28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.14 BLAS 2 algorithms [linalg.algs.blas2]

28.9.14.6 Rank-1 (outer product) update of a matrix [linalg.algs.blas2.rank1]

template<in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
  void matrix_rank_1_update(InVec1 x, InVec2 y, InOutMat A);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
  void matrix_rank_1_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A);

These functions perform a nonsymmetric nonconjugated rank-1 update.

[Note 1:

These functions correspond to the BLAS functions xGER (for real element types) and xGERU (for complex element types)[bib].

— end note]

Mandates: possibly-multipliable<InOutMat, InVec2, InVec1>() is true.

Preconditions: multipliable(A, y, x) is true.

Effects: Computes a matrix

A^{'}

such that

A^{'} = A + x y^{T}

, and assigns each element of

A^{'}

to the corresponding element of A.

Complexity:

O (x.extent(0) \times y.extent(0))

🔗

template<in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
  void matrix_rank_1_update_c(InVec1 x, InVec2 y, InOutMat A);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
  void matrix_rank_1_update_c(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A);

These functions perform a nonsymmetric conjugated rank-1 update.

[Note 2:

These functions correspond to the BLAS functions xGER (for real element types) and xGERC (for complex element types)[bib].

— end note]

Effects:

(7.1)
For the overloads without an ExecutionPolicy argument, equivalent to: matrix_rank_1_update(x, conjugated(y), A);
(7.2)
otherwise, equivalent to: matrix_rank_1_update(std::forward<ExecutionPolicy>(exec), x, conjugated(y), A);