---
# GCC + GotoBLAS(GCC)
R Benchmark 2.5
===============
Number of times each test is run__________________________: 3
I. Matrix calculation
---------------------
Creation, transp., deformation of a 2500x2500 matrix (sec): 0.776333333333333
2400x2400 normal distributed random matrix ^1000____ (sec): 0.597
Sorting of 7,000,000 random values__________________ (sec): 0.838
2800x2800 cross-product matrix (b = a' * a)_________ (sec): 0.376333333333333
Linear regr. over a 3000x3000 matrix (c = a \ b')___ (sec): 0.293
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.558725402933605
II. Matrix functions
--------------------
FFT over 2,400,000 random values____________________ (sec): 0.785666666666668
Eigenvalues of a 640x640 random matrix______________ (sec): 2.092
Determinant of a 2500x2500 random matrix____________ (sec): 0.303666666666667
Cholesky decomposition of a 3000x3000 matrix________ (sec): 0.292999999999999
Inverse of a 1600x1600 random matrix________________ (sec): 0.396333333333331
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.455580734019386
III. Programmation
------------------
3,500,000 Fibonacci numbers calculation (vector calc)(sec): 1.07166666666667
Creation of a 3000x3000 Hilbert matrix (matrix calc) (sec): 0.608999999999999
Grand common divisors of 400,000 pairs (recursion)__ (sec): 2.848
Creation of a 500x500 Toeplitz matrix (loops)_______ (sec): 0.675666666666665
Escoufier's method on a 45x45 matrix (mixed)________ (sec): 0.591000000000001
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.761149272082565
Total time for all 15 tests_________________________ (sec): 12.5466666666667
Overall mean (sum of I, II and III trimmed means/3)_ (sec): 0.578643662905733
--- End of test ---
# ICC + build-in BLAS
R Benchmark 2.5
===============
Number of times each test is run__________________________: 3
I. Matrix calculation
---------------------
Creation, transp., deformation of a 2500x2500 matrix (sec): 0.722333333333333
2400x2400 normal distributed random matrix ^1000____ (sec): 0.398
Sorting of 7,000,000 random values__________________ (sec): 0.853333333333333
2800x2800 cross-product matrix (b = a' * a)_________ (sec): 23.2723333333333
Linear regr. over a 3000x3000 matrix (c = a \ b')___ (sec): 9.48066666666666
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 1.80121303632586
II. Matrix functions
--------------------
FFT over 2,400,000 random values____________________ (sec): 0.919666666666667
Eigenvalues of a 640x640 random matrix______________ (sec): 1.01100000000001
Determinant of a 2500x2500 random matrix____________ (sec): 4.84600000000001
Cholesky decomposition of a 3000x3000 matrix________ (sec): 3.71033333333332
Inverse of a 1600x1600 random matrix________________ (sec): 6.53100000000001
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 2.62935462784594
III. Programmation
------------------
3,500,000 Fibonacci numbers calculation (vector calc)(sec): 0.825333333333333
Creation of a 3000x3000 Hilbert matrix (matrix calc) (sec): 0.588666666666654
Grand common divisors of 400,000 pairs (recursion)__ (sec): 2.65866666666667
Creation of a 500x500 Toeplitz matrix (loops)_______ (sec): 0.665000000000001
Escoufier's method on a 45x45 matrix (mixed)________ (sec): 0.55400000000003
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.686183322572556
Total time for all 15 tests_________________________ (sec): 57.0363333333334
Overall mean (sum of I, II and III trimmed means/3)_ (sec): 1.4812151139281
--- End of test ---
# ICC + GotoBLAS(ICC)
R Benchmark 2.5
===============
Number of times each test is run__________________________: 3
I. Matrix calculation
---------------------
Creation, transp., deformation of a 2500x2500 matrix (sec): 0.738666666666667
2400x2400 normal distributed random matrix ^1000____ (sec): 0.388000000000001
Sorting of 7,000,000 random values__________________ (sec): 0.857333333333333
2800x2800 cross-product matrix (b = a' * a)_________ (sec): 0.633333333333333
Linear regr. over a 3000x3000 matrix (c = a \ b')___ (sec): 0.537666666666667
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 0.631245051729315
II. Matrix functions
--------------------
FFT over 2,400,000 random values____________________ (sec): 0.938333333333333
Eigenvalues of a 640x640 random matrix______________ (sec): 5.53166666666667
Determinant of a 2500x2500 random matrix____________ (sec): 0.957666666666666
Cholesky decomposition of a 3000x3000 matrix________ (sec): 0.601000000000001
Inverse of a 1600x1600 random matrix________________ (sec): 1.741
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 1.16088739499808
III. Programmation
------------------
3,500,000 Fibonacci numbers calculation (vector calc)(sec): 0.813
Creation of a 3000x3000 Hilbert matrix (matrix calc) (sec): 0.591333333333334
Grand common divisors of 400,000 pairs (recursion)__ (sec): 2.663
Creation of a 500x500 Toeplitz matrix (loops)_______ (sec): 0.669333333333332
Escoufier's method on a 45x45 matrix (mixed)________ (sec): 4.883
--------------------------------------------
Trimmed geom. mean (2 extremes eliminated): 1.13162201708511
Total time for all 15 tests_________________________ (sec): 22.5443333333333
Overall mean (sum of I, II and III trimmed means/3)_ (sec): 0.939499363744844
--- End of test ---
通过比较GCC/ICC 与 R自带的BLAS/GotoBLAS的4种组合，在我们的服务器系统下GCC+GotoBLAS最快。
注：
LAPACK是对BLAS的再次封装，因此我们不需要改变libRlapack.so。这一点可以通过’nm -g libRlapack.so’，查看dgemm_的定义为‘U’（说明这个函数没有在该文件中实现），而通过’ldd libRlapack.so’可以发现它会调用libRblas.so
其他资源：