MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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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.