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Level 3: matrix-matrix operations, O(n^3) work
Dense LA » MAGMA BLAS and Auxiliary

Matrix-matrix operations that perform \(O(n^3)\) work on \(O(n^2)\) data. More...

## Topics

| 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

## Detailed Description

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.