Initialization |
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Utilities |
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Linear Systems | Solve \( Ax = b \) |
 LU solve | Solve \( Ax = b \), using LU factorization for general \( A \) |
  LU solve: driver | Whole \( Ax=b \) problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  LU solve: computational | Major computational phases of solving \( Ax=b \) |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  LU solve: auxiliary | Low-level functions |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Tiled LU | Functions for tiled algorithms (incremental pivoting) |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
 Cholesky solve | Solve \( Ax = b \), using Cholesky factorization for symmetric positive definite (SPD) \( A \) |
  Cholesky solve: driver | Whole \( Ax=b \) (SPD) problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Cholesky solve: computational | Major computational phases of solving \( Ax=b \) (SPD) |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Cholesky solve: auxiliary | Low-level functions |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
 Least Squares | Solve over- or under-determined \( Ax = b \) |
  Least Squares solve: driver | Whole \( Ax=b \) (least squares) problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Least Squares solve: computational | Major computational phases of solving \( Ax=b \) (least squares); |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
Orthogonal factorizations |
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 QR factorization | Factor \( A = QR \) |
  QR factorization: computational | Major computational phase of least squares and SVD problems |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  QR with pivoting | Slower but more stable QR, especially for rank-deficient matrices |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Tiled QR factorization | Functions for tiled algorithms |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
 RQ factorization | Factor \( A = RQ \) |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 QL factorization | Factor \( A = QL \) |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 LQ factorization | Factor \( A = LQ \) |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
Eigenvalue |
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 Non-symmetric eigenvalue | Solve \( Ax = \lambda x \) for non-symmetric \( A \) |
  Non-symmetric eigenvalue: driver | Whole \( Ax = \lambda x \) non-symmetric eigenvalue problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Non-symmetric eigenvalue: computational | Major computational phases of non-symmetric eigenvalue problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Non-symmetric eigenvalue: auxiliary | Low-level functions |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
 Symmetric eigenvalue | Solve \( Ax = \lambda x \) for symmetric \( A \) |
  Symmetric eigenvalue: driver | Whole \( Ax = \lambda x \) eigenvalue problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Generalized symmetric eigenvalue: driver | Whole \( Ax = \lambda Bx \), or \( ABx = \lambda x \), or \( BAx = \lambda x \) generalized symmetric eigenvalue problem |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Symmetric eigenvalue: computational | Major computational phases of eigenvalue problem, 1-stage algorithm |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Symmetric eigenvalue: computational, 2-stage | Major computational phases of eigenvalue problem, 2-stage algorithm |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
  Symmetric eigenvalue: auxiliary | Low-level functions |
   single precision | |
   double precision | |
   single-complex precision | |
   double-complex precision | |
Singular Value Decomposition (SVD) |
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 SVD: driver | Whole SVD problem |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 SVD: computational | Major computational phases of SVD problem |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 SVD: auxiliary | Low-level functions |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
BLAS and auxiliary |
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 Level-1 BLAS | Level-1, vector operations: \( O(n) \) operations on \( O(n) \) data; memory bound |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Level-2 BLAS | Level-2, matrix–vector operations: \( O(n^2) \) operations on \( O(n^2) \) data; memory bound |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Level-3 BLAS | Level-3, matrix–matrix operations: \( O(n^3) \) operations on \( O(n^2) \) data; compute bound |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Math auxiliary | Element operations, \( O(1) \) operations on \( O(1) \) data |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Level-1 auxiliary | Additional auxiliary Level-1 functions |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Level-2 auxiliary | Additional auxiliary Level-2 functions |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Level-3 auxiliary | Additional auxiliary Level-3 functions |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |
 Communication | CPU to GPU communication |
  single precision | |
  double precision | |
  single-complex precision | |
  double-complex precision | |