MAGMA
2.7.1
Matrix Algebra for GPU and Multicore Architectures
|
Matrix-matrix operations that perform \( O(n^3) \) work on \( O(n^2) \) data. More...
Modules | |
gemm: General matrix multiply: C = AB + C | |
\( C = \alpha \;op(A) \;op(B) + \beta C \) | |
hemm: Hermitian matrix multiply | |
\( C = \alpha A B + \beta C \) or \( C = \alpha B A + \beta C \) where \( A \) is Hermitian | |
herk: Hermitian rank k update | |
\( C = \alpha A A^T + \beta C \) where \( C \) is Hermitian | |
her2k: Hermitian rank 2k update | |
\( C = \alpha A B^T + \alpha B A^T + \beta C \) 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 | |
\( B = \alpha \;op(A)\; B \) or \( B = \alpha B \;op(A) \) where \( A \) is triangular | |
trsm: Triangular solve matrix | |
\( C = op(A)^{-1} B \) or \( C = B \;op(A)^{-1} \) where \( A \) is triangular | |
trtri: Triangular inverse; used in getri, potri | |
\( A = A^{-1} \) where \( A \) is triangular | |
trtri_diag: Invert diagonal blocks of triangular matrix; used in trsm | |
Matrix-matrix operations that perform \( O(n^3) \) work on \( O(n^2) \) data.
These benefit from cache reuse, since many operations can be performed for every read from main memory.