▼Linear systems | Solve \(AX = B\) |
►General non-symmetric: LU | |
Driver | Solve \(AX = B\) |
Computational | Factor, forward and back solve, invert |
Target implementations | |
Internal | |
Tile | |
►General non-symmetric, band: LU | |
Driver | Solve \(AX = B\) |
Computational | Factor, forward and back solve |
Target implementations | |
►Positive definite: Cholesky | |
Driver | Solve \(AX = B\) |
Computational | Factor, forward and back solve, invert |
Target implementations | |
Internal | |
Tile | |
►Positive definite, band: Cholesky | |
Driver | Solve \(AX = B\) |
Computational | Factor, forward and back solve |
Target implementations | |
►Hermitian/symmetric indefinite: Aasen | |
Driver | Solve \(AX = B\) |
Computational | Factor, forward and back solve |
Target implementations | |
►Triangular | |
Computational | Inverse, multiply |
Target implementations | |
Internal | |
Tile | |
►Utilities | |
Permute, internal | |
▼Least squares | Solve \(AX \cong B\) |
Linear least squares | Solve \(AX \cong B\), over-determined (tall \(A\)) or under-determined (wide \(A\)) |
▼Orthogonal/unitary factorizations (QR, etc.) | |
►QR | |
Computational | Factor \(A = QR\), multiply by \(Q\), generate \(Q\) |
Target implementations | |
Internal | |
Tile | |
►LQ | |
Computational | Factor \(A = LQ\), multiply by \(Q\), generate \(Q\) |
Target implementations | |
Internal | |
Tile | |
▼Symmetric/Hermitian eigenvalues | |
Driver | \(Ax = \lambda x\) |
Computational | |
Target implementations | |
Target implementations | |
Internal | |
▼generalized Symmetric/Hermitian-definite eigenvalues | |
Driver | \(Ax = \lambda B x\), etc |
Computational | |
Target implementations | |
Internal | |
Tile | |
▼Singular Value Decomposition (SVD) | |
Driver | \(A = U \Sigma V^H\) |
Computational | |
Target implementations | |
▼Level 2 BLAS and Auxiliary: O(n^2) work | Matrix and Matrix-vector operations that perform \(O(n^2)\) work on \(O(n^2)\) data |
►Initialize and copy | |
Set matrix elements | |
Copy matrix | |
Generate test matrix | |
►Matrix norms | |
Driver | \(\left\lVert A \right\rVert\) (one, inf, fro, max) |
Target implementations | |
Internal | |
Tile | |
►Parellel BLAS (PBLAS) | |
add: Add matrices | \(B = \alpha A + \beta B\) |
►Target implementations | |
set | |
scale | |
copy | |
add | |
►Internal | Internal routines implement one step of BLAS routine |
set | |
scale | |
copy | |
add | |
►Tile | Tile routines |
set | |
scale | |
copy | |
swap | |
add | |
gemv | |
symv | |
ger | |
her2 | |
►Condition number estimate | |
Driver | \(rcond = \frac{1}{\|\|A\|\| \times \|\|A^{-1}\|\|}\) |
▼Level 3 BLAS: O(n^3) work | Matrix-matrix operations that perform \(O(n^3)\) work on \(O(n^2)\) data |
►Parellel BLAS (PBLAS) | |
gemm: General matrix multiply | \(C = \alpha A B + \beta C\) |
gbmm: General band matrix multiply | \(C = \alpha A B + \beta C\) where \(A\) or \(B\) is band |
hemm: Hermitian matrix multiply | \(C = \alpha A B + \beta C\) or \(C = \alpha B A + \beta C\) where \(A\) is Hermitian |
hbmm: Hermitian band matrix multiply | \(C = \alpha A B + \beta C\) or \(C = \alpha B A + \beta C\) where \(A\) is Hermitian |
herk: Hermitian rank k update | \(C = \alpha A A^H + \beta C\) where \(C\) is Hermitian |
her2k: Hermitian rank 2k update | \(C = \alpha A B^H + \alpha B A^H + \beta C\) where \(C\) is Hermitian |
symm: Symmetric matrix multiply | \(C = \alpha A B + \beta C\) or \(C = \alpha B A + \beta C\) where \(A\) is symmetric |
syrk: Symmetric rank k update | \(C = \alpha A A^T + \beta C\) where \(C\) is symmetric |
syr2k: Symmetric rank 2k update | \(C = \alpha A B^T + \alpha B A^T + \beta C\) where \(C\) is symmetric |
trmm: Triangular matrix multiply | \(B = \alpha A B\) or \(B = \alpha B A\) where \(A\) is triangular |
trsm: Triangular solve matrix | \(C = A^{-1} B\) or \(C = B A^{-1}\) where \(A\) is triangular |
tbsm: Triangular solve band matrix | \(C = A^{-1} B\) or \(C = B A^{-1}\) where \(A\) is band triangular |
►Target implementations | |
gemm: General matrix multiply | |
gbmm: General band matrix multiply | |
hemm: Hermitian matrix multiply | |
hbmm: Hermitian band matrix multiply | |
herk: Hermitian rank k update | |
her2k: Hermitian rank 2k update | |
symm: Symmetric matrix multiply | |
syrk: Symmetric rank k update | |
syr2k: Symmetric rank 2k update | |
trmm: Triangular matrix multiply | |
trsm: Triangular solve matrix | |
tbsm: Triangular solve band matrix | |
►Internal | Internal routines implement one step of BLAS routine, e.g., one block outer product |
gemm: General matrix multiply | |
hemm: Hermitian matrix multiply | |
herk: Hermitian rank k update | |
her2k: Hermitian rank 2k update | |
symm: Symmetric matrix multiply | |
syrk: Symmetric rank k update | |
syr2k: Symmetric rank 2k update | |
trmm: Triangular matrix multiply | |
trsm: Triangular solve matrix | |
►Tile | |
gemm: General matrix multiply | |
hemm: Hermitian matrix multiply | |
herk: Hermitian rank k update | |
her2k: Hermitian rank 2k update | |
symm: Symmetric matrix multiply | |
syrk: Symmetric rank k update | |
syr2k: Symmetric rank 2k update | |
trmm: Triangular matrix multiply | |
trsm: Triangular solve matrix | |
Enumerations | |
▼Utilities | |
Constructor functions | Useful functions for SLATE's "lambda" constructors |