MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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Level 2: matrix-vector operations, O(n^2) work

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

Modules

 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
 \( A = \alpha A \)
 
 lascl_diag: Scale matrix by diagonal
 \( A = D A \)
 
 lascl_2x2: Scale matrix by 2-by-2 pivot
 \( A = D A \)
 
 laset: Set matrix to constants
 \( A_{ij} = \) diag if \( i=j \); \( A_{ij} = \) offdiag otherwise.
 
 laset_band: Set band of 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.