BLAS

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源文件

BLAS

BLAS 的命名规则

BLAS 中的函数名一般规则是 <character><name><mode> ()

  • <character> 指明数据类型
    • s real, single precision
    • c complex, single precision
    • d real, double precision
    • z complex, double precision
  • <name> 指明矩阵类型 BLAS 2 and 3
    • ge general matrix
    • gb general band matrix
    • sy symmetric matrix
    • sp symmetric matrix (packed storage)
    • sb symmetric band matrix
    • he hermitian matrix
    • hp hermitian matrix (packed storage)
    • hb hermitian band matrix
    • tr triangular matrix
    • tp triangular matrix (packed storage)
    • tb triangular band matrix
  • <mod> 指明操作的细节
    • c conjugated vector
    • u unconjugated vector
    • g Givens rotation construction
    • m modified Givens rotation
    • mg modified Givens rotation construction
    • mv matrix-vector product
    • sv solving a system of linear equations with a single unknown vector
    • r rank-1 update of matrix
    • r2 rank-2 update of matrix
    • mm matrix-matrix product
    • sm solving a system of linear equations with multiple unkonwn vectors
    • rk rank-k update of matrix
    • r2k rank-2k update of a matrix

CBLAS 约定

CBLAS 是 BLAS 的 c 接口， BLAS 是 fortran 标准。

CBLAS 函数都遵循以下约定

  • 输入参数是 const 指针
  • 非复数标量输入参数传值
  • 复标量参数传 void 指针
  • 数组参数传地址
  • BLAS 特征参数由适当的枚举类型代替
  • level 2 和 level 3 需要一个额外的 CBLAS_LAYOUT 类型的参数来指定矩阵是行优先 CblasRowMajor 还是列优先 CblasColMajor

枚举类型

   enum CBLAS_LAYOUT {
      CblasRowMajor=101,    /* row-major arrays */
      CblasColMajor=102};   /* column-major arrays */

   enum CBLAS_TRANSPOSE {
      CblasNoTrans=111,     /* trans='N' */
      CblasTrans=112,       /* trans='T' */
      CblasConjTrans=113};  /* trans='C' */

   enum CBLAS_UPLO {
      CblasUpper=121,        /* uplo ='U' */
      CblasLower=122};       /* uplo ='L' */

   enum CBLAS_DIAG {
      CblasNonUnit=131,      /* diag ='N' */
      CblasUnit=132};        /* diag ='U' */

   enum CBLAS_SIDE {
      CblasLeft=141,         /* side ='L' */
      CblasRight=142};       /* side ='R' */

矩阵存储方式

  1. 完全存储矩阵 \(A_{ij}_{}\) 在二维数组列存储 a[i + j*lda] 行存储 a[i*lda + j]
  2. packed storage 可以用更有效的方式存储矩阵

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