-
函数库接口标准：BLAS (Basic Linear Algebra Subprograms)和LAPACK (Linear Algebra PACKage)
1979年，Netlib首先用Fortran实现基本的
向量乘法、矩阵乘法的函数库（该库没有对运算做过多优化）。后来该代码库对应的接口规范被称为BLAS。
LAPACK也是Netlib用Fortan编写的代码库，实现了高级的线性运算功能，例如矩阵分解，求逆等，底层是调用的BLAS代码库。后来LAPACK也变成一套代码接口标准。
后来，Netlib还在BLAS/LAPACK的基础上，增加了C语言的调用方式，称为CBLAS/CLAPACK
因此，BLAS/LAPACK都有两个含义，一个是Netlib通过Fortran或C实现的代码库，一个是这个两个代码库对应的接口标准。
http://www.icl.utk.edu/~mgates3/docs/
现在大多数函数库都是基于BLAS/LAPACK接口标准实现
https://en.wikipedia.org/wiki/List_of_numerical_libraries
-
开源函数库
开源社区对对BLAS/LAPACK的实现，比较著名是 ATLAS(Automatically Tuned Linear Algebra Software)和OpenBLAS。它们都实现了BLAS的全部功能，以及LAPACK的部分功能，并且他们都对计算过程进行了优化。
-
商业函数库
商业公司对BLAS/LAPACK的实现，有Intel的MKL，AMD的ACML。他们对自己的cpu架构，进行了相关计算过程的优化，实现算法效率也很高。
NVIDIA针对其GPU，也推出了cuBLAS，用以在GPU上做矩阵运行。
附录：Lapack中的函数命名规则
============================================================================
lapack naming: x-yy-zzz, or x-yy-zz
x (data type)
------------------------------
s float
d double
c float-complex
z double-complex
ds input data is double, internal use float
zc input data is double-complex, internal use float-complex
Matrix type (yy) | full | packed | RFP | banded | tridiag | generalized problem
================================================================================
general | ge gb gt gg
symmetric | sy sp sf sb st
Hermitian | he hp hf hb
positive definite| po pp pf pb pt
--------------------------------------------------------------------------------
triangular | tr tp tf tb tg
upper Hessenberg | hs hg
trapezoidal | tz
--------------------------------------------------------------------------------
orthogonal | or op
unitary | un up
--------------------------------------------------------------------------------
diagonal | di
bidiagonal | bd
(zzz) algorithm
------------------------------
* Triangular factorization
-trf — factorize: General LU, Cholesky decomposition
-tri — calculate the inverse matrix
* Orthogonal factorization
-qp3 — QR factorization, with pivoting
-qrf — QR factorization
* Eigenvalue
-ev — all eigenvalues, [eigenvectors]
-evx — expert; also subset
-evd — divide-and-conquer; faster but more memory
-evr — relative robust; fastest and least memory
* SVD singular value decomposition
-svd — singular values
* Linear system, solve Ax = b
-sv — solve
-sdd — divide-and-conquer; faster but more memory
* Linear least squares, minimize ||b?Ax||2
-ls — full rank, rank(A) = min(m,n), uses QR.
-lsy — rank deficient, uses complete orthogonal factorization.
-lsd — rank deficient, uses SVD.