MAGMA 2.9.0
Matrix Algebra for GPU and Multicore Architectures
Loading...
Searching...
No Matches
Level 2: matrix-vector operations, O(n^2) work

Topics

 geadd: Add matrices
 \(B = \alpha A + \beta B\)
 
 gemv: General matrix-vector multiply
 \(y = \alpha Ax + \beta y\)
 
 ger: General matrix rank 1 update
 \(A = \alpha xy^T + A\)
 
 hemv: Hermitian matrix-vector multiply
 \(y = \alpha Ax + \beta y\)
 
 her: Hermitian rank 1 update
 \(A = \alpha xx^T + A\)
 
 her2: Hermitian rank 2 update
 \(A = \alpha xy^T + \alpha yx^T + A\)
 
 symv: Symmetric matrix-vector multiply
 \(y = \alpha Ax + \beta y\)
 
 syr: Symmetric rank 1 update
 \(A = \alpha xx^T + A\)
 
 syr2: Symmetric rank 2 update
 \(A = \alpha xy^T + \alpha yx^T + A\)
 
 trmv: Triangular matrix-vector multiply
 \(x = Ax\)
 
 trsv: Triangular matrix-vector solve
 \(x = op(A^{-1})\; b\)
 
 swapblk: Swap several rows
 
 
 swapdblk: Swap diagonal blocks
 
 
 symmetrize: Symmetrize matrix
 \(\text{upper}(A) = \text{lower}(A)^T\) or \(\text{lower}(A) = \text{upper}(A)^T\)
 
 transpose: Transpose matrix
 \(B = A^T\) or \(B = A^H\)
 
 lacgv: Conjugate vector
 \(x = conj(x)\)
 
 lacpy: Copy matrix
 \(B = A\)
 
 lascl: Scale matrix by scalar
 \(A = \alpha A\)
 
 lascl2: Scale matrix by diagonal
 \(A = D A\)
 
 laset: Set matrix to constants
 \(A_{ij} =\) diag if \(i=j\); \(A_{ij} =\) offdiag otherwise.
 

Detailed Description

Matrix operations that perform \(O(n^2)\) work on \(O(n^2)\) data. These are memory bound, since every operation requires a memory read or write.