| Initialization |
|
| Utilities |
|
| ▼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/Hermitian 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 | |
| ►Symmetric indefinite solve | Solve \( Ax = b \), using indefinite factorization for symmetric/Hermitian \( A \) |
| ►Symmetric indefinite solve: driver | Whole \( Ax=b \) (symmetric/Hermitian) problem |
| single precision | |
| double precision | |
| Hermitian single-complex precision | |
| Hermitian double-complex precision | |
| symmetric single-complex precision | |
| symmetric double-complex precision | |
| ►Symmetric indefinite solve: computational | Major computational phases of solving \( Ax=b \) (symmetric/Hermitian) |
| single precision | |
| double precision | |
| Hermitian single-complex precision | |
| Hermitian double-complex precision | |
| symmetric single-complex precision | |
| symmetric double-complex precision | |
| Symmetric indefinite solve: auxiliary | Low-level functions { |
| single precision | |
| double precision | |
| Hermitian single-complex precision | |
| Hermitian double-complex precision | |
| symmetric single-complex precision | |
| symmetric 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 |
|
| ►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 factorization: auxiliary | Low-level functions |
| 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 | |
| ►QR with pivoting: auxiliary | Low-level functions |
| 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 | |
| ►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 |
|
| ►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) |
|
| ►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 |
|
| ►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 | |
| ▼Sparse |
|
| ►Sparse linear systems | Solve \( Ax = b \) |
| ►General solver | Solve \( Ax = b \), for general \( A \) |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Symmetric positive definite solver | Solve \( Ax = b \), for symmetric/Hermitian positive definite (SPD) \( A \) |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Sparse eigenvalue | Solve \( Ax = \lambda x \) |
| ►Symmetric eigenvalue | Solve \( Ax = \lambda x \) for symmetric/Hermitian \( A \) |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Sparse preconditioner | Preconditioner for solving \( Ax = \lambda x \) |
| ►General preconditioner | Preconditioner for \( Ax = \lambda x \) for non-symmetric \( A \) |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Hermitian preconditioner | Preconditioner for \( Ax = \lambda x \) for symmetric/Hermitian \( A \) |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►GPU kernels for sparse LA | |
| ►GPU kernels for non-symmetric sparse LA | |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►GPU kernels for symmetric/Hermitian sparse LA | |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Sparse BLAS | |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Sparse auxiliary | |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |
| ►Sparse unfiled | |
| single precision | |
| double precision | |
| single-complex precision | |
| double-complex precision | |