MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
Level 3: matrix-matrix operations, O(n^3) work

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

## 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.