Routines

Here is a list of all modules:

[detail level 123]

▼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